Ibn Zuhr was one of the greatest physicians and clinicians of the Muslim golden era and has rather been held by some historians of science as the greatest of them. Contrary to the general practice of the Muslim scholars of that era, he confined his work to only one field : medicine. This enabled him to produce works of everlasting fame.

As a physician, he made several discoveries and breakthroughs. He described correctly, for the first time, scabies, the itch mite and may thus be regarded as the first parasitologist. Likewise, he prescribed tracheotomy and direct feeding through the gullet and rectum in the cases where normal feeding was not possible. He also gave clinical descriptions of mediastinal tumors, intestinal phthisis, inflammation of the middle ear, pericarditis, etc.

Abu Marwan Abd al-Malik ibn Zuhr (Arabic: ??? ????? ??? ????? ?? ????) (also known as Ibn Zuhr, Avenzoar, Abumeron or Ibn-Zohr) (1091-1161) was an Arab Muslim physician, pharmacist, surgeon, parasitologist, Islamic scholar, and teacher.

Early life

He was born in Seville, and studied at the University of Cordoba. He belonged to the Banu Zuhr family, which produced five generations of physicians, including two female physicians who served the Almohad ruler Abu Yusuf Ya’qub al-Mansur. Ibn Zuhr was also the teacher of Averroes. He began his medical practice and training under his father, Abu’l-Ala Zuhr (d. 1131).

Flight from Seville

Around 1130, he fell out of favour of with the Almoravid ruler, Ali bin Yusuf bin Tashufin, and fled from Seville. He was however, apprehended and jailed in Marrakesh. Later in 1147 when the Almohad dynasty conquered Seville, he returned and devoted himself to medical practice and teaching. He died at Seville in 1161.

Achievements

He is considered the father of experimental surgery, for introducing the experimental method into surgery, introducing the methods of human dissection and autopsy, inventing the surgical procedure of tracheotomy, performing the first parenteral nutrition of humans with a silver needle, discovering the cause of scabies and inflammation, discovering the existence of parasites, and refuting the theory of four humours.

Al-Taisir

Ibn Zuhr’s most famous work is his Al-Taisir, in which he introduced the experimental method into surgery, for which he is considered the father of experimental surgery. He was the first to employ animal testing in order to experiment with surgical procedures before applying them to human patients.� He also performed the first dissections and postmortem autopsies on humans as well as animals.

He invented the surgical procedure of tracheotomy, as he was the first to give a correct description of the tracheotomy operation for suffocating patients. He perfected this surgical procedure through his experiments on a goat. He also performed postmortem autopsies on a sheep during his clinical trials on the treatment of ulcerating diseases of the lungs. He also wrote on the prophylaxis against urinary tract infections and described the importance of dietary management in maintaining the prophylaxis.

He established surgery as an independent field of medicine, by introducing a training course designed specifically for future surgeons, in order that they be qualified before being allowed to perform operations independently, and for defining the roles of a general practitioner and a surgeon in the treatment of a surgical condition.

The Method of Preparing Medicines and Diet

He performed the first parenteral nutrition of humans with a silver needle, and wrote a book on it entitled The Method of Preparing Medicines and Diet.

Anatomy, Physiology, Etiology and Parasitology

During his medical experiments on anatomy and physiology, Ibn Zuhr was the first physician known to have carried out human dissection and postmortem autopsy. He proved that the skin disease scabies was caused by a parasite, which contradicted the erroneous theory of four humours supported by Hippocrates, Galen and Avicenna. The removal of the parasite from the patient’s body did not involve purging, bleeding or any other traditional treatments associated with the four humours. His works show that he was often highly critical of previous medical authorities, including Avicenna’s The Canon of Medicine.

He was one of the first physicians to reject the erroneous theory of four humours, which dates back to Hippocrates and Galen. Avenzoar also confirmed the presence of blood in the body.

Ibn Zuhr was also the first to provide a real scientific etiology for the inflammatory diseases of the ear, and the first to clearly discuss the causes of stridor. He also proved that the skin disease scabies was caused by a parasite.

Anesthesiology

In anesthesiology, modern anesthesia was developed in Islamic Spain by the Muslim anesthesiologists Ibn Zuhr and Abu al-Qasim al-Zahrawi. They were the first to utilize oral as well as inhalant anesthetics, and they performed hundreds of surgeries under inhalant anesthesia with the use of narcotic-soaked sponges which were placed over the face.

Neurology and Neuropharmacology

Ibn Zuhr gave the first accurate descriptions on neurological disorders, including meningitis, intracranial thrombophlebitis, and mediastinal tumours, and made contributions to modern neuropharmacology.

Pharmacopoeia and drug therapy

Ibn Zuhr wrote an early pharmacopoeia, which later became the first Arabic book to be printed with a movable type in 1491.

Ibn Zuhr (and other Muslim physicians such as al-Kindi, Ibn Sahl, Abulcasis, al-Biruni, Avicenna, Averroes, Ibn al-Baitar, Ibn Al-Jazzar and Ibn al-Nafis) developed drug therapy and medicinal drugs for the treatment of specific symptoms and diseases. His use of practical experience and careful observation was extensive.

Al-Khwarizmi was born in the epicentre of an Islamic empire which then stretched from the Mediterranean to India. This was a very fortuitous time for Arabic learning. The rulers of the Abbasid dynasty who were leading this huge empire, founded an academy in Baghdad called the House of Wisdom where the learned men collected and translated all the scientific works that they could get hold of. House of Wisdom had a large library – first famous library established after the library of Alexandria was destroyed.

Al-Khwarizmi was one of the learned men who worked in the House of Wisdom. His interests lied in the fields of algebra, geometry, astronomy and geography. His now most famous work is that from which we got the name for algebra itself – Hisab al-jabr w’al-muqabala.

Abu Ja’far Mu?ammad ibn Musa al-Khwarizmi (c. 780, Khwarizm – c. 850) was a Persian mathematician, astronomer, and geographer, who worked most of his life as a scholar in the House of Wisdom in Baghdad.

His Algebra was the first book on the systematic solution of linear and quadratic equations. Consequently he is considered to be the father of algebra, a title he shares with Diophantus. Latin translations of his Arithmetic, on the Indian numerals, introduced the decimal positional number system to the Western world in the twelfth century. He revised and updated Ptolemy’s Geography as well as writing several works on astronomy and astrology.

His contributions not only made a great impact on mathematics, but on language as well. The word algebra is derived from al-jabr, one of the two operations used to solve quadratic equations, as described in his book. The words algorism and algorithm stem from Algoritmi, the Latinization of his name. His name is also the origin of the Spanish word guarismo and of the Portuguese word algarismo, both meaning digit.

Life

Few details about al-Khwarizmi’s life are known; it is not even certain where he was born. His name indicates he might have come from Khwarezm (Khiva), then part of Greater Khorasan, which at that time was part of the Persian Empire (the eastern part of the territory of Persia), now Xorazm Province of Uzbekistan. Abu Rayhan Biruni (a native Chorasmian) explicitly states: “The people of Khwarizm are a branch of the Persian tree”.

The historian Tabari gave his name as Muhammad ibn Musa al-Khwarizmi al-Majousi al-Katarbali (Arabic: ???? ?? ???? ?????????? ????????? ???????????). The epithet al-Qutrubbulli indicates he might instead have come from Qutrubbull, a small town near Baghdad. However, Rashed points out that:

There is no need to be an expert on the period or a philologist to see that al-Tabari’s second citation should read “Muhammad ibn Musa al-Khwarizmi and al-Majusi al-Qutrubbulli,” and that there are two people (al-Khwarizmi and al-Majusi al-Qutrubbulli) between whom the letter wa [Arabic �?' for the article �and'] has been omitted in an early copy. This would not be worth mentioning if a series of errors concerning the personality of al-Khwarizmi, occasionally even the origins of his knowledge, had not been made. Recently, G. J. Toomer with naive confidence constructed an entire fantasy on the error which cannot be denied the merit of amusing the reader.

Regarding al-Khwarizmi’s religion, Toomer writes:

Another epithet given to him by al-?abari, “al-Majusi,” would seem to indicate that he was an adherent of the old Zoroastrian religion. This would still have been possible at that time for a man of Iranian origin, but the pious preface to al-Khwarizmi’s Algebra shows that he was an orthodox Muslim, so al-?abari’s epithet could mean no more than that his forebears, and perhaps he in his youth, had been Zoroastrians.

In Ibn al-Nadim’s Kitab al-Fihrist we find a short biography on al-Khwarizmi, together with a list of the books he wrote. Al-Khwarizmi accomplished most of his work in the period between 813 and 833. After the Islamic conquest of Persia, Baghdad became the centre of scientific studies and trade, and many merchants and scientists from as far as China and India traveled to this city-as such apparently so did Al-Khwarizmi. He worked in Baghdad as a scholar at the House of Wisdom established by Caliph al-Ma?mun, where he studied the sciences and mathematics, which included the translation of Greek and Sanskrit scientific manuscripts.

Contributions

His major contributions to mathematics, astronomy, astrology, geography and cartography provided foundations for later and even more widespread innovation in algebra, trigonometry, and his other areas of interest. His systematic and logical approach to solving linear and quadratic equations gave shape to the discipline of algebra, a word that is derived from the name of his 830 book in the Arabic language on the subject, al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabala (Arabic ?????? ??????? ?? ???? ????? ?????????) or: “The Compendious Book on Calculation by Completion and Balancing”. The book was first translated into Latin in the twelfth century.

His book On the Calculation with Hindu Numerals written about 825, was principally responsible for the diffusion of the Indian system of numeration in the Middle-East and then Europe. This book also translated into Latin in the twelfth century, as Algoritmi de numero Indorum. From the name of the author, rendered in Latin as algoritmi, originated the term algorithm.

Some of his contributions were based on earlier Persian and Babylonian Astronomy, Indian numbers, and Greek sources.

Al-Khwarizmi systematized and corrected Ptolemy’s data in geography as regards to Africa and the Middle east. Another major book was his Kitab surat al-ard (”The Image of the Earth”; translated as Geography), which presented the coordinates of localities in the known world based, ultimately, on those in the Geography of Ptolemy but with improved values for the length of the Mediterranean Sea and the location of cities in Asia and Africa.

He also assisted in the construction of a world map for the caliph al-Ma’mun and participated in a project to determine the circumference of the Earth, supervising the work of 70 geographers to create the map of the then “known world”.

When his work was copied and transferred to Europe through Latin translations, it had a profound impact on the advancement of basic mathematics in Europe. He also wrote on mechanical devices like the astrolabe and sundial.

Algebra

A page from al-Khwarizmi’s algebra

Al-Kitab al-mukhta?ar fi ?isab al-jabr wa-l-muqabala (Arabic: ?????? ??????? ?? ???? ????? ????????? “The Compendious Book on Calculation by Completion and Balancing”) is a mathematical book written approximately 830 CE. The term algebra is derived from the name of one of the basic operations with equations (al-jabr) described in this book. The book was translated in Latin as Liber algebrae et almucabala by Robert of Chester (Segovia, 1145) hence “algebra”, and also by Gerard of Cremona. A unique Arabic copy is kept at Oxford and was translated in 1831 by F. Rosen. A Latin translation is kept in Cambridge.

The al-jabr is considered the foundational text of modern algebra. It provided an exhaustive account of solving polynomial equations up to the second degree, and introduced the fundamental methods of “reduction” and “balancing”, referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation.

Al-Khwarizmi’s method of solving linear and quadratic equations worked by first reducing the equation to one of six standard forms (where b and c are positive integers)

• squares equal roots (ax² = bx)
• squares equal number (ax² = c)
• roots equal number (bx = c)
• squares and roots equal number (ax² + bx = c)
• squares and number equal roots (ax² + c = bx)
• roots and number equal squares (bx + c = ax²)

by dividing out the coefficient of the square and using the two operations al-?abr (Arabic: ????? “restoring” or “completion”) and al-muqabala (”balancing”). Al-?abr is the process of removing negative units, roots and squares from the equation by adding the same quantity to each side. For example, x² = 40x ? 4x² is reduced to 5x² = 40x. Al-muqabala is the process of bringing quantities of the same type to the same side of the equation. For example, x² + 14 = x + 5 is reduced to x² + 9 = x.

Several authors have also published texts under the name of Kitab al-?abr wa-l-muqabala, including Abu ?anifa al-Dinawari, Abu Kamil Shuja ibn Aslam, Abu Mu?ammad al-?Adli, Abu Yusuf al-Mi??i?i, ‘Abd al-Hamid ibn Turk, Sind ibn ?Ali, Sahl ibn Bi�r, and �arafaddin al-?usi.

J. J. O’Conner and E. F. Robertson wrote in the MacTutor History of Mathematics archive:

“Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as “algebraic objects”. It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before.”

R. Rashed and Angela Armstrong write:

“Al-Khwarizmi’s text can be seen to be distinct not only from the Babylonian tablets, but also from Diophantus’ Arithmetica. It no longer concerns a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study. On the other hand, the idea of an equation for its own sake appears from the beginning and, one could say, in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems.”

Page from a Latin translation, beginning with “Dixit algorizmi”

Arithmetic

Al-Khwarizmi’s second major work was on the subject of arithmetic, which survived in a Latin translation but was lost in the original Arabic. The translation was most likely done in the twelfth century by Adelard of Bath, who had also translated the astronomical tables in 1126.

The Latin manuscripts are untitled, but are commonly referred to by the first two words with which they start: Dixit algorizmi (”So said al-Khwarizmi”), or Algoritmi de numero Indorum (”al-Khwarizmi on the Hindu Art of Reckoning”), a name given to the work by Baldassarre Boncompagni in 1857. The original Arabic title was possibly Kitab al-Jam? wa-l-tafriq bi-?isab al-Hind(”The Book of Addition and Subtraction According to the Hindu Calculation”)

Al-Khwarizmi’s work on arithmetic was responsible for introducing the Arabic numerals, based on the Hindu-Arabic numeral system developed in Indian mathematics, to the Western world. The term “algorithm” is derived from the algorism, the technique of performing arithmetic with Hindu-Arabic numerals developed by al-Khwarizmi. Both “algorithm” and “algorism” are derived from the Latinized forms of al-Khwarizmi’s name, Algoritmi and Algorismi, respectively.

Astronomy

Corpus Christi College MS 283

Al-Khwarizmi’s Zij al-Sindhind (Arabic: ??? “astronomical tables of Sind and Hind”) is a work consisting of approximately 37 chapters on calendrical and astronomical calculations and 116 tables with calendrical, astronomical and astrological data, as well as a table of sine values. This is the first of many Arabic Zijes based on the Indian astronomical methods known as the sindhind. The work contains tables for the movements of the sun, the moon and the five planets known at the time. This work marked the turning point in Islamic astronomy. Hitherto, Muslim astronomers had adopted a primarily research approach to the field, translating works of others and learning already discovered knowledge. Al-Khwarizmi’s work marked the beginning of non-traditional methods of study and calculations.

The original Arabic version (written c. 820) is lost, but a version by the Spanish astronomer Maslamah Ibn Ahmad al-Majriti (c. 1000) has survived in a Latin translation, presumably by Adelard of Bath (January 26, 1126). The four surviving manuscripts of the Latin translation are kept at the Biblioth�que publique (Chartres), the Biblioth�que Mazarine (Paris), the Bibliotheca Nacional (Madrid) and the Bodleian Library (Oxford).

Al-Khwarizmi made several important improvements to the theory and construction of sundials, which he inherited from his Indian and Hellenistic predecessors. He made tables for these instruments which considerably shortened the time needed to make specific calculations. His sundial was universal and could be observed from anywhere on the Earth. From then on, sundials were frequently placed on mosques to determine the time of prayer. The shadow square, an instrument used to determine the linear height of an object, in conjunction with the alidade for angular observations, was also invented by al-Khwarizmi in ninth-century Baghdad.

The first quadrants and mural instruments were invented by al-Khwarizmi in ninth century Baghdad. The sine quadrant, invented by al-Khwarizmi, was used for astronomical calculations. The first horary quadrant for specific latitudes, was also invented by al-Khwarizmi in Baghdad, then center of the development of quadrants. It was used to determine time (especially the times of prayer) by observations of the Sun or stars. The Quadrans Vetus was a universal horary quadrant, an ingenious mathematical device invented by al-Khwarizmi in the ninth century and later known as the Quadrans Vetus (Old Quadrant) in medieval Europe from the thirteenth century. It could be used for any latitude on Earth and at any time of the year to determine the time in hours from the altitude of the Sun. This was the second most widely used astronomical instrument during the Middle Ages after the astrolabe. One of its main purposes in the Islamic world was to determine the times of Salah.

Geography

Hubert Daunicht’s reconstruction of al-Khwarizmi’s planisphere.

Al-Khwarizmi’s third major work is his Kitab ?urat al-Ar? (Arabic: ???? ???? ????? “Book on the appearance of the Earth” or “The image of the Earth” translated as Geography), which was finished in 833. It is a revised and completed version of Ptolemy’s Geography, consisting of a list of 2402 coordinates of cities and other geographical features following a general introduction.

There is only one surviving copy of Kitab ?urat al-Ar?, which is kept at the Strasbourg University Library. A Latin translation is kept at the Biblioteca Nacional de Espa�a in Madrid. The complete title translates as Book of the appearance of the Earth, with its cities, mountains, seas, all the islands and rivers, written by Abu Ja’far Muhammad ibn Musa al-Khwarizmi, according to the geographical treatise written by Ptolemy the Claudian.

