- Have you always loved math? What's the earliest memory you have of loving math?
- What is Art of Problem Science (AoPS) and what inspired you to start the school?
- What's your experience of math competitions?
- What does it take to score really well on a math competition? How much is brain power, how much is discipline, how much is having seen lots of different problems, how much is tricks and techniques?
- How many hours a day/week do students typically spend preparing for math competitions?
- AoPS is not just about competitions, is it?
- Brag a bit about how many students you've prepped for competitions who have done really well.
- Tell us about your courses, books, videos, community, and other offerings.

Art of Problem Solving was founded by Richard Rusczyk in 2003 to create interactive educational opportunities for avid math students. Richard Rusczyk is one of the co-authors of the Art of Problem Solving classic textbooks, author of Art of Problem Solving's Introduction to Algebra, Introduction to Geometry, and Precalculus textbooks, co-author of Art of Problem Solving's Intermediate Algebra and Prealgebra, one of the co-creators of the Mandelbrot Competition, and a past Director of the USA Mathematical Talent Search. He was a participant in National MATHCOUNTS, a three-time participant in the Math Olympiad Summer Program, and a USA Mathematical Olympiad winner (1989). He graduated from Princeton University in 1993, and worked as a bond trader for D.E. Shaw & Company for four years. AoPS marks Richard's return to his vocation - educating motivated students.

You find a math problem in a book, or maybe on a contest, or maybe your teacher tells you the problem. You work on it for a half-hour. Then another half-hour. It bugs you and bugs you because you know that other kid who wins all the trophies knows how to do the problem. You want to win the trophies, too, but that's not why you spend another half-hour on the problem. You want to know the answer. More than just the answer, you want to know how to do the problem.

Finally, you give up and look up the answer. The solution mostly makes sense, but you're not entirely satisfied. You may not even know why you're not satisfied. You're not satisfied because the solution didn't answer the most important question...

How would I have thought of that?

The creators of this site were this student once. We were the kids who wanted to win the trophies. We worked hard and became the kids who won the trophies. The trophies are in attics now. The problem-solving skills, the love of mathematics, and the friendships forged with peers with similar interests remain. We've applied the skills we've developed through mathematics to a variety of fields in college, then in the professional world. (More.)

Sue and I shared a delightful chat about what math is, what the book is about, and how we can all get more inspired to engage in math with our kids. And, Sue sprinkles the conversation with some interesting open-ended math problems. Think part coffee table conversation part math circle.

"I love teaching math, yet throughout my twenty-some years of teaching I've struggled with the fact that what I want to teach is problem solving but what I do teach most of the time is how to follow recipes (here’s how you find the slope or the vertex, here’s how you factor, and so on). Until recently, I never felt that I had made much progress in resolving this dilemma. In early 2008, I started reading Living Math Forum, an email group where participants discuss how to help their children learn math. In the years since that discovery, my life has been full of math-play adventures. I’m still learning how to bring that spirit into my students’ lives."

From PlayingWithMath.org

**Why play with math? Because play is the best way to learn.**

From the introduction of the book:

Math, more than any other subject, has to be approached by each student at their own pace, and in their own way. There may be one right answer, but there are more ways to think about the path from question to answer than you’d expect.

**What is math?**

Most people think it’s adding, subtracting, multiplying, and dividing; knowing your times tables; knowing how to divide fractions; knowing how to follow the rules to find the answer. Math is so much more than that! Math is seeing patterns, solving puzzles, using logic, finding ways to connect disparate ideas, and so much more. People who do math play with infinity, shapes, map coloring, tiling, and probability; they analyze how things change over time, or how one particular change will affect a whole system. Math is about concepts, connections, patterns. It can be a game, a language, an art form. Everything is connected, often in surprising and beautiful ways. The stories in this book will be full of examples that show math from these angles. More.

Go to Incited.org

Anyway, the second time was a charm, and we produced a good audio discussing all things related to MATHCOUNTS and how the organization inspires kids to improve their relationship with Math. If you read the transcript, or even if you didn't, check out the podcast!

As executive director of MATHCOUNTS®, Lou DiGioia leads the largest nonprofit organization dedicated to extracurricular middle school mathematics. As a former Mathlete®, DiGioia is the first executive director to have participated the MATHCOUNTS Competition Series as a student. During his tenure, he led the creation of The National Math Club, which builds student enthusiasm for math by providing schools with free resources to hold afterschool math clubs; and the Math Video Challenge, an online competition that has teams create innovative teaching videos based on MATHCOUNTS problems. In 2013, he orchestrated the organization’s successful Guinness World Record attempt of the fastest time to create the first 25 rows of Pascal’s Triangle in human formation. DiGioia holds a BA from Georgetown University and an MBA from George Mason University.