The book opens with the list of latitudes and longitudes, in order of “weather zones”, that is to say in blocks of latitudes and, in each weather zone, by order of longitude. As Paul Gallez points out, this excellent system allows us to deduce many latitudes and longitudes where the only document in our possession is in such a bad condition as to make it practically illegible.

Neither the Arabic copy nor the Latin translation include the map of the world itself, however Hubert Daunicht was able to reconstruct the missing map from the list of coordinates. Daunicht read the latitudes and longitudes of the coastal points in the manuscript, or deduces them from the context where they were not legible. He transferred the points onto graph paper and connected them with straight lines, obtaining an approximation of the coastline as it was on the original map. He then does the same for the rivers and towns.

Al-Khwarizmi corrected Ptolemy’s gross overestimate for the length of the Mediterranean Sea^[30] (from the Canary Islands to the eastern shores of the Mediterranean); Ptolemy overestimated it at 63 degrees of longitude, while al-Khwarizmi almost correctly estimated it at nearly 50 degrees of longitude. He “also depicted the Atlantic and Indian Oceans as open bodies of water, not land-locked seas as Ptolemy had done.” Al-Khwarizmi thus set the Prime Meridian of the Old World at the eastern shore of the Mediterranean, 10-13 degrees to the east of Alexandria (the prime meridian previously set by Ptolemy) and 70 degrees to the west of Baghdad. Most medieval Muslim geographers continued to use al-Khwarizmi’s prime meridian.

Jewish calendar

Al-Khwarizmi wrote several other works including a treatise on the Hebrew calendar (Risala fi istikhraj ta?rikh al-yahud “Extraction of the Jewish Era”). It describes the 19-year intercalation cycle, the rules for determining on what day of the week the first day of the month Tishri shall fall; calculates the interval between the Jewish era (creation of Adam) and the Seleucid era; and gives rules for determining the mean longitude of the sun and the moon using the Jewish calendar. Similar material is found in the works of al-Biruni and Maimonides.

Other works

Several Arabic manuscripts in Berlin, Istanbul, Tashkent, Cairo and Paris contain further material that surely or with some probability comes from al-Khwarizmi. The Istanbul manuscript contains a paper on sundials, which is mentioned in the Fihirst. Other papers, such as one on the determination of the direction of Mecca, are on the spherical astronomy.

Two texts deserve special interest on the morning width (Ma?rifat sa?at al-mashriq fi kull balad) and the determination of the azimuth from a height (Ma?rifat al-samt min qibal al-irtifa?).

He also wrote two books on using and constructing astrolabes. Ibn al-Nadim in his Kitab al-Fihrist (an index of Arabic books) also mentions Kitab ar-Ru?ama(t) (the book on sundials) and Kitab al-Tarikh (the book of history) but the two have been lost.The shaping of our mathematics can be attributed to Al-Khwarizmi (c.780-c.850), the chief librarian of the observatory, research center and library called the House of Wisdom in Baghdad. His treatise, “Hisab al-jabr w’al-muqabala” (Calculation by Restoration and Reduction), which covers linear and quadratic equations, solved trade imbalances, inheritance questions and problems arising from land surveyance and allocation. In passing, he also introduced into common usage our present numerical system, which replaced the old, cumbersome Roman one.

Italian mathematician and philosopher, considered to be the first woman in the Western world to have achieved a reputation in mathematics.

Maria Gaetana Agnesi (May 16, 1718 – January 9, 1799) was an Italian linguist, mathematician, and philosopher. Agnesi is credited with writing the first book discussing both differential and integral calculus. She was an honorary member of the faculty at the University of Bologna. According to Dirk Jan Struik, Agnesi is “the first important woman mathematician since Hypatia (fifth century A.D.)”.

Early life

Her father, Pietro, was a wealthy man of business and a professor of mathematics at the University of Bologna who desired to elevate his family into the Milanese nobility.

Having been born in Milan, Maria was recognized as a child prodigy very early; she could speak both French and Italian at five years of age. By her eleventh birthday she had acquired Greek, Hebrew, Spanish, German, Latin, and was referred to as the “Walking Polyglot”. She even educated her younger brothers. When she was 9 years old, she composed and delivered an hour-long speech in Latin to an academic gathering. The subject was women’s right to be educated. When she was fifteen, her father began to regularly gather in his house a circle of the most learned men in Bologna, before whom she read and maintained a series of theses on the most abstruse philosophical questions. Records of these meetings are given in Charles de Brosses’ Lettres sur l’Italie and in the Propositiones Philosophicae, which her father had published in 1738. These displays, being probably not altogether congenial to Maria (who wanted to retire) ceased by her twentieth year because she strongly desired to enter a convent at that time. Although her father refused to grant this wish, he agreed to let her live from that time on in an almost conventual semi-retirement, avoiding all interactions with society and devoting herself entirely to the study of mathematics. During that time, Maria studied both differential and integral calculus. Pietro Agnesi also married twice more after Maria’s mother died, so that Maria Agnesi ended up the eldest of 21 children. In addition to her performances and lessons, her responsibility was to teach her siblings. This task kept her from her own goal of entering a convent. Scholars thought she was dazzingly beautiful and hers was recognized as one of the richest noble families in Milan.

Contributions to mathematics

Instituzioni analitiche

First page of Instituzioni analitiche (1748)

The most valuable result of her labours was the Instituzioni analitiche ad uso della gioventu italiana, a work of great merit, which was published at Milan in 1748 and “was regarded as the best introduction extant to the works of Euler.” The first volume treats of the analysis of finite quantities and the second of the analysis of infinitesimals. A French translation of the second volume by P. T. d’Antelmy, with additions by Charles Bossut (1730-1814), appeared at Paris in 1775; and an English translation of the whole work by John Colson (1680-1760), the Lucasian Professor of Mathematics at Cambridge, “inspected” by John Hellins, was published in 1801 at the expense of Baron Maseres.

Witch of Agnesi

Madame Agnesi also wrote a commentary on the Traite analytique des sections coniques du marquis de l’H�pital, which, though highly praised by those who saw it in manuscript, was never published. She discussed the curve known as the “witch of Agnesi” or “versiera” as she named it in 1748. The name derives from the Italian for the rope that turns a sail, taken from the Latin vertere, versus meaning “to turn,” which was the term used by Luigi Grandi before her. Colson, who translated Agnesi’s text to English, perhaps confused “la versiera” with “l’avversiera”, and so mistranslated it as “she-devil” or “the witch”, with the result that English-speakers and, for some reason, Spanish speakers from Mexico, Cuba, and Spain, know the curve as the “Witch of Agnesi” (La Bruja de Agnesi).). Struik mentions that:

The word [versiera] is derived from Latin vertere, to turn, but is also an abbreviation of Italian avversiera, female devil. Some wit in England once translated it ‘witch’, and the silly pun is still lovingly preserved in most of our textbooks in English language. The curve had already appeared in the writings of Fermat (Oeuvres, I, 279-280; III, 233-234) and of others; the name versiera is from Guido Grandi (Quadratura circuli et hyperbolae, Pisa, 1703). The curve is type 63 in Newton’s classification. The first to use the term ‘witch’ in this sense may have been B. Williamson, Integral calculus, 7 (1875), 173; see Oxford English Dictionary.

Agnesi’s diploma from Universit� di Bologna

Examples of the curve are those given by the equations:

where a is any non-zero constant. The equation:

is the simplest among these.

She has achieved international acclaim for her work in growth factor research, having discovered and characterized, together with Dr Sporn, the cytokine transforming growth factor-? (TGF-?).

Anita B. Roberts (Born: April 3, 1942 ; Died: May 26, 2006) was a molecular biologist who made pioneering observations of a protein, TGF-?, that is critical in healing wounds and bone fractures and that has a dual role in blocking or stimulating cancers. Roberts was the 49th most-cited scientist in the world and the second most-cited female scientist as of 2005.

Roberts was born in Pittsburgh, Pennsylvania, where she grew up. She attended Oberlin College and earned her doctorate in biochemistry from the University of Wisconsin-Madison in 1968. After postdoctoral work at Harvard Medical School, Dr. Roberts joined the National Cancer Institute in 1976. From 1995 to 2004, she served as Chief of the institute’s, and continued her research until her death in 2006.

In the early-1980s, Dr. Roberts and her colleagues at the National Cancer Institute, part of the National Institutes of Health in Bethesda, Maryland began to experiment with the protein, called TGF-?, short for transforming growth factor beta.

Dr. Roberts isolated the protein from bovine kidney tissue and compared her results with TGF-? taken from human blood platelets and placental tissue. Institute researchers then began a series of experiments to determine the protein’s characteristics. They discovered that it helps play a central role in signaling other growth factors in the body to heal wounds and fractures speedily.

TGF-? was later shown to have an effect on regulation of the heartbeat and the response of the eye to aging.

In later research, Dr. Roberts and others found that TGF-? inhibits the growth of some cancers while stimulating growth in advanced cancers, including cancers of the breast and lung.

Dr. Roberts was a former president of the Wound Healing Society. In 2005, she was elected to the American Academy of Arts and Sciences. Roberts herself was diagnosed cancer, stage IV gastric cancer, in March 2004. She received a degree of fame in the cancer community for her blog, detailing her daily struggles with the disease. She died on May 26, 2006, aged 64.

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A Toronto-based researcher has built what he claims is the world’s first fully functional female robot — a lifelike android named Aiko that is capable of recognizing faces, identifying medication, and even buttering toast.

33-year-old researcher Le Trung, a graduate of York University, built Aiko with silicon and computer parts. Programming her internal software took over a year.

To date, Trung has spent $24,000 building his robo-girl.

Aiko sports delicate, Geisha-like features and is armed with sensors that allow her to respond to touch and voice commands. A camera in her neck provides her with visual input. All told, the robot weighs in at about 70 pounds.

With a vocabulary of more than 13,000 words, Aiko can, among other things, tell you what the weather is outside.

Despite her lifelike appearance and 32-23-33, anatomically correct measurements, Trung insists Aiko is not a sex doll. “I’m attached to it, but do I sleep with it? No,” said Aiko, in an interview published Thursday in Toronto’s Globe & Mail newspaper.

Aiko is now seeking investors so he can conduct further robotics research and make continued improvements to Aiko. “Her fingertips are still made of cardboard, see. I don’t have money for titanium,” Trung told the Globe.

Though similar, science fiction literature generally distinguishes between robots and androids — with the former only capable of carrying out preprogrammed commands while the latter is supposedly able to think independently. Trung claims Aiko is able to spell out words he hasn’t taught her.

Can a date with Data be far behind?

French chemist who, through a conscious revolution, became the father of modern chemistry. As a student, he stated “I am young and avid for glory.” He was educated in a radical tradition, a friend of Condillac and read Maquois’s dictionary. He won a prize on lighting the streets of Paris, and designed a new method for preparing saltpeter. He also married a young, beautiful 13-year-old girl named Marie-Anne, who translated from English for him and illustrated his books. Lavoisier demonstrated with careful measurements that transmutation of water to earth was not possible, but that the sediment observed from boiling water came from the container. He burnt phosphorus and sulfur in air, and proved that the products weighed more than he original. Nevertheless, the weight gained was lost from the air. Thus he established the Law of Conservation of Mass.

Antoine-Laurent de Lavoisier (26 August 1743�- 8 May 1794), the father of modern chemistry, was a French noble prominent in the histories of chemistry and biology. He stated the first version of the law of conservation of mass, recognized and named oxygen (1778) and hydrogen (1783), abolished the phlogiston theory, introduced the metric system, wrote the first extensive list of elements, and helped to reform chemical nomenclature. The concept of the finite nature of matter was first introduced by Antoine Lavoisier during the 18th century. He discovered that, although matter may change its form or shape, its mass always remains the same. Thus, for instance, if water is heated to steam, if salt is dissolved in water or if a piece of wood is burned to ashes, the total mass remains unchanged. The principles of this discovery were elaborated centuries before by Islamic Persia’s great scholar, Abu Rayhan Biruni. Lavoisier was a disciple of the Muslim chemists and physicists and referred to their books frequently. He was also an investor and administrator of the “Ferme Generale” a private tax collection company; chairman of the board of the Discount Bank (later the Banque de France); and a powerful member of a number of other aristocratic administrative councils. All of these political and economic activities enabled him to fund his scientific research. Because of his prominence in the pre-revolutionary government in France, he was beheaded at the height of the French Revolution.

Early life

Born to a wealthy family in Paris, Antoine Laurent Lavoisier inherited a large fortune at the age of five with the passing of his mother. He attended the College Mazarin from 1754 to 1761, studying chemistry, botany, astronomy, and mathematics. His education was filled with the ideals of the French Enlightenment of the time, and he felt fascination for Maquois’s dictionary. From 1761 to 1763, he studied some law at the University of Paris where he received his Bachelor of Law in 1763. At the same time, he continued attending lectures in the natural sciences. Lavoisier’s devotion and passion for chemistry was largely influenced by �tienne Condillac, a prominent French scholar of the 18th century. His first chemical publication appeared in 1764. In collaboration with Jean-�tienne Guettard, Lavoisier worked on a geological survey of Alsace-Lorraine in 1767. At the age of 25, he was elected a member of the French Academy of Sciences, France’s most elite scientific society, for an essay on street lighting and in recognition for his earlier research. In 1769, he worked on the first geological map of France.

Portrait of Monsieur Lavoisier and his Wife, by Jacques-Louis David

In 1771, Lavoisier at age 28, married the 13-year-old Marie-Anne Pierrette Paulze, the daughter of a co-owner of the Ferme. Over time, she proved to be a scientific colleague to her husband. She translated documents from English for him, including Richard Kirwan’s Essay on Phlogiston and Joseph Priestley’s research. She created many sketches and carved engravings of the laboratory instruments used by Lavoisier and his colleagues. She also edited and published Lavoisier’s memoirs (whether any English translations of those memoirs have survived is unknown as of today) and hosted parties at which eminent scientists discussed ideas and problems related to chemistry.

Contributions to chemistry

Research on gases, water, and combustion

Antoine Lavoisier’s famous phlogiston experiment. Engraving by Mme Lavoisier in the 1780s taken from Traite elementaire de chimie (Elementary treatise on chemistry).

The work of Lavoisier was translated in Japan in the 1840s, through the process of Rangaku. Page from Udagawa Y?an’s 1840 Seimi Kais?.

Lavoisier also demonstrated the role of oxygen in the rusting of metal, as well as oxygen’s role in animal and plant respiration. Working with Pierre-Simon Laplace, Lavoisier conducted experiments that showed that respiration was essentially a slow combustion of organic material using inhaled oxygen. Lavoisier’s explanation of combustion disproved the phlogiston theory, which postulated that materials released a substance called phlogiston when they burned.

Lavoisier also discovered that Henry Cavendish’s ‘inflammable air’, which Lavoisier had termed hydrogen (Greek for “water-former”), combined with oxygen to produce a dew which, as Joseph Priestley had reported, appeared to be water. Lavoisier’s work was partly based on the research of Priestley. However, he tried to take credit for Priestley’s discoveries. This tendency to use the results of others without acknowledgment, then draw conclusions of his own, is said to be characteristic of Lavoisier. In “Sur la combustion en general” (”On Combustion in general,” 1777) and “Considerations Generales sur la Nature des Acides” (”General Considerations on the Nature of Acids,” 1778), he demonstrated that the “air” responsible for combustion was also the source of acidity. In 1779, he named this part of the air “oxygen” (Greek for “becoming sharp” because he claimed that the sharp taste of acids came from oxygen), and the other “azote” (Greek for “no life”). In “Reflexions sur la Phlogistique” (”Reflections on Phlogiston,” 1783), Lavoisier showed the phlogiston theory to be inconsistent.

Pioneer of stoichiometry

Laboratory instruments used by Lavoisier circa 1780s

Lavoisier’s researches included some of the first truly quantitative chemical experiments. He carefully weighed the reactants and products in a chemical reaction, which was a crucial step in the advancement of chemistry. He showed that, although matter can change its state in a chemical reaction, the quantity of matter is the same at the end as at the beginning of every chemical change. These experiments supported the law of conservation of mass, which Lavoisier was the first to state, although Mikhail Lomonosov (1711-1765) had previously expressed similar ideas in 1748 and proved them in experiments. Others who anticipated the work of Lavoisier include Joseph Black (1728-1799), Henry Cavendish (1731-1810), and Jean Rey (1583-1645).

Analytical chemistry and chemical nomenclature

Chemist’s laboratory, from Diderot’s Encyclopedie, with alchemical table of elements

Lavoisier investigated the composition of water and air, which at the time were considered elements. He determined that the components of water were oxygen and hydrogen, and that air was a mixture of gases, primarily nitrogen and oxygen. With the French chemists Claude-Louis Berthollet, Antoine Fourcroy and Guyton de Morveau, Lavoisier devised a systematic chemical nomenclature. He described it in Methode de nomenclature chimique (Method of Chemical Nomenclature, 1787). This system facilitated communication of discoveries between chemists of different backgrounds and is still largely in use today, including names such as sulfuric acid, sulfates, and sulfites.

Lavoisier’s Traite �lementaire de Chimie (Treatise of Elementary Chemistry, 1789, translated into English by Scotsman Robert Kerr) is considered to be the first modern chemistry textbook. It presented a unified view of new theories of chemistry, contained a clear statement of the law of conservation of mass, and denied the existence of phlogiston. This text clarified the concept of an element as a substance that could not be broken down by any known method of chemical analysis, and presented Lavoisier’s theory of the formation of chemical compounds from elements.

While many leading chemists of the time refused to accept Lavoisier’s new ideas, the Traite �lementaire was sufficiently sound to convince the next generation.

Combustion generated by focusing sunlight over flammable materials using lenses, an experiment conducted by Lavoisier in the 1770s

Detail of picture of a combustion experiment

Constant pressure calorimeter , engraving made by madame Lavoisier for thermochemistry experiments.

Legacy

Lavoisier’s fundamental contributions to chemistry were a result of a conscious effort to fit all experiments into the framework of a single theory. He established the consistent use of the chemical balance, used oxygen to overthrow the phlogiston theory, and developed a new system of chemical nomenclature which held that oxygen was an essential constituent of all acids (which later turned out to be erroneous). Lavoisier also did early research in physical chemistry and thermodynamics in joint experiments with Laplace. They used a calorimeter to estimate the heat evolved per unit of carbon dioxide produced, eventually finding the same ratio for a flame and animals, indicating that animals produced energy by a type of combustion reaction.

Lavoisier also contributed to early ideas on composition and chemical changes by stating the radical theory, believing that radicals, which function as a single group in a chemical process, combine with oxygen in reactions. He also introduced the possibility of allotropy in chemical elements when he discovered that diamond is a crystalline form of carbon.

However, much to his professional detriment, Lavoisier actually discovered no new substances, devised no really novel apparatus, and worked out no improved methods of preparation. He was essentially a theorist, and his great merit lay in the capacity of taking over experimental work that others had carried out–without always, unfortunately, adequately recognizing their claims–and by a rigorous logical procedure, reinforced by his own quantitative experiments, of expounding the true explanation of the results. He completed the work of Black, Priestley and Cavendish, and gave a correct explanation of their experiments.

Overall, his contributions are considered the most important in advancing chemistry to the level reached in physics and mathematics during the 18th century.

Lavoisier conducting an experiment on respiration in the 1770s.

Contributions to biology

Lavoisier used a calorimeter to measure heat production as a result of respiration in a guinea pig. The outer shell of the calorimeter was packed with snow, which melted to maintain a constant temperature of 0 �C around an inner shell filled with ice. The guinea pig in the center of the chamber produced heat which melted the ice. The water that flowed out of the calorimeter was collected and weighed. Lavoisier found that 1 kg of melted ice corresponded to 80 kcal of heat production by the guinea pig. Lavoisier concluded, “la respiration est donc une combustion”, that is, respiratory gas exchange is a combustion, like that of a candle burning.^[6]

Law and politics

Lavoisier received a law degree and was admitted to the bar, but never practiced as a lawyer. He did become interested in French politics, and at the age of 26 he obtained a position as a tax collector in the Ferme Generale, a tax farming company, where he attempted to introduce reforms in the French monetary and taxation system to help the peasants. While in government work, he helped develop the metric system to secure uniformity of weights and measures throughout France.

Final days, execution, and aftermath

Statue of Lavoisier, at H�tel de Ville, Paris.

As one of twenty-eight French tax collectors and a powerful figure in the unpopular Ferme Generale, Lavoisier was branded a traitor during the Reign of Terror by French Revolutionists in 1794. Lavoisier had also intervened on behalf of a number of foreign-born scientists including mathematician Joseph Louis Lagrange, granting them exception to a mandate stripping all foreigners of possessions and freedom. Lavoisier was tried, convicted, and guillotined on 8 May in Paris, at the age of 50.

Lavoisier was actually one of the few liberals in his position. One of his actions that may have sealed his fate was a clash a few years earlier with the young Jean-Paul Marat whom he dismissed curtly after being presented with a preposterous ’scientific invention’. Marat subsequently became a leading revolutionary and one of the French Revolution’s more extreme “professional common men.”

An appeal to spare his life so that he could continue his experiments was cut short by the judge: “The Republic needs neither scientists nor chemists; the course of justice can not be delayed.”

Lavoisier’s importance to science was expressed by Lagrange who lamented the beheading by saying: “Cela leur a pris seulement un instant pour lui couper la t�te, mais la France pourrait ne pas en produire un autre pareil en un si�cle.” (”It took them only an instant to cut off his head, but France may not produce another like it in a century.”)

One and a half years following his death, Lavoisier was exonerated by the French government. When his private belongings were delivered to his widow, a brief note was included reading “To the widow of Lavoisier, who was falsely convicted.”

About a century after his death, a statue of Lavoisier was erected in Paris. It was later discovered that the sculptor had not actually copied Lavoisier’s head for the statue, but used a spare head of the Marquis de Condorcet, the Secretary of the Academy of Sciences during Lavoisier’s last years. Lack of money prevented alterations being made. The statue was melted down during the Second World War and has not since been replaced. However, one of the main “lycees” (highschools) in Paris and a street in the 8th arrondissement are named after Lavoisier, and statues of him are found on the H�tel de Ville (photograph, right) and on the fa�ade of the Cour Napoleon of the Louvre.

English physicist and mathematician who was born into a poor farming family. Luckily for humanity, Newton was not a good farmer, and was sent to Cambridge to study to become a preacher. At Cambridge, Newton studied mathematics, being especially strongly influenced by Euclid, although he was also influenced by Baconian and Cartesian philosophies. Newton was forced to leave Cambridge when it was closed because of the plague, and it was during this period that he made some of his most significant discoveries. With the reticence he was to show later in life, Newton did not, however, publish his results.

Sir Isaac Newton, FRS (4 January 1643�- 31 March 1727 was an English physicist, mathematician, astronomer, natural philosopher, alchemist, theologian and one of the most influential men in human history. His Philosophiae Naturalis Principia Mathematica, published in 1687, is considered to be the most influential book in the history of science. In this work, Newton described universal gravitation and the three laws of motion, laying the groundwork for classical mechanics, which dominated the scientific view of the physical universe for the next three centuries and is the basis for modern engineering. Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws by demonstrating the consistency between Kepler’s laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the scientific revolution.
In mechanics, Newton enunciated the principles of conservation of momentum and angular momentum. In optics, he built the first “practical” reflecting telescope^[6] and developed a theory of colour based on the observation that a prism decomposes white light into a visible spectrum. He also formulated an empirical law of cooling and studied the speed of sound.

In mathematics, Newton shares the credit with Gottfried Leibniz for the development of the differential and integral calculus. He also demonstrated the generalised binomial theorem, developed the so-called “Newton’s method” for approximating the zeroes of a function, and contributed to the study of power series.

Newton was also highly religious (though unorthodox), producing more work on Biblical hermeneutics than the natural science he is remembered for today.

Newton’s stature among scientists remains at the very top rank, as demonstrated by a 2005 survey of scientists in Britain’s Royal Society asking who had the greater effect on the history of science, Newton was deemed much more influential than Albert Einstein.

Biography

Early years

Isaac Newton was born on 4 January 1643� at Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, a hamlet in the county of Lincolnshire. At the time of Newton’s birth, England had not adopted the latest papal calendar and therefore his date of birth was recorded as Christmas Day, 25 December 1642. Newton was born three months after the death of his father. Born prematurely, he was a small child; his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabus Smith, leaving her son in the care of his maternal grandmother, Margery Ayscough. The young Isaac disliked his stepfather and held some enmity towards his mother for marrying him, as revealed by this entry in a list of sins committed up to the age of 19: Threatening my father and mother Smith to burn them and the house over them.

According to E.T. Bell and H. Eves:

Newton began his schooling in the village schools and was later sent to The King’s School, Grantham, where he became the top student in the school. At King’s, he lodged with the local apothecary, William Clarke and eventually became engaged to the apothecary’s stepdaughter, Anne Storer, before he went off to the University of Cambridge at the age of 19. As Newton became engrossed in his studies, the romance cooled and Miss Storer married someone else. It is said he kept a warm memory of this love, but Newton had no other recorded “sweet-hearts” and never married.

There are rumours that he remained a confirmed celibate. However, Bell and Eves’ sources for this claim, William Stukeley and Mrs. Vincent (the former Miss Storer�- actually named Katherine, not Anne), merely say that Newton entertained “a passion” for Storer while he lodged at the Clarke house.

From the age of about twelve until he was seventeen, Newton was educated at The King’s School, Grantham (where his signature can still be seen upon a library window sill). He was removed from school, and by October 1659, he was to be found at Woolsthorpe-by-Colsterworth, where his mother, widowed by now for a second time, attempted to make a farmer of him. He hated farming. Henry Stokes, master at the King’s School, persuaded his mother to send him back to school so that he might complete his education. This he did at the age of eighteen, achieving an admirable final report.

In June 1661, he was admitted to Trinity College, Cambridge. According to John Stillwell, he entered Trinity as a sizar.^[11] At that time, the college’s teachings were based on those of Aristotle, but Newton preferred to read the more advanced ideas of modern philosophers such as Descartes and astronomers such as Copernicus, Galileo, and Kepler. In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that would later become infinitesimal calculus. Soon after Newton had obtained his degree in August of 1665, the University closed down as a precaution against the Great Plague. Although he had been undistinguished as a Cambridge student, Newton’s private studies at his home in Woolsthorpe over the subsequent two years saw the development of his theories on calculus, optics and the law of gravitation.

Middle years

Mathematics

Most modern historians believe that Newton and Leibniz developed infinitesimal calculus independently, using their own unique notations. According to Newton’s inner circle, Newton had worked out his method years before Leibniz, yet he published almost nothing about it until 1693, and did not give a full account until 1704. Meanwhile, Leibniz began publishing a full account of his methods in 1684. Moreover, Leibniz’s notation and “differential Method” were universally adopted on the Continent, and after 1820 or so, in the British Empire. Whereas Leibniz’s notebooks show the advancement of the ideas from early stages until maturity, there is only the end product in Newton’s known notes. Newton claimed that he had been reluctant to publish his calculus because he feared being mocked for it. Newton had a very close relationship with Swiss mathematician Nicolas Fatio de Duillier, who from the beginning was impressed by Newton’s gravitational theory. In 1691 Duillier planned to prepare a new version of Newton’s Philosophiae Naturalis Principia Mathematica, but never finished it. However, in 1694 the relationship between the two men changed. At the time, Duillier had also exchanged several letters with Leibniz^{[citation needed]}.

Starting in 1699, other members of the Royal Society (of which Newton was a member) accused Leibniz of plagiarism, and the dispute broke out in full force in 1711. Newton’s Royal Society proclaimed in a study that it was Newton who was the true discoverer and labeled Leibniz a fraud. This study was cast into doubt when it was later found that Newton himself wrote the study’s concluding remarks on Leibniz. Thus began the bitter Newton v. Leibniz calculus controversy, which marred the lives of both Newton and Leibniz until the latter’s death in 1716.

Newton is generally credited with the generalised binomial theorem, valid for any exponent. He discovered Newton’s identities, Newton’s method, classified cubic plane curves (polynomials of degree three in two variables), made substantial contributions to the theory of finite differences, and was the first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations. He approximated partial sums of the harmonic series by logarithms (a precursor to Euler’s summation formula), and was the first to use power series with confidence and to revert power series. He also discovered a new formula for calculating pi.

He was elected Lucasian Professor of Mathematics in 1669. In that day, any fellow of Cambridge or Oxford had to be an ordained Anglican priest. However, the terms of the Lucasian professorship required that the holder not be active in the church (presumably so as to have more time for science). Newton argued that this should exempt him from the ordination requirement, and Charles II, whose permission was needed, accepted this argument. Thus a conflict between Newton’s religious views and Anglican orthodoxy was averted.

Optics

From 1670 to 1672, Newton lectured on optics. During this period he investigated the refraction of light, demonstrating that a prism could decompose white light into a spectrum of colours, and that a lens and a second prism could recompose the multicoloured spectrum into white light.

He also showed that the coloured light does not change its properties by separating out a coloured beam and shining it on various objects. Newton noted that regardless of whether it was reflected or scattered or transmitted, it stayed the same colour. Thus, he observed that colour is the result of objects interacting with already-coloured light rather than objects generating the colour themselves. This is known as Newton’s theory of colour.

A replica of Newton’s 6-inch (150�mm) reflecting telescope of 1672 for the Royal Society

From this work he concluded that any refracting telescope would suffer from the dispersion of light into colours (chromatic aberration), and invented a type reflecting telescope (today known as a Newtonian telescope) to bypass that problem. By grinding his own mirrors, using Newton’s rings to judge the quality of the optics for his telescopes, he was able to produce a superior instrument to the refracting telescope, due primarily to the wider diameter of the mirror. In 1671 the Royal Society asked for a demonstration of his reflecting telescope. Their interest encouraged him to publish his notes On Colour, which he later expanded into his Opticks. When Robert Hooke criticised some of Newton’s ideas, Newton was so offended that he withdrew from public debate. The two men remained enemies until Hooke’s death.

Newton argued that light is composed of particles or corpuscles, which were refracted by accelerating toward the denser medium, but he had to associate them with waves to explain the diffraction of light (Opticks Bk. II, Props. XII-L). Later physicists instead favoured a purely wavelike explanation of light to account for diffraction. Today’s quantum mechanics, photons and the idea of wave-particle duality bear only a minor resemblance to Newton’s understanding of light.

In his Hypothesis of Light of 1675, Newton posited the existence of the ether to transmit forces between particles. The contact with the theosophist Henry More, revived his interest in alchemy. He replaced the ether with occult forces based on Hermetic ideas of attraction and repulsion between particles. John Maynard Keynes, who acquired many of Newton’s writings on alchemy, stated that “Newton was not the first of the age of reason: he was the last of the magicians.” Newton’s interest in alchemy cannot be isolated from his contributions to science. (This was at a time when there was no clear distinction between alchemy and science.) Had he not relied on the occult idea of action at a distance, across a vacuum, he might not have developed his theory of gravity. (See also Isaac Newton’s occult studies.)

In 1704 Newton published Opticks, in which he expounded his corpuscular theory of light. He considered light to be made up of extremely subtle corpuscles, that ordinary matter was made of grosser corpuscles and speculated that through a kind of alchemical transmutation “Are not gross Bodies and Light convertible into one another, …and may not Bodies receive much of their Activity from the Particles of Light which enter their Composition?” Newton also constructed a primitive form of a frictional electrostatic generator, using a glass globe (Optics, 8th Query).

Mechanics and gravitation

Newton’s own copy of his Principia, with hand-written corrections for the second edition

In 1677, Newton returned to his work on mechanics, i.e., gravitation and its effect on the orbits of planets, with reference to Kepler’s laws of planetary motion, and consulting with Hooke and Flamsteed on the subject. He published his results in De motu corporum in gyrum (1684). This contained the beginnings of the laws of motion that would inform the Principia.

The Philosophiae Naturalis Principia Mathematica (now known as the Principia) was published on 5 July 1687 with encouragement and financial help from Edmond Halley. In this work Newton stated the three universal laws of motion that were not to be improved upon for more than two hundred years. He used the Latin word gravitas (weight) for the effect that would become known as gravity, and defined the law of universal gravitation. In the same work he presented the first analytical determination, based on Boyle’s law, of the speed of sound in air. Newton’s postulate of an invisible force able to act over vast distances led to him being criticised for introducing “occult agencies” into science^.

With the Principia, Newton became internationally recognised. He acquired a circle of admirers, including the Swiss-born mathematician Nicolas Fatio de Duillier, with whom he formed an intense relationship that lasted until 1693. The end of this friendship led Newton to a nervous breakdown.^{[clarification needed][citation needed]}

Later life

In the 1690s, Newton wrote a number of religious tracts dealing with the literal interpretation of the Bible. Henry More’s belief in the universe and rejection of Cartesian dualism may have influenced Newton’s religious ideas. A manuscript he sent to John Locke in which he disputed the existence of the Trinity was never published. Later works�- The Chronology of Ancient Kingdoms Amended (1728) and Observations Upon the Prophecies of Daniel and the Apocalypse of St. John (1733)�- were published after his death. He also devoted a great deal of time to alchemy (see above).

Newton was also a member of the Parliament of England from 1689 to 1690 and in 1701, but his only recorded comments were to complain about a cold draught in the chamber and request that the window be closed.

Newton moved to London to take up the post of warden of the Royal Mint in 1696, a position that he had obtained through the patronage of Charles Montagu, 1st Earl of Halifax, then Chancellor of the Exchequer. He took charge of England’s great recoining, somewhat treading on the toes of Master Lucas (and securing the job of deputy comptroller of the temporary Chester branch for Edmond Halley). Newton became perhaps the best-known Master of the Mint upon Lucas’ death in 1699, a position Newton held until his death. These appointments were intended as sinecures, but Newton took them seriously, retiring from his Cambridge duties in 1701, and exercising his power to reform the currency and punish clippers and counterfeiters. As Master of the Mint in 1717 Newton unofficially moved the Pound Sterling from the silver standard to the gold standard by creating a relationship between gold coins and the silver penny in the “Law of Queen Anne”; these were all great reforms at the time, adding considerably to the wealth and stability of England. It was his work at the Mint, rather than his earlier contributions to science, that earned him a knighthood from Queen Anne in 1705.