[From the overview page.]

The MATHCOUNTS Foundation is a 501(c)(3) non-profit organization that strives to engage middle school students of all ability and interest levels in fun, challenging math programs, in order to expand their academic and professional opportunities. Middle school students exist at a critical juncture in which their love for mathematics must be nurtured, or their fear of mathematics must be overcome. MATHCOUNTS provides students with the kinds of experiences that foster growth and transcend fear to lay a foundation for future success.

For more than 30 years MATHCOUNTS has provided enriching, extracurricular opportunities to students and free, high-quality resources to educators. Every child is unique, but we believe all children are capable of seeing the beauty and joy of math, whether they come to us already passionate about math, or intimidated by it.

There are many paths to math. We work to ensure that all students discover theirs.

]]>Here are some of the questions we discussed.

1. What is your background and your experience teaching high school math to students and to teachers?

2. I attended the Ross program and you have a key role in a program that has its roots in the Ross program. Tell me about this program and your involvement with it.

3. There's something special about number theory and algebra that makes it accessible to bright students without a deep background in math. What do you think of that thought?

4. What is "Learning Modern Algebra" about and who is the audience?

5. How does Fermat's Last Theorem unite the book's chapters?

6. What are the challenges with how Modern Algebra is taught?

7. Why is exploration so important and how do you promote it?

8. Rigorous thinking about open-ended problems runs through the book. PODASIP (prove or disprove and salvage if possible) problems contribute to this. Can you speak to that?

9. Why is historical setting important in learning math and how do you weave history into the book?

10. Tell us about the importance of the "Connections" sections in the book.

11. Is there a next book or project?

12. The question I ask everyone: "What advice would you give to a parent whose child was struggling with math?"

From the EDC web-site:

Al Cuoco is the lead author of CME Project, a National Science Foundation (NSF)-funded high school curriculum published by Pearson. Recently, he served as part of a team that revised the Conference Board of the Mathematical Sciences (CBMS) recommendations for teacher preparation and professional development.

Cuoco is carrying out several professional development streams of work devoted to the implementation of the Common Core State Standards for Mathematics (CCSSM) Standards for Mathematical Practice, including EDC’s Mathematical Practice Institute (MPI). Through the MPI, he and his colleagues have launched a new course for teachers and facilitators, Developing Mathematical Practice in High School.

He co-directs Focus on Mathematics, a partnership among universities, school districts, and EDC that has established a community of mathematical practice involving mathematicians, teachers, and mathematics educators. The partnership evolved from his 25-year collaboration with Glenn Stevens on Boston University’s PROMYS for Teachers, a professional development program for teachers based on an immersion experience in mathematics. He also co-directs the development of the course for secondary teachers in the Institute for Advanced Study program at the Park City Mathematics Institute. More

Learning Modern Algebra aligns with the CBMS Mathematical Education of Teachers–II recommendations, in both content and practice. It emphasizes rings and fields over groups, and it makes explicit connections between the ideas of abstract algebra and the mathematics used by high school teachers. It provides opportunities for prospective and practicing teachers to experience mathematics for themselves, before the formalities are developed, and it is explicit about the mathematical habits of mind that lie beneath the definitions and theorems.

This book is designed for prospective and practicing high school mathematics teachers, but it can serve as a text for standard abstract algebra courses as well. The presentation is organized historically: the Babylonians introduced Pythagorean triples to teach the Pythagorean theorem; these were classified by Diophantus, and eventually this led Fermat to conjecture his Last Theorem. The text shows how much of modern algebra arose in attempts to prove this; it also shows how other important themes in algebra arose from questions related to teaching. Indeed, modern algebra is a very useful tool for teachers, with deep connections to the actual content of high school mathematics, as well as to the mathematics teachers use in their profession that doesn't necessarily "end up on the blackboard." More

]]>"Count Like an Egyptian" is a delightful book, full of color illustrations, fun stories, lots of hands-on exercises, and an appreciation for the power of simple but deep ideas.

David Reimer was a pleasure to interview. He is a brilliant mathematician who hasn't lost sight of the power and beauty of mathematics. He taught me and modeled that, despite the stereotype, the more advanced mathematicians are the ones who are more likely to communicate ideas well.

We discussed these questions plus some nice tangents!

1. How did you get interested enough in Egyptian computation to write a book about it? What is the book about and who is the audience?