Newton was made President of the Royal Society in 1703 and an associate of the French Academie des Sciences. In his position at the Royal Society, Newton made an enemy of John Flamsteed, the Astronomer Royal, by prematurely publishing Flamsteed’s star catalogue, which Newton had used in his studies.

Newton died in London on 31 March 1727 and was buried in Westminster Abbey. His half-niece, Catherine Barton Conduitt, served as his hostess in social affairs at his house on Jermyn Street in London; he was her “very loving Uncle,” according to his letter to her when she was recovering from smallpox. Although Newton, who had no children, had divested much of his estate onto relatives in his last years, he actually died intestate.

After his death, Newton’s body was discovered to have had massive amounts of mercury in it, probably resulting from his alchemical pursuits. Mercury poisoning could explain Newton’s eccentricity in late life.

Religious views

Historian Stephen D. Snobelen says of Newton, “Isaac Newton was a heretic. But like Nicodemus, the secret disciple of Jesus, he never made a public declaration of his private faith – which the orthodox would have deemed extremely radical. He hid his faith so well that scholars are still unravelling his personal beliefs.”Snobelen concludes that Newton was at least a Socinian sympathiser (he owned and had thoroughly read at least eight Socinian books), possibly an Arian and almost certainly an antitrinitarian. In an age notable for its religious intolerance there are few public expressions of Newton’s radical views, most notably his refusal to take holy orders and his refusal, on his death bed, to take the sacrament when it was offered to him.

In a view disputed by Snobelen, T.C. Pfizenmaier argues that Newton held the Eastern Orthodox view of the Trinity rather than the Western one held by Roman Catholics, Anglicans, and most Protestants.^[21] In his own day, he was also accused of being a Rosicrucian (as were many in the Royal Society and in the court of Charles II).

Although the laws of motion and universal gravitation became Newton’s best-known discoveries, he warned against using them to view the universe as a mere machine, as if akin to a great clock. He said, “Gravity explains the motions of the planets, but it cannot explain who set the planets in motion. God governs all things and knows all that is or can be done.”

His scientific fame notwithstanding, Newton’s studies of the Bible and of the early Church Fathers were also noteworthy. Newton wrote works on textual criticism, most notably An Historical Account of Two Notable Corruptions of Scripture. He also placed the crucifixion of Jesus Christ at 3 April, AD 33, which agrees with one traditionally accepted date. He also attempted, unsuccessfully, to find hidden messages within the Bible.

In his own lifetime, Newton wrote more on religion than he did on natural science. He believed in a rationally immanent world, but he rejected the hylozoism implicit in Leibniz and Baruch Spinoza. Thus, the ordered and dynamically informed universe could be understood, and must be understood, by an active reason, but this universe, to be perfect and ordained, had to be regular.

Newton’s effect on religious thought

Newton and Robert Boyle’s mechanical philosophy was promoted by rationalist pamphleteers as a viable alternative to the pantheists and enthusiasts, and was accepted hesitantly by orthodox preachers as well as dissident preachers like the latitudinarians.^[25] Thus, the clarity and simplicity of science was seen as a way to combat the emotional and metaphysical superlatives of both superstitious enthusiasm and the threat of atheism, and, at the same time, the second wave of English deists used Newton’s discoveries to demonstrate the possibility of a “Natural Religion.”

The attacks made against pre-Enlightenment “magical thinking,” and the mystical elements of Christianity, were given their foundation with Boyle’s mechanical conception of the universe. Newton gave Boyle’s ideas their completion through mathematical proofs and, perhaps more importantly, was very successful in popularising them. Newton refashioned the world governed by an interventionist God into a world crafted by a God that designs along rational and universal principles. These principles were available for all people to discover, allowed people to pursue their own aims fruitfully in this life, not the next, and to perfect themselves with their own rational powers.

Newton saw God as the master creator whose existence could not be denied in the face of the grandeur of all creation. But the unforeseen theological consequence of his conception of God, as Leibniz pointed out, was that God was now entirely removed from the world’s affairs, since the need for intervention would only evidence some imperfection in God’s creation, something impossible for a perfect and omnipotent creator. Leibniz’s theodicy cleared God from the responsibility for “l’origine du mal” by making God removed from participation in his creation. The understanding of the world was now brought down to the level of simple human reason, and humans, as Odo Marquard argued, became responsible for the correction and elimination of evil.

On the other hand, latitudinarian and Newtonian ideas taken too far resulted in the millenarians, a religious faction dedicated to the concept of a mechanical universe, but finding in it the same enthusiasm and mysticism that the Enlightenment had fought so hard to extinguish.

Views of the end of the world

In a manuscript he wrote in 1704 in which he describes his attempts to extract scientific information from the Bible, he estimated that the world would end no earlier than 2060. In predicting this he said, “This I mention not to assert when the time of the end shall be, but to put a stop to the rash conjectures of fanciful men who are frequently predicting the time of the end, and by doing so bring the sacred prophesies into discredit as often as their predictions fail.”

Newton and the counterfeiters

As warden of the Royal Mint, Newton estimated that 20% of the coins taken in during The Great Recoinage were counterfeit. Counterfeiting was high treason, punishable by being hanged, drawn and quartered. Despite this, convictions of the most flagrant criminals could be extremely difficult to achieve; however, Newton proved to be equal to the task.

Disguised as an habitue of bars and taverns, he gathered much of that evidence himself. For all the barriers placed to prosecution, and separating the branches of government, English law still had ancient and formidable customs of authority. Newton was made a justice of the peace and between June 1698 and Christmas 1699 conducted some 200 cross-examinations of witnesses, informers and suspects. Newton won his convictions and in February 1699, he had ten prisoners waiting to be executed.

Possibly Newton’s greatest triumph as the king’s attorney was against William Chaloner. One of Chaloner’s schemes was to set up phony conspiracies of Catholics and then turn in the hapless conspirators whom he entrapped. Chaloner made himself rich enough to posture as a gentleman. Petitioning Parliament, Chaloner accused the Mint of providing tools to counterfeiters (a charge also made by others). He proposed that he be allowed to inspect the Mint’s processes in order to improve them. He petitioned Parliament to adopt his plans for a coinage that could not be counterfeited, while at the same time striking false coins. Newton was outraged, and went about the work to uncover anything about Chaloner. During his studies, he found that Chaloner was engaged in counterfeiting. He immediately put Chaloner on trial, but Chaloner had friends in high places and, to Newton’s horror, Chaloner walked free. Newton put him on trial a second time with conclusive evidence. Chaloner was convicted of high treason and hanged, drawn and quartered on 23 March 1699 at Tyburn gallows.

Enlightenment philosophers

Enlightenment philosophers chose a short history of scientific predecessors-Galileo, Boyle, and Newton principally-as the guides and guarantors of their applications of the singular concept of Nature and Natural Law to every physical and social field of the day. In this respect, the lessons of history and the social structures built upon it could be discarded.

It was Newton’s conception of the universe based upon Natural and rationally understandable laws that became the seed for Enlightenment ideology. Locke and Voltaire applied concepts of Natural Law to political systems advocating intrinsic rights; the physiocrats and Adam Smith applied Natural conceptions of psychology and self-interest to economic systems and the sociologists criticised the current social order for trying to fit history into Natural models of progress. Monboddo and Samuel Clarke resisted elements of Newton’s work, but eventually rationalised it to conform with their strong religious views of nature.

Newton’s laws of motion

Classical mechanics

Newton’s Second Law

The famous three laws of motion:

Newton’s First Law (also known as the Law of Inertia) states that an object at rest tends to stay at rest and that an object in uniform motion tends to stay in uniform motion unless acted upon by a net external force.

Newton’s Second Law states that an applied force, , on an object equals the rate of change of its momentum, , with time. Mathematically, this is expressed as

Because this relation only holds when the mass is constant, that is, when , the first term vanishes, and the equation can be written in the iconic form

where

This equation states that a force applied to an object of mass m causes it to accelerate at a rate .

This equality requires a consistent set of units for measuring mass, length, and time. One such set is the SI system, where mass is in kilograms, length in metres, and time in seconds. This leads to force being in newtons, named in his honour, and acceleration in metres per second per second. The English analogous system is slugs, feet, and seconds.

Newton’s Third Law states that for every action there is an equal and opposite reaction. This means that any force exerted onto an object has a counterpart force that is exerted in the opposite direction back onto the first object. The most common example is of two ice skaters pushing against each other and sliding apart in opposite directions. Another example is the recoil of a firearm, in which the force propelling the bullet is exerted equally back onto the gun and is felt by the shooter. Since the objects in question do not necessarily have the same mass, the resulting acceleration of the two objects can be different (as in the case of firearm recoil).

Newton’s apple

Reputed descendants of Newton’s apple tree, at the Botanic Gardens in Cambridge and the Instituto Balseiro library garden

Newton himself often told that story that he was inspired to formulate his theory of gravitation by watching the fall of an apple from a tree. It fell straight down–why was that, he asked?

Cartoons have gone further to suggest the apple actually hit Newton’s head, and that its impact somehow made him aware of the force of gravity. We know from his notebooks that Newton was grappling in the late 1660s with the idea that terrestrial gravity extends, in an inverse-square proportion, to the Moon; however it took him two decades to develop the full-fledged theory. John Conduitt, Newton’s assistant at the Royal Mint and husband of Newton’s niece, described the event when he wrote about Newton’s life:

The question was not whether gravity existed, but whether it extended so far from Earth that it could also be the force holding the moon to its orbit. Newton showed that if the force decreased as the inverse square of the distance, one could indeed calculate the Moon’s orbital period, and get good agreement. He guessed the same force was responsible for other orbital motions, and hence named it “universal gravitation”.

A contemporary writer, William Stukeley, recorded in his Memoirs of Sir Isaac Newton’s Life a conversation with Newton in Kensington on 15 April 1726, in which Newton recalled “when formerly, the notion of gravitation came into his mind. It was occasioned by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself. Why should it not go sideways or upwards, but constantly to the earth’s centre.” In similar terms, Voltaire wrote in his Essay on Epic Poetry (1727), “Sir Isaac Newton walking in his gardens, had the first thought of his system of gravitation, upon seeing an apple falling from a tree.” These accounts are probably exaggerations of Newton’s own tale about sitting by a window in his home (Woolsthorpe Manor) and watching an apple fall from a tree.

Various trees are claimed to be “the” apple tree which Newton describes. The King’s School, Grantham, claims that the tree was purchased by the school, uprooted and transported to the headmaster’s garden some years later, the staff of the [now] National Trust-owned Woolsthorpe Manor dispute this, and claim that a tree present in their gardens is the one described by Newton. A descendant of the original tree can be seen growing outside the main gate of Trinity College, Cambridge, below the room Newton lived in when he studied there. The National Fruit Collection at Brogdale can supply grafts from their tree (ref 1948-729), which appears identical to Flower of Kent, a coarse-fleshed cooking variety^{[clarification needed]}.

Writings by Newton

• Method of Fluxions (1671)
• Of Natures Obvious Laws & Processes in Vegetation (unpublished, c. 1671-75)
• De Motu Corporum in Gyrum (1684)
• Philosophiae Naturalis Principia Mathematica (1687)
• Opticks (1704)
• Reports as Master of the Mint (1701-25)
• Arithmetica Universalis (1707)
• The System of the World, Optical Lectures, The Chronology of Ancient Kingdoms, (Amended) and De mundi systemate (published posthumously in 1728)
• Observations on Daniel and The Apocalypse of St. John (1733)
• An Historical Account of Two Notable Corruptions of Scripture (1754)

Fame

French mathematician Joseph-Louis Lagrange often said that Newton was the greatest genius who ever lived, and once added that he was also “the most fortunate, for we cannot find more than once a system of the world to establish.” English poet Alexander Pope was moved by Newton’s accomplishments to write the famous epitaph:

Newton himself was rather more modest of his own achievements, famously writing in a letter to Robert Hooke in February 1676

Historians generally think the above quote was an attack on Hooke (who was short and hunchbacked), rather than�- or in addition to�- a statement of modesty. The two were in a dispute over optical discoveries at the time. The latter interpretation also fits with many of his other disputes over his discoveries�- such as the question of who discovered calculus as discussed above.

And then in a memoir later

Newton in popular culture

Newton is an important character in The Baroque Cycle by Neal Stephenson. A major theme of these novels is the emergence of modern science, with Newton’s work in the Principia being prominent. Newton’s interest in alchemy and the dispute over the discovery of calculus are prominent plot points, and there is a (fictional) debate on metaphysics between Newton and Gottfried Leibniz moderated by Caroline of Ansbach. The development of an economy based on money and credit is also a major theme, with Newton’s time with the Royal Mint and intrigues against counterfeit leading to a Trial of the Pyx.

In 2007, David Warner portrayed Newton in the Doctor Who audio drama Circular Time.

Monuments and commemoration

Newton’s monument (1731) can be seen in Westminster Abbey, at the north of the entrance to the choir against the choir screen. It was executed by the sculptor Michael Rysbrack (1694-1770) in white and grey marble with design by the architect William Kent (1685-1748). The monument features a figure of Newton reclining on top of a sarcophagus, his right elbow resting on several of his great books and his left hand pointing to a scroll with a mathematical design. Above him is a pyramid and a celestial globe showing the signs of the Zodiac and the path of the comet of 1680. A relief panel depicts putti using instruments such as a telescope and prism. The Latin inscription on the base translates as:

A statue of Isaac Newton, standing over an apple, can be seen at the Oxford University Museum of Natural History.

From 1978 until 1988, an image of Newton designed by Harry Ecclestone appeared on Series D �1 banknotes issued by the Bank of England (the last �1 notes to be issued by the Bank of England). Newton was shown on the reverse of the notes holding a book and accompanied by a telescope, a prism and a map of the Solar System.

Biographical knowledge

Little is known about Euclid other than his writings. What biographical information we do have comes largely from commentaries by Proclus and Pappus of Alexandria. Euclid was active at the great Library of Alexandria and may have studied at Plato’s Academy in Greece. The date and place of Euclid’s birth and the date and circumstances of his death are unknown.

Some writers in the Middle Ages confused him with Euclid of Megara, a Greek Socratic philosopher who lived approximately one century earlier.

The Elements

Although many of the results in Elements originated with earlier mathematicians, one of Euclid’s accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later.

Although best-known for its geometric results, the Elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers, Euclid’s lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers.

The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called Non-Euclidean geometries that mathematicians discovered in the 19th century.

Other works

In addition to the Elements, at least five works of Euclid have survived to the present day.

• Data deals with the nature and implications of “given” information in geometrical problems; the subject matter is closely related to the first four books of the Elements.
• On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. It is similar to a third century AD work by Heron of Alexandria.
• Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution to Euclid is doubtful. Its author may have been Theon of Alexandria.
• Phaenomena is a treatise on spherical Astronomy, it survives in Greek and is quite similar to “On the Moving Sphere”, by Autolycus of Pitane, who flourished around 310 BC.
• Optics is the earliest surviving Greek treatise on perspective. In its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth: “Things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal.” In the 36 propositions that follow, Euclid relates the apparent size of an object to its distance from the eye and investigates the apparent shapes of cylinders and cones when viewed from different angles. Proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. Pappus believed these results to be important in astronomy and included Euclid’s Optics, along with his Phaenomena, in the Little Astronomy, a compendium of smaller works to be studied before the Syntaxis (Almagest) of Claudius Ptolemy.

All of these works follow the basic logical structure of the Elements, containing definitions and proved propositions.

There are also works credibly attributed to Euclid which have been lost.

• Conics was a work on conic sections that was later extended by Apollonius of Perga into his famous work on the subject. It is likely that the first four books of Apollonius’s work come directly from Euclid. According to Pappus, “Apollonius, having completed Euclid’s four books of conics and added four others, handed down eight volumes of conics.” The Conics of Apollonius quickly supplanted the former work, and by the time of Pappus, Euclid’s work was already lost.
• Porisms might have been an outgrowth of Euclid’s work with conic sections, but the exact meaning of the title is controversial.
• Pseudaria, or Book of Fallacies, was an elementary text about errors in reasoning.
• Surface Loci concerned either loci (sets of points) on surfaces or loci which were themselves surfaces; under the latter interpretation, it has been hypothesized that the work might have dealt with quadric surfaces.
• Several works on mechanics are attributed to Euclid by Arabic sources. On the Heavy and the Light contains, in nine definitions and five propositions, Aristotelian notions of moving bodies and the concept of specific gravity. On the Balance treats the theory of the lever in a similarly Euclidean manner, containing one definition, two axioms, and four propositions. A third fragment, on the circles described by the ends of a moving lever, contains four propositions. These three works complement each other in such a way that it has been suggested that they are remnants of a single treatise on mechanics written by Euclid.

German-American physicist who, in 1905, published three papers, each of which had a profound effect on the development of physics. In one paper, he proposed the theory of special relativity, Eric Weisstein’s World of Physics which provides a correct description for particles traveling at high speeds. The two postulates of the special theory of relativity were that the speed of light Eric Weisstein’s World of Physics in a vacuum is constant and that the laws of physics are the same for all inertial reference frames. Einstein did know about the Michelson-Morley experiment Eric Weisstein’s World of Physics null result, but was not familiar with Lorentz’s work after 1895, so he reinvented the Lorentz transformation Eric Weisstein’s World of Math for himself (Pais 1982, p. 133).

Albert Einstein (14 March 1879�- 18 April 1955) was a German-born theoretical physicist. He is best known for his theory of relativity and specifically mass-energy equivalence, expressed by the equation E =�mc². Einstein received the 1921 Nobel Prize in Physics “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.”

Einstein’s many contributions to physics include his special theory of relativity, which reconciled mechanics with electromagnetism, and his general theory of relativity, which was intended to extend the principle of relativity to non-uniform motion and to provide a new theory of gravitation. His other contributions include advances in the fields of relativistic cosmology, capillary action, critical opalescence, classical problems of statistical mechanics and their application to quantum theory, an explanation of the Brownian movement of molecules, atomic transition probabilities, the quantum theory of a monatomic gas, thermal properties of light with low radiation density (which laid the foundation for the photon theory), a theory of radiation including stimulated emission, the conception of a unified field theory, and the geometrization of physics.

Einstein published over 300 scientific works and over 150 non-scientific works. In 1999 Time magazine named him the “Person of the Century”. In wider culture the name “Einstein” has become synonymous with genius, and he has since been regarded as one of the most influential people in human history.

Albert Einstein was born into a Jewish family in Ulm, in the Kingdom of Wurttemberg in the German Empire on 14 March 1879. His father was Hermann Einstein, a salesman and engineer. His mother was Pauline Einstein (nee Koch). In 1880, the family moved to Munich, where his father and his uncle founded a company, Elektrotechnische Fabrik J. Einstein & Cie, that manufactured electrical equipment.

The Einsteins were not observant of Jewish religious practices, and Albert attended a Catholic elementary school. Although Einstein had early speech difficulties, he was a top student in elementary school.

Albert Einstein in 1893 (age 14), taken before the family moved to Italy

When Einstein was five, his father showed him a pocket compass. Einstein realized that there must be something in the space, previously thought to be empty, that was moving the needle and later stated that this experience made “a deep and lasting impression”. At his mother’s insistence, he took violin lessons starting at age six, and although he disliked them and eventually quit, he later took great pleasure in Mozart’s violin sonatas. As he grew, Einstein built models and mechanical devices for fun, and began to show a talent for mathematics.

In 1889, family friend Max Talmud, a medical student, introduced the ten-year-old Einstein to key science, mathematics, and philosophy texts, including Kant’s Critique of Pure Reason and Euclid’s Elements (Einstein called it the “holy little geometry book”). From Euclid, Einstein began to understand deductive reasoning, and by the age of twelve, he had learned Euclidean geometry. Soon thereafter he began to investigate infinitesimal calculus.

In his early teens, Einstein attended the progressive Luitpold Gymnasium. His father intended for him to pursue electrical engineering, but Einstein clashed with authorities and resented the school regimen. He later wrote that the spirit of learning and creative thought were lost in strict rote learning.

In 1894, when Einstein was fifteen, his father’s business failed, and the Einstein family moved to Italy, first to Milan and then, after a few months, to Pavia. During this time, Einstein wrote his first scientific work, “The Investigation of the State of Aether in Magnetic Fields”. Einstein had been left behind in Munich to finish high school, but in the spring of 1895, he withdrew to join his family in Pavia, convincing the school to let him go by using a doctor’s note.

Rather than completing high school, Einstein decided to apply directly to the ETH Zurich, the Swiss Federal Institute of Technology in Zurich, Switzerland. Lacking a school certificate, he was required to take an entrance examination, which he did not pass, although he got exceptional marks in mathematics and physics. Einstein wrote that it was in that same year, at age 16, that he first performed his famous thought experiment visualizing traveling alongside a beam of light (Einstein 1979).

The Einsteins sent Albert to Aarau, Switzerland to finish secondary school. While lodging with the family of Professor Jost Winteler, he fell in love with the family’s daughter, Marie. (Albert’s sister Maja later married Paul Winteler.) In Aarau, Einstein studied Maxwell’s electromagnetic theory. At age 17 he graduated, renounced his German citizenship to avoid military service (with his father’s approval), and finally enrolled in the mathematics program at ETH. Marie moved to Olsberg, Switzerland for a teaching post.

In 1896, Einstein’s future wife, Mileva Maric, also enrolled at ETH, as the only woman studying mathematics. During the next few years, Einstein and Maric’s friendship developed into romance. Einstein graduated in 1900 from ETH with a degree in physics. That same year, Einstein’s friend Michele Besso introduced him to the work of Ernst Mach. The next year, Einstein published a paper in the prestigious Annalen der Physik on the capillary forces of a straw (Einstein 1901). On 21 February 1901, he gained Swiss citizenship, which he never revoked.

Patent office

The ‘Einsteinhaus’ on the Kramgasse in Berne where Einstein lived with Mileva on the first floor during his Annus Mirabilis

Following graduation, Einstein could not find a teaching post. After almost two years of searching, a former classmate’s father helped him get a job in Berne, at the Federal Office for Intellectual Property,^[14] the patent office, as an assistant examiner. His responsibility was evaluating patent applications for electromagnetic devices. In 1903, Einstein’s position at the Swiss Patent Office was made permanent, although he was passed over for promotion until he “fully mastered machine technology”.

With friends he met in Berne, Einstein formed a weekly discussion club on science and philosophy, jokingly named “The Olympia Academy”. Their readings included Poincare, Mach, and Hume, who influenced Einstein’s scientific and philosophical outlook.

During this period Einstein had almost no personal contact with the physics community. Much of his work at the patent office related to questions about transmission of electric signals and electrical-mechanical synchronization of time: two technical problems that show up conspicuously in the thought experiments that eventually led Einstein to his radical conclusions about the nature of light and the fundamental connection between space and time.

Marriage and family life

Einstein and Mileva Maric had a daughter, Lieserl Einstein, born in early 1902. Her fate is unknown.

Einstein married Mileva on 6 January 1903, although his mother had objected to the match because she had a prejudice against Serbs and thought Maric “too old” and “physically defective.” Their relationship was for a time a personal and intellectual partnership. In a letter to her, Einstein called Maric “a creature who is my equal and who is as strong and independent as I am.” There has been debate about whether Maric influenced Einstein’s work, however, most historians do not think she made major contributions. On 14 May 1904, Albert and Mileva’s first son, Hans Albert Einstein, was born in Berne, Switzerland. Their second son, Eduard, was born in Munich on 28 July 1910.

Albert and Maric divorced on 14 February 1919, having lived apart for five years. On 2 June of that year, Einstein married Elsa Lowenthal, who had nursed him through an illness. Elsa was Albert’s first cousin maternally and his second cousin paternally. Together the Einsteins raised Margot and Ilse, Elsa’s daughters from her first marriage. Their union produced no children.

Annus Mirabilis and special relativity

Albert Einstein, 1905

In 1905, while he was working in the patent office, Einstein had four papers published in the Annalen der Physik, the leading German physics journal. These are the papers that history has come to call the Annus Mirabilis Papers:

• His paper on the particulate nature of light put forward the idea that certain experimental results, notably the photoelectric effect, could be simply understood from the postulate that light interacts with matter as discrete “packets” (quanta) of energy, an idea that had been introduced by Max Planck in 1900 as a purely mathematical manipulation, and which seemed to contradict contemporary wave theories of light (Einstein 1905a). This was the only work of Einstein’s that he himself called “revolutionary.”
• His paper on Brownian motion explained the random movement of very small objects as direct evidence of molecular action, thus supporting the atomic theory. (Einstein 1905c)
• His paper on the electrodynamics of moving bodies introduced the radical theory of special relativity, which showed that the observed independence of the speed of light on the observer’s state of motion required fundamental changes to the notion of simultaneity. Consequences of this include the time-space frame of a moving body slowing down and contracting (in the direction of motion) relative to the frame of the observer. This paper also argued that the idea of a luminiferous aether-one of the leading theoretical entities in physics at the time-was superfluous. (Einstein 1905d)
• In his paper on mass-energy equivalence (previously considered to be distinct concepts), Einstein deduced from his equations of special relativity what has been called the twentieth century’s most well known equation: E =�mc². This suggests that tiny amounts of mass could be converted into huge amounts of energy and presaged the development of nuclear power. (Einstein 1905e)

All four papers are today recognized as tremendous achievements-and hence 1905 is known as Einstein’s “Wonderful Year”. At the time, however, they were not noticed by most physicists as being important, and many of those who did notice them rejected them outright. Some of this work-such as the theory of light quanta-remained controversial for years.

At the age of 26, having studied under Alfred Kleiner, Professor of Experimental Physics, Einstein was awarded a PhD by the University of Zurich. His dissertation was entitled A New Determination of Molecular Dimensions. (Einstein 1905b)

Light and general relativity

One of the 1919 eclipse photographs taken during Arthur Stanley Eddington’s expedition, which confirmed Einstein’s predictions of the gravitational bending of light.

In 1906, the patent office promoted Einstein to Technical Examiner Second Class, but he had not given up on academia. In 1908, he became a privatdozent at the University of Bern. In 1910, he wrote a paper on critical opalescence that described the cumulative effect of light scattered by individual molecules in the atmosphere, i.e., why the sky is blue.^[31]

During 1909, Einstein published “Uber die Entwicklung unserer Anschauungen uber das Wesen und die Konstitution der Strahlung” (”The Development of Our Views on the Composition and Essence of Radiation“), on the quantization of light. In this and in an earlier 1909 paper, Einstein showed that Max Planck’s energy quanta must have well-defined momenta and act in some respects as independent, point-like particles. This paper introduced the photon concept (although the term itself was introduced by Gilbert N. Lewis in 1926) and inspired the notion of wave-particle duality in quantum mechanics.

In 1911, Einstein became an associate professor at the University of Zurich. However, shortly afterward, he accepted a full professorship at the Charles University of Prague. While in Prague, Einstein published a paper about the effects of gravity on light, specifically the gravitational redshift and the gravitational deflection of light. The paper appealed to astronomers to find ways of detecting the deflection during a solar eclipse. German astronomer Erwin Finlay-Freundlich publicized Einstein’s challenge to scientists around the world.

In 1912, Einstein returned to Switzerland to accept a professorship at his alma mater, the ETH. There he met mathematician Marcel Grossmann who introduced him to Riemannian geometry and more generally differential geometry, and at the recommendation of Italian mathematician Tullio Levi-Civita, Einstein began exploring the usefulness of general covariance (essentially the use of tensors) for his gravitational theory. Although for a while Einstein thought that there were problems with that approach, he later returned to it and by late 1915 had published his general theory of relativity in the form that is still used today (Einstein 1915). This theory explains gravitation as distortion of the structure of spacetime by matter, affecting the inertial motion of other matter.

After many relocations, Mileva established a permanent home with the children in Zurich in 1914, just before the start of World War I. Einstein continued on alone to Berlin, where he became a member of the Prussian Academy of Sciences. As part of the arrangements for his new position, he also became a professor at the Humboldt University of Berlin, although with a special clause freeing him from most teaching obligations. From 1914 to 1932 he was also director of the Kaiser Wilhelm Institute for Physics.

During World War I, the speeches and writings of Central Powers scientists were available only to Central Powers academics, for national security reasons. Some of Einstein’s work did reach the United Kingdom and the United States through the efforts of the Austrian Paul Ehrenfest and physicists in the Netherlands, especially 1902 Nobel Prize-winner Hendrik Lorentz and Willem de Sitter of the Leiden University. After the war ended, Einstein maintained his relationship with the Leiden University, accepting a contract as an Extraordinary Professor; he travelled to Holland regularly to lecture there between 1920 and 1930.

In 1917, Einstein published an article in Physikalische Zeitschrift that proposed the possibility of stimulated emission, the physical process that makes possible the maser and the laser (Einstein 1917b). He also published a paper introducing a new notion, the cosmological constant, into the general theory of relativity in an attempt to model the behavior of the entire universe (Einstein 1917a).

1917 was the year astronomers began taking Einstein up on his 1911 challenge from Prague. The Mount Wilson Observatory in California, U.S., published a solar spectroscopic analysis that showed no gravitational redshift. In 1918, the Lick Observatory, also in California, announced that they too had disproven Einstein’s prediction, although their findings were not published.

However, in May 1919, a team led by British astronomer Arthur Stanley Eddington claimed to have confirmed Einstein’s prediction of gravitational deflection of starlight by the Sun while photographing a solar eclipse in Sobral, northern Brazil, and Pr�ncipe. On 7 November 1919, leading British newspaper The Times printed a banner headline that read: “Revolution in Science�- New Theory of the Universe�- Newtonian Ideas Overthrown”. In an interview Nobel laureate Max Born praised general relativity as the “greatest feat of human thinking about nature”; fellow laureate Paul Dirac was quoted saying it was “probably the greatest scientific discovery ever made”.

From this point on, the international media guaranteed Einstein’s global renown. There have been later claims that scrutiny of the specific photographs taken on the Eddington expedition showed the experimental uncertainty to be of about the same magnitude as the effect Eddington claimed to have demonstrated, and that a 1962 British expedition concluded that the method was inherently unreliable, the deflection of light during a solar eclipse has been confirmed by later, more accurate observations.

There was some resentment toward the newcomer Einstein’s fame in the scientific community, notably among German physicists, who later started the Deutsche Physik (German Physics) movement.

Nobel Prize

Einstein, 1921. Age 42.

In 1922 Einstein was awarded the 1921 Nobel Prize in Physics, “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect”. This refers to his 1905 paper on the photoelectric effect: “On a Heuristic Viewpoint Concerning the Production and Transformation of Light”, which was well supported by the experimental evidence by that time. The presentation speech began by mentioning “his theory of relativity [which had] been the subject of lively debate in philosophical circles [and] also has astrophysical implications which are being rigorously examined at the present time.” (Einstein 1923)

It was long reported that Einstein gave the Nobel prize money to his first wife, Mileva Maric, in compliance with their 1919 divorce settlement. However, personal correspondence made public in 2006 shows that this did not happen. He invested the bulk of it in the United States, and saw much of it wiped out in the Depression.

Einstein traveled to New York City in the United States for the first time on 2 April 1921. When asked where he got his scientific ideas, Einstein explained that he believed scientific work best proceeds from an examination of physical reality and a search for underlying axioms, with consistent explanations that apply in all instances and avoid contradicting each other. He also recommended theories with visualizable results (Einstein 1954).

Unified field theory

Einstein’s research after general relativity consisted primarily of a long series of attempts to generalize his theory of gravitation in order to unify and simplify the fundamental laws of physics, particularly gravitation and electromagnetism. In 1950, he described this “unified field theory” in a Scientific American article entitled “On the Generalized Theory of Gravitation” (Einstein 1950). Although he continued to be lauded for his work in theoretical physics, Einstein became increasingly isolated in his research, and his efforts were ultimately unsuccessful. In his pursuit of a unification of the fundamental forces, he ignored some mainstream developments in physics, most notably the strong and weak nuclear forces, which were not well understood until many years after his death. Einstein’s dream of unifying the laws of physics under a single model survives in the current drive for the grand unification theory.

Collaboration and conflict

Bose-Einstein statistics

In 1924, Einstein received a description of a statistical model from Indian physicist Satyendra Nath Bose, based on a counting method that assumed that light could be understood as a gas of indistinguishable particles. Bose’s statistics applied to some atoms as well as to the proposed light particles, and Einstein submitted his translation of Bose’s paper to the Zeitschrift fur Physik. Einstein also published his own articles describing the model and its implications, among them the Bose-Einstein condensate phenomenon that should appear at very low temperatures (Einstein 1924). It was not until 1995 that the first such condensate was produced experimentally by Eric Allin Cornell and Carl Wieman using ultra-cooling equipment built at the NIST-JILA laboratory at the University of Colorado at Boulder. Bose-Einstein statistics are now used to describe the behaviors of any assembly of “bosons”. Einstein’s sketches for this project may be seen in the Einstein Archive in the library of the Leiden University.

Schrodinger gas model

Einstein suggested to Erwin Schrodinger an application of Max Planck’s idea of treating energy levels for a gas as a whole rather than for individual molecules, and Schrodinger applied this in a paper using the Boltzmann distribution to derive the thermodynamic properties of a semiclassical ideal gas. Schrodinger urged Einstein to add his name as co-author, although Einstein declined the invitation.

Einstein refrigerator

In 1926, Einstein and his former student Leo Szilard, a Hungarian physicist who later worked on the Manhattan Project and is credited with the discovery of the chain reaction, co-invented (and in 1930, patented) the Einstein refrigerator, revolutionary for having no moving parts and using only heat, not ice, as an input.

Bohr versus Einstein

Einstein and Niels Bohr. Photo taken by Paul Ehrenfest during their 1925 Leiden visit.

In the 1920s, quantum mechanics developed into a more complete theory. Einstein was unhappy with the “Copenhagen interpretation” of quantum theory developed by Niels Bohr and Werner Heisenberg, wherein quantum phenomena are inherently probabilistic, with definite states resulting only upon interaction with classical systems. A public debate between Einstein and Bohr followed, lasting for many years (including during the Solvay Conferences). Einstein formulated thought experiments against the Copenhagen interpretation, which were all rebutted by Bohr. In a 1926 letter to Max Born, Einstein wrote: “I, at any rate, am convinced that He [God] does not throw dice.” (Einstein 1969).

Einstein was never satisfied by what he perceived to be quantum theory’s intrinsically incomplete description of nature, and in 1935 he further explored the issue in collaboration with Boris Podolsky and Nathan Rosen, noting that the theory seems to require non-local interactions; this is known as the EPR paradox (Einstein 1935). The EPR experiment has since been performed, with results confirming quantum theory’s predictions.