2. You're a math professor. What courses do you teach and at what level?

3. You researched the Rhind Papyrus to figure out how Egyptians did computations. Where did you get a hold of the Papyrus? How much time did you spend unraveling its secrets?

4. I'm fascinated with the idea that children can learn to do multiplication and division by just learning to double and add numbers. How did we develop such a cumbersome system of multiplication that requires memorizing tables?

5. I find it interesting that computers doing multiplication (and all other arithmetic) in binary equates to Egyptians doubling and adding numbers. Can you connect the dots for our listeners? (Nice video here, btw: https://www.youtube.com/watch?v=EDLLPnfpMfU)

6. Tell us about how Egyptians worked with fractions and why it was so novel.

7. One reviewer said this: "Of course our system is more apt for us (or for machines) to do calculations just following recipes, which need no insight or wit, but what we lose is that the Egyptian system keeps the practitioner sharp, forcing him or her to think about the problem and the result of the calculations." What do you think of the statement?

8. In addition to exploring Egyptian computation you also write about other mathematical systems. Tell us about those.

9. Is there a next book or big project?

10. The question I ask everyone: What advice would you give to a parent whose child was struggling with math in school?

In high school I was a mediocre student at best. But I did far better on my SATs than was expected. I passed a number of AP exams never having taken any AP courses but learning from published study guides. This got me into Colgate. I started as a computer science major but quickly found that I knew more than my professors, at least in practical computing. I toyed with becoming a physics major, winning the school’s award for the best freshman physics student. I eventually settled on math as everyone in my family did.

Over the summers I worked at Creative Computing, which was then the largest computer magazine in the world and for Prudential Insurance, where I wrote the database for the central office’s purchasing department. I passed two actuarial exams and was offered a job but decided to take a try as a freelance programmer. On one project, which we spent six months on, the company cancelled and refused to pay us. Desperately needing money I taught night school calculus as an adjunct. I immediately knew that this is what I wanted to do for the rest of my life.

I got into the graduate math program at Rutgers. While most grad students taught recitations and graded papers, the department noticed my teaching skill and gave me my own higher level classes even giving me a 300-level course. I finished up my Phd. thesis while making some money as a full instructor first at Rutgers and then at Middlesex Community College. While there I was told that my proof of the Vandenberg-Kesten conjecture won the Polya Prize in Discrete Mathematics which is given every four years to what is considered to be the best work in discrete math during that period. The conjecture is a generalization of a probabilistic proposition often used in percolation, the theory of how things like epidemics and fires spread. Being overly simplistic it basically says that given two events that can happen anywhere but not in the same place, the probability of both happening is less than what would be expected if they were independent events. Based on this theorem I got what most would call a post doc at the Institute for Advanced Study in Princeton (where Einstein worked) and then a job at the College of New Jersey where I am today.

Contact info: http://mathstat.pages.tcnj.edu/faculty-profiles/faculty/dave-reimer/

(From the Princeton University Press book page)

The mathematics of ancient Egypt was fundamentally different from our math today. Contrary to what people might think, it wasn't a primitive forerunner of modern mathematics. In fact, it can't be understood using our current computational methods. Count Like an Egyptian provides a fun, hands-on introduction to the intuitive and often-surprising art of ancient Egyptian math. David Reimer guides you step-by-step through addition, subtraction, multiplication, and more. He even shows you how fractions and decimals may have been calculated--they technically didn't exist in the land of the pharaohs. You'll be counting like an Egyptian in no time, and along the way you'll learn firsthand how mathematics is an expression of the culture that uses it, and why there's more to math than rote memorization and bewildering abstraction.

Reimer takes you on a lively and entertaining tour of the ancient Egyptian world, providing rich historical details and amusing anecdotes as he presents a host of mathematical problems drawn from different eras of the Egyptian past. Each of these problems is like a tantalizing puzzle, often with a beautiful and elegant solution. As you solve them, you'll be immersed in many facets of Egyptian life, from hieroglyphs and pyramid building to agriculture, religion, and even bread baking and beer brewing.

Fully illustrated in color throughout, Count Like an Egyptian also teaches you some Babylonian computation--the precursor to our modern system--and compares ancient Egyptian mathematics to today's math, letting you decide for yourself which is better.

]]>So, what did Lou and I talk about?

In a nutshell, Lou answered all of my questions about MATHCOUNTS. I had always assumed that MATHCOUNTS was the organization that puts on math competitions for the brightest of the bright middle school students. I was delighted to discover that there is much much more to how MATHCOUNTS serves students.