Einstein’s disagreement with Bohr revolved around the idea of scientific determinism. For this reason the repercussions of the Einstein-Bohr debate have found their way into philosophical discourse as well.

Religious views

The question of scientific determinism gave rise to questions about Einstein’s position on theological determinism, and whether or not he believed in a God. In 1929, Einstein told Rabbi Herbert S. Goldstein “I believe in Spinoza’s God, who reveals Himself in the lawful harmony of the world, not in a God Who concerns Himself with the fate and the doings of mankind.” In a 1950 letter to M. Berkowitz, Einstein stated that “My position concerning God is that of an agnostic. I am convinced that a vivid consciousness of the primary importance of moral principles for the betterment and ennoblement of life does not need the idea of a law-giver, especially a law-giver who works on the basis of reward and punishment.” Einstein also stated: “I have repeatedly said that in my opinion the idea of a personal God is a childlike one. You may call me an agnostic, but I do not share the crusading spirit of the professional atheist whose fervor is mostly due to a painful act of liberation from the fetters of religious indoctrination received in youth.” He is reported to have said in a conversation with Hubertus, Prince of Lowenstein-Wertheim-Freudenberg, “In view of such harmony in the cosmos which I, with my limited human mind, am able to recognize, there are yet people who say there is no God. But what really makes me angry is that they quote me for the support of such views.”Einstein clarified his religious views in a letter he wrote in response to those who claimed that he worshipped a Judeo-Christian god: “It was, of course, a lie what you read about my religious convictions, a lie which is being systematically repeated. I do not believe in a personal god and I have never denied this but have expressed it clearly. If something is in me which can be called religious then it is the unbounded admiration for the structure of the world so far as our science can reveal it.” In his book The World as I See It, he wrote: “A knowledge of the existence of something we cannot penetrate, of the manifestations of the profoundest reason and the most radiant beauty, which are only accessible to our reason in their most elementary forms-it is this knowledge and this emotion that constitute the truly religious attitude; in this sense, and in this alone, I am a deeply religious man.”

In a 1930 New York Times article, Einstein distinguished three styles which are usually intermixed in actual religion. The first is motivated by fear and poor understanding of causality, and hence invents supernatural beings. The second is social and moral, motivated by desire for love and support. Einstein noted that both have an anthropomorphic concept of God. The third style, which Einstein deemed most mature, is motivated by a deep sense of awe and mystery. He said, “The individual feels the sublimity and marvelous order which reveal themselves in nature and he wants to experience the universe as a single significant whole.” Einstein saw science as an antagonist of the first two styles of religion, but as a partner of the third style.

Einstein was also a Humanist and a supporter of Ethical Culture. He served on the advisory board of the First Humanist Society of New York. For the seventy-fifth anniversary of the New York Society for Ethical Culture, he noted that the idea of Ethical Culture embodied his personal conception of what is most valuable and enduring in religious idealism. He observed, “Without ‘ethical culture’ there is no salvation for humanity.”

Einstein published a paper in Nature in 1940 entitled “Science and Religion” in which he said that: “a person who is religiously enlightened appears to me to be one who has, to the best of his ability, liberated himself from the fetters of his selfish desires and is preoccupied with thoughts, feelings and aspirations to which he clings because of their super-personal value regardless of whether any attempt is made to unite this content with a Divine Being, for otherwise it would not be possible to count Buddha and Spinoza as religious personalities. Accordingly a religious person is devout in the sense that he has no doubt of the significance of those super-personal objects and goals which neither require nor are capable of rational foundation In this sense religion is the age-old endeavour of mankind to become clearly and completely conscious of these values and goals, and constantly to strengthen their effects.” He argued that conflicts between science and religion “have all sprung from fatal errors.” “Even though the realms of religion and science in themselves are clearly marked off from each other” there are “strong reciprocal relationships and dependencies science without religion is lame, religion without science is blind a legitimate conflict between science and religion cannot exist.” In Einstein’s view, “neither the rule of human nor Divine Will exists as an independent cause of natural events. To be sure, the doctrine of a personal God interfering with natural events could never be refuted by science, for it can always take refuge in those domains in which scientific knowledge has not yet been able to set foot.” (Einstein 1940, pp.�605-607)

In a letter to Eric Gutkind in 1954 Einstein said: “The word God is for me nothing more than the expression and product of human weaknesses, the Bible a collection of honorable, but still primitive legends which are nevertheless pretty childish.” In the same letter, Einstein rejected the idea that the Jews are God’s chosen people: “For me the Jewish religion like all others is an incarnation of the most childish superstitions. And the Jewish people to whom I gladly belong and with whose mentality I have a deep affinity have no different quality for me than all other people. As far as my experience goes, they are no better than other human groups, although they are protected from the worst cancers by a lack of power. Otherwise I cannot see anything ‘chosen’ about them.”

His friend Max Jammer explored Einstein’s views on religion thoroughly in the 1999 book Einstein and Religion: Physics and Theology.

Politics

Einstein and Indian poet and Nobel laureate Rabindranath Tagore during their widely publicized 14 July 1930 conversation

With increasing public demands, his involvement in political, humanitarian, and academic projects in various countries, and his new acquaintances with scholars and political figures from around the world, Einstein was less able to achieve the productive isolation that he needed in order to work. Due to his fame and genius, Einstein found himself called on to give conclusive judgments on matters that had nothing to do with theoretical physics or mathematics. He was not timid, and he was aware of the world around him, with no illusion that ignoring politics would make world events fade away. His very visible position allowed him to speak and write frankly, even provocatively, at a time when many people of conscience could only flee to the underground or keep doubts about developments within their own movements to themselves for fear of internecine fighting. Einstein flouted the ascendant Nazi movement, tried to be a voice of moderation in the tumultuous formation of the State of Israel and braved anti-communist politics and resistance to the civil rights movement in the United States. He participated in the 1927 congress of the League against Imperialism in Brussels.

Zionism

Einstein was a socialist Zionist who opposed nationalism. In 1931, The Macmillan Company published About Zionism: Speeches and Lectures by Professor Albert Einstein. Querido, an Amsterdam publishing house, collected eleven of Einstein’s essays into a 1933 book entitled Mein Weltbild, translated to English as The World as I See It; Einstein’s foreword dedicates the collection “to the Jews of Germany”.

Albert Einstein, seen here with his wife Elsa Einstein and Zionist leaders, including future President of Israel Chaim Weizmann, his wife Dr. Vera Weizmann, Menahem Ussishkin, and Ben-Zion Mossinson on arrival in New York City in 1921.

Einstein publicly stated reservations about the proposal to partition the British-supervised British Mandate of Palestine into independent Arab and Jewish countries. In a 1938 speech, “Our Debt to Zionism”, he said: “I am afraid of the inner damage Judaism will sustain-especially from the development of a narrow nationalism within our own ranks, against which we have already had to fight strongly, even without a Jewish state. If external necessity should after all compel us to assume this burden, let us bear it with tact and patience.” In a 1947 letter to Indian Prime Minister Jawaharlal Nehru, Einstein stated that the Balfour Declaration’s proposal to establish a national home for Jews in Palestine “redresses the balance” of justice and history.

The United Nations did divide the mandate, demarcating the borders of several new countries including the State of Israel, and war broke out immediately. Einstein was one of the authors of a 1948 letter to the New York Times criticizing Menachem Begin’s Herut (Freedom) Party for the Deir Yassin massacre (Einstein et al. 1948).

Einstein served on the Board of Governors of The Hebrew University of Jerusalem. In his Will of 1950, Einstein bequeathed literary rights to his writings to The Hebrew University, where many of his original documents are held in the Albert Einstein Archives.

When President Chaim Weizmann died in 1952, Einstein was asked to be Israel’s second president, but he declined, stating that he had “neither the natural ability nor the experience to deal with human beings.” He wrote: “I am deeply moved by the offer from our State of Israel, and at once saddened and ashamed that I cannot accept it. ”

Anti-Nazism

In January 1933, Adolf Hitler was appointed Chancellor of Germany. One of the first actions of Hitler’s administration was the Law for the Restoration of the Professional Civil Service, which removed Jews and politically suspect government employees (including university professors) from their jobs, unless they had demonstrated their loyalty to Germany by serving in World War I. In response to this growing threat Einstein had prudently traveled to the U.S. in December 1932. For several years he had been wintering at the California Institute of Technology in Pasadena, California, and also was a guest lecturer at Abraham Flexner’s newly founded Institute for Advanced Study in Princeton, New Jersey.

The Einsteins bought a house in Princeton (where Elsa died in 1936), and Einstein remained an integral contributor to the Institute for Advanced Study until his death in 1955. During the 1930s and into World War II, Einstein wrote affidavits recommending United States visas for a huge number of European Jews who were trying to flee persecution. He raised money for Zionist organizations and was, in part, responsible for the formation, in 1933, of the International Rescue Committee.

Meanwhile, in Germany, a campaign to eliminate Einstein’s work from the German lexicon as unacceptable “Jewish physics” (Judische Physik) was led by Nobel laureates Philipp Lenard and Johannes Stark. Deutsche Physik activists published pamphlets and even textbooks denigrating Einstein, and instructors who taught his theories were blacklisted-including Nobel laureate Werner Heisenberg, who had debated quantum probability with Bohr and Einstein. Philipp Lenard claimed that the mass-energy equivalence formula needed to be credited to Friedrich Hasenohrl to make it an Aryan creation. An anti-Einstein organization was formed, and a man who was convicted of composing a plot to kill Einstein was fined a mere six dollars.

Einstein became a citizen of the United States in 1940 and remained there the rest of his life, although he retained his Swiss citizenship.

Atomic bomb

Concerned scientists, many of them refugees from European anti-Semitism in the U.S., recognized the danger of German scientists developing an atomic bomb based on the newly discovered phenomena of nuclear fission. In 1939, the Hungarian emigre Leo Szilard, having failed to arouse U.S. government interest on his own, worked with Einstein to write a letter to U.S. President Franklin Delano Roosevelt, which Einstein signed, urging U.S. development of such a weapon. In August 1939, Roosevelt received the Einstein-Szilard letter and authorized secret research into the harnessing of nuclear fission for military purposes.

By 1942 this effort had become the Manhattan Project, the largest secret scientific endeavor undertaken up to that time. By late 1945, the U.S. had developed operational nuclear weapons, and used them on the Japanese cities of Hiroshima and Nagasaki. Einstein himself did not play a role in the development of the atomic bomb other than signing the letter. He did help the United States Navy with some unrelated theoretical questions it was working on during the war.

According to Linus Pauling, Einstein later expressed regret about his letter to Roosevelt. In 1947, Einstein wrote an article for The Atlantic Monthly arguing that the United States should not try to pursue an atomic monopoly, and instead should equip the United Nations with nuclear weapons for the sole purpose of maintaining deterrence.

Cold War era

When he was a visible figure working against the rise of Nazism, Einstein had sought help and developed working relationships in both the West and what was to become the Soviet bloc. After World War II, enmity between the former allies became a very serious issue for people with international resumes. To make things worse, during the first days of McCarthyism Einstein was writing about a single world government; it was at this time that he wrote, “I do not know how the third World War will be fought, but I can tell you what they will use in the Fourth-rocks!” In a 1949 Monthly Review article entitled “Why Socialism?” Albert Einstein described a chaotic capitalist society, a source of evil to be overcome, as the “predatory phase of human development” (Einstein 1949). With Albert Schweitzer and Bertrand Russell, Einstein lobbied to stop nuclear testing and future bombs. Days before his death, Einstein signed the Russell-Einstein Manifesto, which led to the Pugwash Conferences on Science and World Affairs.

Einstein was a member of several civil rights groups, including the Princeton chapter of the NAACP. When the aged W. E. B. Du Bois was accused of being a Communist spy, Einstein volunteered as a character witness, and the case was dismissed shortly afterward. Einstein’s friendship with activist Paul Robeson, with whom he served as co-chair of the American Crusade to End Lynching, lasted twenty years.

In 1946, Einstein collaborated with Rabbi Israel Goldstein, Middlesex University heir C. Ruggles Smith, and activist attorney George Alpert on the Albert Einstein Foundation for Higher Learning, which was formed to create a Jewish-sponsored secular university, open to all students, on the grounds of the former Middlesex University in Waltham, Massachusetts. Middlesex was chosen in part because it was accessible from both Boston and New York City, Jewish cultural centers of the U.S. Their vision was a university “deeply conscious both of the Hebraic tradition of Torah looking upon culture as a birthright, and of the American ideal of an educated democracy.” The collaboration was stormy, however. Finally, when Einstein wanted to appoint British economist Harold Laski as the university’s president, George Alpert wrote that Laski was “a man utterly alien to American principles of democracy, tarred with the Communist brush.” Einstein withdrew his support and barred the use of his name. The university opened in 1948 as Brandeis University. In 1953, Brandeis offered Einstein an honorary degree, but he declined.

Given Einstein’s links to Germany and Zionism, his socialist ideals, and his links to Communist figures, the U.S. Federal Bureau of Investigation kept a file on Einstein that grew to 1,427 pages. Many of the documents in the file were sent to the FBI by concerned citizens: some objecting to his immigration, while others asked the FBI to protect him.

Although Einstein had long been sympathetic to the notion of vegetarianism, it was only near the start of 1954 that he adopted a strict vegetarian diet.

Death

On 17 April 1955, Albert Einstein experienced internal bleeding caused by the rupture of an aortic aneurysm, which had previously been diagnosed and reinforced. He took a draft of a speech he was preparing for a television appearance commemorating the State of Israel’s seventh anniversary with him to the hospital, but he did not live long enough to complete it. He died in Princeton Hospital early the next morning at the age of 76, having continued to work until near the end. Einstein’s remains were cremated and his ashes were scattered.

Before the cremation, Princeton Hospital pathologist Thomas Stoltz Harvey removed Einstein’s brain for preservation, without the permission of his family, in hope that the neuroscience of the future would be able to discover what made Einstein so intelligent.

Legacy

While travelling, Einstein had written daily to his wife Elsa and adopted stepdaughters, Margot and Ilse, and the letters were included in the papers bequeathed to The Hebrew University. Margot Einstein permitted the personal letters to be made available to the public, but requested that it not be done until twenty years after her death (she died in 1986). Barbara Wolff, of The Hebrew University’s Albert Einstein Archives, told the BBC that there are about 3,500 pages of private correspondence written between 1912 and 1955.

The United States’ National Academy of Sciences commissioned the Albert Einstein Memorial, a monumental bronze and marble sculpture by Robert Berks, dedicated in 1979 at its Washington, D.C. campus adjacent to the National Mall.

Einstein bequeathed the royalties from use of his image to The Hebrew University of Jerusalem. Corbis, successor to The Roger Richman Agency, licenses the use of his name and associated imagery, as agent for the Hebrew University.

Honors

In 1999, Albert Einstein was named “Person of the Century” by Time magazine, a Gallup poll recorded him as the fourth most admired person of the 20th century and according to The 100: A Ranking of the Most Influential Persons in History, Einstein is “the greatest scientist of the twentieth century and one of the supreme intellects of all time.”

A partial list of his memorials:

• The International Union of Pure and Applied Physics named 2005 the “World Year of Physics” in commemoration of the 100th anniversary of the publication of the Annus Mirabilis Papers.^[113]
• The Albert Einstein Institute
• The Albert Einstein Memorial by Robert Berks
• A unit used in photochemistry, the einstein
• The chemical element 99, einsteinium
• The asteroid 2001 Einstein
• The Albert Einstein Award
• The Albert Einstein Peace Prize

In 1990, his name was added to the Walhalla temple.

Impact on popular culture

In the period before World War II, Albert Einstein was so well-known in America that he would be stopped on the street by people wanting him to explain “that theory”. He finally figured out a way to handle the incessant inquiries. He told his inquirers “Pardon me, sorry! Always I am mistaken for Professor Einstein.”

Albert Einstein has been the subject of or inspiration for many novels, films, and plays. Einstein is a favorite model for depictions of mad scientists and absent-minded professors; his expressive face and distinctive hairstyle have been widely copied and exaggerated. Time magazine’s Frederic Golden wrote that Einstein was “a cartoonist’s dream come true.”

Einstein’s association with great intelligence has made the name Einstein synonymous with genius, often used in ironic expressions such as “Nice job, Einstein!”.

Galileo Galilei (15 February 1564 – 8 January 1642) was a Tuscan (Italian) physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations, and support for Copernicanism. Galileo has been called the “father of modern observational astronomy”, the “father of modern physics“, the “father of science“, and “the Father of Modern Science.” The motion of uniformly accelerated objects, taught in nearly all high school and introductory college physics courses, was studied by Galileo as the subject of kinematics. His contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the discovery of the four largest satellites of Jupiter, named the Galilean moons in his honour, and the observation and analysis of sunspots. Galileo also worked in applied science and technology, improving compass design.

Galileo’s championing of Copernicanism was controversial within his lifetime. The geocentric view had been dominant since the time of Aristotle, and the controversy engendered by Galileo’s presentation of heliocentrism as proven fact resulted in the Catholic Church’s prohibiting its advocacy as empirically proven fact, because it was not empirically proven at the time and was contrary to the literal meaning of Scripture. Galileo was eventually forced to recant his heliocentrism and spent the last years of his life under house arrest on orders of the Roman Inquisition.

Life

Galileo was born in Pisa (then part of the Grand Duchy of Tuscany), the first of six children of Vincenzo Galilei, a famous lutenist and music theorist, and Giulia Ammannati. Of the six children four survived infancy, and the youngest Michelangelo (or Michelagnolo) became a noted lutenist and composer. Galileo’s full name was Galileo Bonaiuti de’ Galilei. At the age of 8, his family moved to Florence, but he was left with Jacopo Borghini for two years. He then was educated in the Camaldolese Monastery at Vallombrosa, 21�mi (34�km) southeast of Florence. Although he seriously considered the priesthood as a young man, he enrolled for a medical degree at the University of Pisa at his father’s urging. He did not complete this degree, but instead studied mathematics. In 1589, he was appointed to the chair of mathematics in Pisa. In 1591 his father died and he was entrusted with the care of his younger brother Michelagnolo. In 1592, he moved to the University of Padua, teaching geometry, mechanics, and astronomy until 1610. During this period Galileo made significant discoveries in both pure science (for example, kinematics of motion, and astronomy) and applied science (for example, strength of materials, improvement of the telescope). His multiple interests included the study of astrology, which in pre-modern disciplinary practice was seen as correlated to the studies of mathematics and astronomy.

Although a devout Roman Catholic, Galileo fathered three children out of wedlock with Marina Gamba. They had two daughters, Virginia in 1600 and Livia in 1601, and one son, Vincenzio, in 1606. Because of their illegitimate birth, their father considered the girls unmarriageable. Their only worthy alternative was the religious life. Both girls were sent to the convent of San Matteo in Arcetri and remained there for the rest of their lives. Virginia took the name Maria Celeste upon entering the convent. She died on 2 April 1634, and is buried with Galileo at the Basilica di Santa Croce di Firenze. Livia took the name Sister Arcangela and was ill for most of her life. Vincenzio was later legitimized and married Sestilia Bocchineri.

In 1610 Galileo published an account of his telescopic observations of the moons of Jupiter, using this observation to argue in favor of the sun-centered, Copernican theory of the universe against the dominant earth-centered Ptolemaic and Aristotelian theories. The next year Galileo visited Rome in order to demonstrate his telescope to the influential philosophers and mathematicians of the Jesuit Collegio Romano, and to let them see with their own eyes the reality of the four moons of Jupiter. While in Rome he was also made a member of the Accademia dei Lincei.

In 1612, opposition arose to the Sun-centered theory of the universe which Galileo supported. In 1614, from the pulpit of Santa Maria Novella, Father Tommaso Caccini (1574-1648) denounced Galileo’s opinions on the motion of the Earth, judging them dangerous and close to heresy. Galileo went to Rome to defend himself against these accusations, but, in 1616, Cardinal Roberto Bellarmino personally handed Galileo an admonition enjoining him neither to advocate nor teach Copernican astronomy. During 1621 and 1622 Galileo wrote his first book, The Assayer (Il Saggiatore), which was approved and published in 1623. In 1630, he returned to Rome to apply for a license to print the Dialogue Concerning the Two Chief World Systems, published in Florence in 1632. In October of that year, however, he was ordered to appear before the Holy Office in Rome.

Following a papal trial in which he was found vehemently suspect of heresy, Galileo was placed under house arrest and his movements restricted by the Pope. From 1634 onward he stayed at his country house at Arcetri, outside of Florence. He went completely blind in 1638 and was suffering from a painful hernia and insomnia, so he was permitted to travel to Florence for medical advice. He continued to receive visitors until 1642, when, after suffering fever and heart palpitations, he died^.

Scientific methods

Galileo made original contributions to the science of motion through an innovative combination of experiment and mathematics^. More typical of science at the time were the qualitative studies of William Gilbert, on magnetism and electricity. Galileo’s father, Vincenzo Galilei, a lutenist and music theorist, had performed experiments establishing perhaps the oldest known non-linear relation in physics: for a stretched string, the pitch varies as the square root of the tension. These observations lay within the framework of the Pythagorean tradition of music, well-known to instrument makers, which included the fact that subdividing a string by a whole number produces a harmonious scale. Thus, a limited amount of mathematics had long related music and physical science, and young Galileo could see his own father’s observations expand on that tradition.

Galileo is perhaps the first to clearly state that the laws of nature are mathematical. In The Assayer he wrote “Philosophy is written in this grand book, the universe�… It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures; …”^. His mathematical analyses are a further development of a tradition employed by late scholastic natural philosophers, which Galileo learned when he studied philosophy. Although he tried to remain loyal to the Catholic Church, his adherence to experimental results, and their most honest interpretation, led to a rejection of blind allegiance to authority, both philosophical and religious, in matters of science. In broader terms, this aided to separate science from both philosophy and religion; a major development in human thought.

By the standards of his time, Galileo was often willing to change his views in accordance with observation. Philosopher of science Paul Feyerabend also noted the supposedly improper aspects of Galileo’s methodology, but he argued that Galileo’s methods could be justified retroactively by their results. The bulk of Feyerabend’s major work, Against Method (1975), was devoted to an analysis of Galileo, using his astronomical research as a case study to support Feyerabend’s own anarchistic theory of scientific method. As he put it: ‘Aristotelians demanded strong empirical support while the Galileans were content with far-reaching, unsupported and partially refuted theories. I do not criticize them for that; on the contrary, I favour Niels Bohr’s “this is not crazy enough.”‘ In order to perform his experiments, Galileo had to set up standards of length and time, so that measurements made on different days and in different laboratories could be compared in a reproducible fashion.

Galileo showed a remarkably modern appreciation for the proper relationship between mathematics, theoretical physics, and experimental physics. He understood the parabola, both in terms of conic sections and in terms of the ordinate (y) varying as the square of the abscissa (x). Galilei further asserted that the parabola was the theoretically ideal trajectory of a uniformly accelerated projectile in the absence of friction and other disturbances. He conceded that there are limits to the validity of this theory, noting on theoretical grounds that a projectile trajectory of a size comparable to that of the Earth could not possibly be a parabola,^[24] but he nevertheless maintained that for distances up to the range of the artillery of his day, the deviation of a projectile’s trajectory from a parabola would only be very slight^. Thirdly, he recognized that his experimental data would never agree exactly with any theoretical or mathematical form, because of the imprecision of measurement, irreducible friction, and other factors.

According to Stephen Hawking, Galileo probably bears more of the responsibility for the birth of modern science than anybody else, and Albert Einstein called him the father of modern science.

Astronomy

Contributions

The phases of Venus, observed by Galileo in 1610

Based only on uncertain descriptions of the telescope, invented in the Netherlands in 1608, Galileo, in the following year, made a telescope with about 3x magnification, and later made others with up to about 30x magnification. With this improved device he could see magnified, upright images on the earth�- it was what is now known as a terrestrial telescope, or spyglass. He could also use it to observe the sky; for a time he was one of those who could construct telescopes good enough for that purpose. On 25 August 1609, he demonstrated his first telescope to Venetian lawmakers. His work on the device made for a profitable sideline with merchants who found it useful for their shipping businesses and trading issues. He published his initial telescopic astronomical observations in March 1610 in a short treatise entitled Sidereus Nuncius (Starry Messenger).

On 7 January 1610 Galileo observed with his telescope what he described at the time as “three fixed stars, totally invisible by their smallness”, all within a short distance of Jupiter, and lying on a straight line through it. Observations on subsequent nights showed that the positions of these “stars” relative to Jupiter were changing in a way that would have been inexplicable if they had really been fixed stars. On 10 January Galileo noted that one of them had disappeared, an observation which he attributed to its being hidden behind Jupiter. Within a few days he concluded that they were orbiting Jupiter: He had discovered three of Jupiter’s four largest satellites (moons): Io, Europa, and Callisto. He discovered the fourth, Ganymede, on 13 January. Galileo named the four satellites he had discovered Medicean stars, in honour of his future patron, Cosimo II de’ Medici, Grand Duke of Tuscany, and Cosimo’s three brothers. Later astronomers, however, renamed them Galilean satellites in honour of Galileo himself.

A planet with smaller planets orbiting it did not conform to the principles of Aristotelian Cosmology, which held that all heavenly bodies should circle the Earth, and many astronomers and philosophers initially refused to believe that Galileo could have discovered such a thing.

Galileo continued to observe the satellites over the next eighteen months, and by mid 1611 he had obtained remarkably accurate estimates for their periods-a feat which Kepler had believed impossible.

From September 1610, Galileo observed that Venus exhibited a full set of phases similar to that of the Moon. The heliocentric model of the solar system developed by Nicolaus Copernicus predicted that all phases would be visible since the orbit of Venus around the Sun would cause its illuminated hemisphere to face the Earth when it was on the opposite side of the Sun and to face away from the Earth when it was on the Earth-side of the Sun. In contrast, the geocentric model of Ptolemy predicted that only crescent and new phases would be seen, since Venus was thought to remain between the Sun and Earth during its orbit around the Earth. Galileo’s observations of the phases of Venus proved that it orbited the Sun and lent support to (but did not prove) the heliocentric model. However, since it refuted the Ptolemaic pure geocentric planetary model, it seems it was the crucial observation that caused the 17th century majority conversion of the scientific community to geoheliocentric geocentric models such as the Tychonic and Capellan models, and was thereby arguably Galileo’s historically most important astronomical observation.

Galileo also observed the planet Saturn, and at first mistook its rings for planets, thinking it was a three-bodied system. When he observed the planet later, Saturn’s rings were directly oriented at Earth, causing him to think that two of the bodies had disappeared. The rings reappeared when he observed the planet in 1616, further confusing him.

Galileo was one of the first Europeans to observe sunspots, although Kepler had unwittingly observed one in 1607, but mistook it for a transit of Mercury.. He also reinterpreted a sunspot observation from the time of Charlemagne, which formerly had been attributed (impossibly) to a transit of Mercury. The very existence of sunspots showed another difficulty with the unchanging perfection of the heavens posited by orthodox Aristotelian celestial physics, but their regular periodic transits also confirmed the dramatic novel prediction of Kepler’s Aristotelian celestial dynamics in his 1609 Astronomia Nova that the sun rotates, which was the first successful novel prediction of post-spherist celestial physics. And the annual variations in sunspots’ motions, discovered by Francesco Sizzi and others in 1612-1613, provided a powerful argument against both the Ptolemaic system and the geoheliocentric system of Tycho Brahe. For the seasonal variation refuted all non-geo-rotational geostatic planetary models such as the Ptolemaic pure geocentric model and the Tychonic geoheliocentric model in which the Sun orbits the Earth daily, whereby the variation should appear daily but does not. But it was explicable by all geo-rotational systems such as Longomontanus’s semi-Tychonic geo-heliocentric model, Capellan and extended Capellan geo-heliocentric models with a daily rotating Earth, and the pure heliocentric model. A dispute over priority in the discovery of sunspots, and in their interpretation, led Galileo to a long and bitter feud with the Jesuit Christoph Scheiner; in fact, there is little doubt that both of them were beaten by David Fabricius and his son Johannes, looking for confirmation of Kepler’s prediction of the sun’s rotation. Scheiner quickly adopted Kepler’s 1615 proposal of the modern telescope design, which gave larger magnification at the cost of inverted images; Galileo apparently never changed to Kepler’s design.

Galileo was the first to report lunar mountains and craters, whose existence he deduced from the patterns of light and shadow on the Moon’s surface. He even estimated the mountains’ heights from these observations. This led him to the conclusion that the Moon was “rough and uneven, and just like the surface of the Earth itself,” rather than a perfect sphere as Aristotle had claimed. Galileo observed the Milky Way, previously believed to be nebulous, and found it to be a multitude of stars packed so densely that they appeared to be clouds from Earth. He located many other stars too distant to be visible with the naked eye. Galileo also observed the planet Neptune in 1612, but did not realize that it was a planet and took no particular notice of it. It appears in his notebooks as one of many unremarkable dim stars.

Controversy over comets and The Assayer

In 1619, Galileo became embroiled in a controversy with Father Orazio Grassi, professor of mathematics at the Jesuit Collegio Romano. It began as a dispute over the nature of comets, but by the time Galileo had published The Assayer (Il Saggiatore) in 1623, his last salvo in the dispute, it had become a much wider argument over the very nature of Science itself. Because The Assayer contains such a wealth of Galileo’s ideas on how Science should be practised, it has been referred to as his scientific manifesto.

Early in 1619, Father Grassi had anonymously published a pamphlet, An Astronomical Disputation on the Three Comets of the Year 1618,^[41] which discussed the nature of a comet that had appeared late in November of the previous year. Grassi concluded that the comet was a fiery body which had moved along a segment of a great circle at a constant distance from the earth, and that it had been located well beyond the moon.

Grassi’s arguments and conclusions were criticized in a subsequent article, Discourse on the Comets,^[43] published under the name of one of Galileo’s disciples, a Florentine lawyer named Mario Guiducci, although it had been largely written by Galileo himself. Galileo and Guiducci offered no definitive theory of their own on the nature of comets, although they did present some tentative conjectures which we now know to be mistaken.

In its opening passage, Galileo and Guiducci’s Discourse gratuitously insulted the Jesuit Christopher Scheiner, and various uncomplimentary remarks about the professors of the Collegio Romano were scattered throughout the work. The Jesuits were offended, and Grassi soon replied with a polemical tract of his own, The Astronomical and Philosophical Balance,^[49] under the pseudonym Lothario Sarsio Sigensano, purporting to be one of his own pupils.

The Assayer was Galileo’s devastating reply to the Astronomical Balance. It has been widely regarded as a masterpiece of polemical literature, in which “Sarsi’s” arguments are subjected to withering scorn. It was greeted with wide acclaim, and particularly pleased the new pope, Urban VIII, to whom it had been dedicated.

Galileo’s dispute with Grassi permanently alienated many of the Jesuits who had previously been sympathetic to his ideas, and Galileo and his friends were convinced that these Jesuits were responsible for bringing about his later condemnation. The evidence for this is at best equivocal, however.

Galileo, Kepler and theories of tides

Cardinal Bellarmine had written in 1615 that the Copernican system could not be defended without “a true physical demonstration that the sun does not circle the earth but the earth circles the sun”. Galileo considered his theory of the tides to provide the required physical proof of the motion of the earth. This theory was so important to Galileo that he originally intended to entitle his Dialogue on the Two Chief World Systems the Dialogue on the Ebb and Flow of the Sea. For Galileo, the tides were caused by the sloshing back and forth of water in the seas as a point on the Earth’s surface speeded up and slowed down because of the Earth’s rotation on its axis and revolution around the Sun. Galileo circulated his first account of the tides in 1616, addressed to Cardinal Orsini.

If this theory were correct, there would be only one high tide per day. Galileo and his contemporaries were aware of this inadequacy because there are two daily high tides at Venice instead of one, about twelve hours apart. Galileo dismissed this anomaly as the result of several secondary causes, including the shape of the sea, its depth, and other factors. Against the assertion that Galileo was deceptive in making these arguments, Albert Einstein expressed the opinion that Galileo developed his “fascinating arguments” and accepted them uncritically out of a desire for physical proof of the motion of the Earth.

Galileo dismissed as a “useless fiction” the idea, held by his contemporary Johannes Kepler, that the moon caused the tides. Galileo also refused to accept Kepler’s elliptical orbits of the planets, considering the circle the “perfect” shape for planetary orbits.

Technology

A replica of the earliest surviving telescope attributed to Galileo Galilei, on display at the Griffith Observatory

Galileo made a number of contributions to what is now known as technology, as distinct from pure physics, and suggested others. This is not the same distinction as made by Aristotle, who would have considered all Galileo’s physics as techne or useful knowledge, as opposed to episteme, or philosophical investigation into the causes of things. Between 1595-1598, Galileo devised and improved a Geometric and Military Compass suitable for use by gunners and surveyors. This expanded on earlier instruments designed by Niccol� Tartaglia and Guidobaldo del Monte. For gunners, it offered, in addition to a new and safer way of elevating cannons accurately, a way of quickly computing the charge of gunpowder for cannonballs of different sizes and materials. As a geometric instrument, it enabled the construction of any regular polygon, computation of the area of any polygon or circular sector, and a variety of other calculations. About 1593, Galileo constructed a thermometer, using the expansion and contraction of air in a bulb to move water in an attached tube.

In 1609, Galileo was among the first to use a refracting telescope as an instrument to observe stars, planets or moons. The name “telescope” was coined for Galileo’s instrument by a Greek mathematician, Giovanni Demisiani, at a banquet held in 1611 by Prince Federico Cesi to make Galileo a member of his Accademia dei Lincei. The name was derived from the Greek tele = ‘far’ and skopein = ‘to look or see’. In 1610, he used a telescope at close range to magnify the parts of insects. By 1624 he had perfected a compound microscope. He gave one of these instruments to Cardinal Zollern in May of that year for presentation to the Duke of Bavaria, and in September he sent another to Prince Cesi.. The Linceans played a role again in naming the “microscope” a year later when fellow academy member Giovanni Faber coined the word for Galileo’s invention from the Greek words ?????? (micron) meaning “small”, and ??????? (skopein) meaning “to look at”. The word was meant to be analogous with “telescope”. Illustrations of insects made using one of Galileo’s microscopes, and published in 1625, appear to have been the first clear documentation of the use of a compound microscope.

In 1612, having determined the orbital periods of Jupiter’s satellites, Galileo proposed that with sufficiently accurate knowledge of their orbits one could use their positions as a universal clock, and this would make possible the determination of longitude. He worked on this problem from time to time during the remainder of his life; but the practical problems were severe. The method was first successfully applied by Giovanni Domenico Cassini in 1681 and was later used extensively for large land surveys; this method, for example, was used by Lewis and Clark. For sea navigation, where delicate telescopic observations were more difficult, the longitude problem eventually required development of a practical portable marine chronometer, such as that of John Harrison.

In his last year, when totally blind, he designed an escapement mechanism for a pendulum clock, a vectorial model of which may be seen here. The first fully operational pendulum clock was made by Christiaan Huygens in the 1650s. Galilei created sketches of various inventions, such as a candle and mirror combination to reflect light throughout a building, an automatic tomato picker, a pocket comb that doubled as an eating utensil, and what appears to be a ballpoint pen.

Physics

Galileo’s theoretical and experimental work on the motions of bodies, along with the largely independent work of Kepler and Rene Descartes, was a precursor of the classical mechanics developed by Sir Isaac Newton.

A biography by Galileo’s pupil Vincenzo Viviani stated that Galileo had dropped balls of the same material, but different masses, from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass. This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones, in direct proportion to weight. While this story has been retold in popular accounts, there is no account by Galileo himself of such an experiment, and it is generally accepted by historians that it was at most a thought experiment which did not actually take place.

In his 1638 Discorsi Galileo’s character Salviati, widely regarded as largely Galileo’s spokesman, held that all unequal weights would fall with the same finite speed in a vacuum. But this had previously been proposed by Lucretius and Simon Stevin. Salviati also held it could be experimentally demonstrated by the comparison of pendulum motions in air with otherwise similar but different weight bobs of lead and of cork.

Galileo proposed that a falling body would fall with a uniform acceleration, as long as the resistance of the medium through which it was falling remained negligible, or in the limiting case of its falling through a vacuum. He also derived the correct kinematical law for the distance travelled during a uniform acceleration starting from rest-namely, that it is proportional to the square of the elapsed time (�d ?�t ² ). However, in neither case were these discoveries entirely original. The time-squared law for uniformly accelerated change was already known to Nicole Oresme in the 14th century, and Domingo de Soto, in the 16th, had suggested that bodies falling through a homogeneous medium would be uniformly accelerated Galileo expressed the time-squared law using geometrical constructions and mathematically-precise words, adhering to the standards of the day. (It remained for others to re-express the law in algebraic terms). He also concluded that objects retain their velocity unless a force-often friction-acts upon them, refuting the generally accepted Aristotelian hypothesis that objects “naturally” slow down and stop unless a force acts upon them (philosophical ideas relating to inertia had been proposed by Ibn al-Haytham centuries earlier, as had Jean Buridan, and according to Joseph Needham, Mo Tzu had proposed it centuries before either of them, but this was the first time that it had been mathematically expressed, verified experimentally, and introduced the idea of frictional force, the key breakthrough in validating inertia). Galileo’s Principle of Inertia stated: “A body moving on a level surface will continue in the same direction at constant speed unless disturbed.” This principle was incorporated into Newton’s laws of motion (first law).

Dome of the cathedral of Pisa with the “lamp of Galileo”

Galileo also claimed (incorrectly) that a pendulum’s swings always take the same amount of time, independently of the amplitude. That is, that a simple pendulum is isochronous. It is popularly believed that he came to this conclusion by watching the swings of the bronze chandelier in the cathedral of Pisa, using his pulse to time it. It appears however, that he conducted no experiments because the claim is true only of infinitesimally small swings as discovered by Christian Huygens. Galileo’s son, Vincenzo, sketched a clock based on his father’s theories in 1642. The clock was never built and, because of the large swings required by its verge escapement, would have been a poor timekeeper. (See Technology above.)

In 1638 Galileo described an experimental method to measure the speed of light by arranging that two observers, each having lanterns equipped with shutters, observe each other’s lanterns at some distance. The first observer opens the shutter of his lamp, and, the second, upon seeing the light, immediately opens the shutter of his own lantern. The time between the first observer’s opening his shutter and seeing the light from the second observer’s lamp indicates the time it takes light to travel back and forth between the two observers. Galileo reported that when he tried this at a distance of less than a mile, he was unable to determine whether or not the light appeared instantaneously.Sometime between Galileo’s death and 1667, the members of the Florentine Accademia del Cimento repeated the experiment over a distance of about a mile and obtained a similarly inconclusive result.

Galileo is lesser known for, yet still credited with, being one of the first to understand sound frequency. By scraping a chisel at different speeds, he linked the pitch of the sound produced to the spacing of the chisel’s skips, a measure of frequency.

In his 1632 Dialogue Galileo presented a physical theory to account for tides, based on the motion of the Earth. If correct, this would have been a strong argument for the reality of the Earth’s motion. In fact, the original title for the book described it as a dialogue on the tides; the reference to tides was removed by order of the Inquisition. His theory gave the first insight into the importance of the shapes of ocean basins in the size and timing of tides; he correctly accounted, for instance, for the negligible tides halfway along the Adriatic Sea compared to those at the ends. As a general account of the cause of tides, however, his theory was a failure. Kepler and others correctly associated the Moon with an influence over the tides, based on empirical data; a proper physical theory of the tides, however, was not available until Newton.

Galileo also put forward the basic principle of relativity, that the laws of physics are the same in any system that is moving at a constant speed in a straight line, regardless of its particular speed or direction. Hence, there is no absolute motion or absolute rest. This principle provided the basic framework for Newton’s laws of motion and is central to Einstein’s special theory of relativity.

Mathematics

While Galileo’s application of mathematics to experimental physics was innovative, his mathematical methods were the standard ones of the day. The analysis and proofs relied heavily on the Eudoxian theory of proportion, as set forth in the fifth book of Euclid’s Elements. This theory had become available only a century before, thanks to accurate translations by Tartaglia and others; but by the end of Galileo’s life it was being superseded by the algebraic methods of Descartes.

Galileo produced one piece of original and even prophetic work in mathematics: Galileo’s paradox, which shows that there are as many perfect squares as there are whole numbers, even though most numbers are not perfect squares. Such seeming contradictions were brought under control 250 years later in the work of Georg Cantor.

Church controversy

Western Christian biblical references Psalm 93:1, Psalm 96:10, and 1 Chronicles 16:30 include (depending on translation) text stating that “the world is firmly established, it cannot be moved.” In the same tradition, Psalm 104:5 says, “the LORD set the earth on its foundations; it can never be moved.” Further, Ecclesiastes 1:5 states that “And the sun rises and sets and returns to its place, etc.”

Galileo defended heliocentrism, and claimed it was not contrary to those Scripture passages. He took Augustine’s position on Scripture: not to take every passage literally, particularly when the scripture in question is a book of poetry and songs, not a book of instructions or history. The writers of the Scripture wrote from the perspective of the terrestrial world, and from that vantage point the sun does rise and set. In fact, it is the earth’s rotation which gives the impression of the sun in motion across the sky. He did, however, openly question the veracity of the Book of Joshua (10:13) wherein the sun and moon were said to have remained unmoved for three days to allow a victory to the Israelites.

By 1616 the attacks on Galileo had reached a head, and he went to Rome to try to persuade the Church authorities not to ban his ideas. In the end, Cardinal Bellarmine, acting on directives from the Inquisition, delivered him an order not to “hold or defend” the idea that the Earth moves and the Sun stands still at the centre. The decree did not prevent Galileo from discussing heliocentrism hypothetically. For the next several years Galileo stayed well away from the controversy. He revived his project of writing a book on the subject, encouraged by the election of Cardinal Barberini as Pope Urban VIII in 1623. Barberini was a friend and admirer of Galileo, and had opposed the condemnation of Galileo in 1616. The book, Dialogue Concerning the Two Chief World Systems, was published in 1632, with formal authorization from the Inquisition and papal permission.

Pope Urban VIII personally asked Galileo to give arguments for and against heliocentrism in the book, and to be careful not to advocate heliocentrism. He made another request, that his own views on the matter be included in Galileo’s book. Only the latter of those requests was fulfilled by Galileo. Whether unknowingly or deliberately, Simplicio (”Stupid”^{[citation needed]}), the defender of the Aristotelian Geocentric view in Dialogue Concerning the Two Chief World Systems, was often caught in his own errors and sometimes came across as a fool. This fact made Dialogue Concerning the Two Chief World Systems appear as an advocacy book; an attack on Aristotelian geocentrism and defense of the Copernican theory. To add insult to injury, Galileo put the words of Pope Urban VIII into the mouth of Simplicio. Most historians agree Galileo did not act out of malice and felt blindsided by the reaction to his book. However, the Pope did not take the suspected public ridicule lightly, nor the blatant bias. Galileo had alienated one of his biggest and most powerful supporters, the Pope, and was called to Rome to defend his writings.

With the loss of many of his defenders in Rome because of Dialogue Concerning the Two Chief World Systems, Galileo was ordered to stand trial on suspicion of heresy in 1633. The sentence of the Inquisition was in three essential parts:

• Galileo was found “vehemently suspect of heresy”, namely of having held the opinions that the Sun lies motionless at the centre of the universe, that the Earth is not at its centre and moves, and that one may hold and defend an opinion as probable after it has been declared contrary to Holy Scripture. He was required to “abjure, curse and detest” those opinions.
• He was ordered imprisoned; the sentence was later commuted to house arrest.
• His offending Dialogue was banned; and in an action not announced at the trial, publication of any of his works was forbidden, including any he might write in the future.

According to popular legend, after recanting his theory that the Earth moved around the Sun, Galileo allegedly muttered the rebellious phrase And yet it moves, but there is no evidence that he actually said this or anything similarly impertinent. The first account of the legend dates to a century after his death.^[89]

After a period with the friendly Ascanio Piccolomini (the Archbishop of Siena), Galileo was allowed to return to his villa at Arcetri near Florence, where he spent the remainder of his life under house arrest, and where he later became blind. It was while Galileo was under house arrest that he dedicated his time to one of his finest works, Two New Sciences. Here he summarized work he had done some forty years earlier, on the two sciences now called kinematics and strength of materials. This book has received high praise from both Sir Isaac Newton and Albert Einstein. As a result of this work, Galileo is often called, the “father of modern physics”.

Galileo died on 8 January 1642. The Grand Duke of Tuscany, Ferdinando II, wished to bury him in the main body of the Basilica of Santa Croce, next to the tombs of his father and other ancestors, and to erect a marble mausoleum in his honour. These plans were scrapped, however, after Pope Urban VIII and his nephew, Cardinal Francesco Barberini, protested. He was instead buried in a small room next to the novices’ chapel at the end of a corridor from the southern transept of the basilica to the sacristy. He was reburied in the main body of the basilica in 1737 after a monument had been erected there in his honour.

The Inquisition’s ban on reprinting Galileo’s works was lifted in 1718 when permission was granted to publish an edition of his works (excluding the condemned Dialogue) in Florence. In 1741 Pope Benedict XIV authorized the publication of an edition of Galileo’s complete scientific works which included a mildly censored version of the Dialogue. In 1758 the general prohibition against works advocating heliocentrism was removed from the Index of prohibited books, although the specific ban on uncensored versions of the Dialogue and Copernicus’s De Revolutionibus remained. All traces of official opposition to heliocentrism by the Church disappeared in 1835 when these works were finally dropped from the Index.

In 1939 Pope Pius XII, in his first speech to the Pontifical Academy of Sciences, within a few months of his election to the papacy, described Galileo as being among the “most audacious heroes of research�… not afraid of the stumbling blocks and the risks on the way, nor fearful of the funereal monuments^“ His close advisor of 40 years, Professor Robert Leiber wrote: “Pius XII was very careful not to close any doors (to science) prematurely. He was energetic on this point and regretted that in the case of Galileo.”

On 15 February 1990, in a speech delivered at the Sapienza University of Rome, Cardinal Ratzinger cited some current views on the Galileo affair as forming what he called “a symptomatic case that permits us to see how deep the self-doubt of the modern age, of science and technology goes today.” Some of the views he cited were those of the philosopher Paul Feyerabend, whom he quoted as saying “The Church at the time of Galileo kept much more closely to reason than did Galileo himself, and she took into consideration the ethical and social consequences of Galileo’s teaching too. Her verdict against Galileo was rational and just and the revision of this verdict can be justified only on the grounds of what is politically opportune.” The Cardinal did not clearly indicate whether he agreed or disagreed with Feyerabend’s assertions. He did, however, say “It would be foolish to construct an impulsive apologetic on the basis of such views”.

On 31 October 1992, Pope John Paul II expressed regret for how the Galileo affair was handled, and officially conceded that the Earth was not stationary, as the result of a study conducted by the Pontifical Council for Culture.

His writings

Galileo’s early works describing scientific instruments include the 1586 tract entitled The Little Balance (La Billancetta) describing an accurate balance to weigh objects in air or water and the 1606 printed manual Le Operazioni del Compasso Geometrico et Militare on the operation of a geometrical and military compass.^[107]

His early works in dynamics, the science of motion and mechanics were his 1590 Pisan De Motu (On Motion) and his circa 1600 Paduan Le Meccaniche (Mechanics). The former was based on Aristotelian-Archimedean fluid dynamics and held that the speed of gravitational fall in a fluid medium was proportional to the excess of a body’s specific weight over that of the medium, whereby in a vacuum bodies would fall with speeds in proportion to their specific weights. It also subscribed to the Hipparchan-Philoponan impetus dynamics in which impetus is self-dissipating and free-fall in a vacuum would have an essential terminal speed according to specific weight after an initial period of acceleration.

Galileo’s 1610 The Starry Messenger (Sidereus Nuncius) was the first scientific treatise to be published based on observations made through a telescope and include the discovery of the Galilean moons. Galileo published a description of sunspots in 1613 entitled Letters on Sunspots suggesting the Sun and heavens are corruptible. It also reported his 1610 telescopic confirmation of the full set of phases of Venus that refuted pure geocentrism and so promoted the 17th century conversion to geoheliocentrism. In 1615 Galileo prepared a manuscript known as the Letter to Grand Duchess Christina which was not published in printed form until 1636. This letter was a revised version of the Letter to Castelli, which was denounced by the Inquisition as an incursion upon theology by advocating Copernicanism both as physically true and as consistent with Scripture. In 1616, after the order by the inquisition for Galileo not to hold or defend the Copernican position, Galileo wrote the Discourse on the tides (Discorso sul flusso e il reflusso del mare) based on the Copernican earth, in the form of a private letter to Cardinal Orsini. In 1619, Mario Guiducci, a pupil of Galileo’s, published a lecture written largely by Galileo under the title Discourse on the Comets (Discorso Delle Comete), arguing against the Jesuit interpretation of comets.^[111]

In 1623, Galileo published The Assayer – Il Saggiatore, which attacked theories based on Aristotle’s authority and promoted experimentation and the mathematical formulation of scientific ideas. The book was highly successful and even found support among the higher echelons of the Christian church.^[112] Following the success of The Assayer, Galileo published the Dialogue Concerning the Two Chief World Systems (Dialogo sopra i due massimi sistemi del mondo) in 1632. Despite taking care to adhere to the Inquisition’s 1616 instructions, the claims in the book favouring Copernican theory and a non Geocentric model of the solar system led to Galileo being tried and banned on publication. Despite the publication ban, Galileo published his Discourses and Mathematical Demonstrations Relating to Two New Sciences (Discorsi e Dimostrazioni Matematiche, intorno a due nuove scienze) in 1638 in Holland, outside the jurisdiction of the Inquisition.

• The Little Balance (1586)
• On Motion (1590)
• Mechanics (c1600)
• The Starry Messenger (1610; in Latin, Sidereus Nuncius)
• Letters on Sunspots (1613)
• Letter to the Grand Duchess Christina (1615; published in 1636)
• Discourse on the Tides (1616; in Italian, Discorso del flusso e reflusso del mare)
• Discourse on the Comets (1619; in Italian, Discorso Delle Comete)
• The Assayer (1623; in Italian, Il Saggiatore)
• Dialogue Concerning the Two Chief World Systems (1632; in Italian Dialogo dei due massimi sistemi del mondo)
• Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638; in Italian, Discorsi e Dimostrazioni Matematiche, intorno a due nuove scienze)

Legacy

Galileo’s astronomical discoveries and investigations into the Copernican theory have led to a lasting legacy which includes the categorisation of the four large moons of Jupiter discovered by Galileo (Io, Europa, Ganymede and Callisto) as the Galilean moons. Other scientific endeavours and principles are named after Galileo including the Galileo spacecraft, the first spacecraft to enter orbit around Jupiter, the proposed Galileo global satellite navigation system, the transformation between inertial systems in classical mechanics denoted Galilean transformation and the Gal (unit), sometimes known as the Galileo which is a non-SI unit of acceleration.

To coincide in part with Galileo’s first recorded astronomical observations using a telescope, the United Nations has scheduled 2009 to be the International Year of Astronomy. A global scheme laid out by the International Astronomical Union (IAU), it has also been endorsed by UNESCO – the UN body responsible for Educational, Scientific and Cultural matters. The International Year of Astronomy 2009 is intended to be a global celebration of astronomy and its contributions to society and culture, stimulating worldwide interest not only in astronomy but science in general, with a particular slant towards young people.

The 20th-century German playwright Bertolt Brecht dramatised Galileo’s life in his Life of Galileo (1943).