We also talked a lot about the making of the MATHCOUNTS 2013 Guinness World Record Pascal's Triangle created by 325 humans, each holding one of the numbers in the first 25 rows of the triangle.

Read the interview and you'll understand why accomplishing this was no easy feat.

Lou also answered these questions.

- Do you have a story about falling in love with math as a youth?
- What is MATHCOUNTS? What is its history, and its mission, and who does MATHCOUNTS serve?
- How did you go from earning a BA and an MBA to becoming the director of MATHCOUNTS?
- Tell us about MATHCOUNTS competitions.
- Tell us about the National Math Club.
- Tell us about the Math Video Challenge.
- Tough question: How would you address the concern that some people raise that contest organizations like MATHCOUNTS mainly serve the kids who are extra bright and extra motivated?
- Tell us about Solve-A-Thon
- What do you do in a typical day?
- Are there some interesting new projects that you are working on?
- The question I ask everyone: What advice would you give to a parent whose child was struggling with math?

Here is the transcript of the interview.

As executive director of MATHCOUNTS®, Lou DiGioia leads the largest nonprofit organization dedicated to extracurricular middle school mathematics. As a former Mathlete®, DiGioia is the first executive director to have participated the MATHCOUNTS Competition Series as a student. During his tenure, he led the creation of The National Math Club, which builds student enthusiasm for math by providing schools with free resources to hold afterschool math clubs; and the Math Video Challenge, an online competition that has teams create innovative teaching videos based on MATHCOUNTS problems. In 2013, he orchestrated the organization’s successful Guinness World Record attempt of the fastest time to create the first 25 rows of Pascal’s Triangle in human formation. DiGioia holds a BA from Georgetown University and an MBA from George Mason University.

[From the overview page.]

The MATHCOUNTS Foundation is a 501(c)(3) non-profit organization that strives to engage middle school students of all ability and interest levels in fun, challenging math programs, in order to expand their academic and professional opportunities. Middle school students exist at a critical juncture in which their love for mathematics must be nurtured, or their fear of mathematics must be overcome. MATHCOUNTS provides students with the kinds of experiences that foster growth and transcend fear to lay a foundation for future success.

For more than 30 years MATHCOUNTS has provided enriching, extracurricular opportunities to students and free, high-quality resources to educators. Every child is unique, but we believe all children are capable of seeing the beauty and joy of math, whether they come to us already passionate about math, or intimidated by it.

There are many paths to math. We work to ensure that all students discover theirs.

]]>Tim is a mathematician and a professional mime. He's got a neat relationship with the Mathematical Association of America, and with the Museum of Mathematics in New York City. He's got a DVD course coming out, and a second book. Tim is quite the math celebrity and a really great guy. I think you'll all enjoy the many topics we manage to touch on in just over an hour. Oh, and if you didn't win a billion dollars in Warren Buffett's March Madness challenge then you might want to listen to the podcast and read the book.

[From http://sites.davidson.edu/mathmovement/about]

Tim Chartier is an Associate Professor in the Department of Mathematics and Computer Science at Davidson College. In 2014, he was named the inaugural Mathematical Association of America’s Math Ambassador. He is a recipient of a national teaching award from the Mathematical Association of America. Published by Princeton University Press, Tim authored Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing and coauthored Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms with Anne Greenbaum. As a researcher, Tim has worked with both Lawrence Livermore and Los Alamos National Laboratories on the development and analysis of computational methods targeted to increase efficiency and robustness of numerical simulation on the lab’s supercomputers, which are among the fastest in the world. Tim’s research with and beyond the labs was recognized with an Alfred P. Sloan Research Fellowship. (More)

[From The Princeton University Press Web-site]

This book provides a fun, hands-on approach to learning how mathematics and computing relate to the world around us and help us to better understand it. How can reposting on Twitter kill a movie's opening weekend? How can you use mathematics to find your celebrity look-alike? What is Homer Simpson's method for disproving Fermat's Last Theorem? Each topic in this refreshingly inviting book illustrates a famous mathematical algorithm or result--such as Google's PageRank and the traveling salesman problem--and the applications grow more challenging as you progress through the chapters. But don't worry, helpful solutions are provided each step of the way.

Math Bytes shows you how to do calculus using a bag of chocolate chips, and how to prove the Euler characteristic simply by doodling. Generously illustrated in color throughout, this lively and entertaining book also explains how to create fractal landscapes with a roll of the dice, pick a competitive bracket for March Madness, decipher the math that makes it possible to resize a computer font or launch an Angry Bird--and much, much more. All of the applications are presented in an accessible and engaging way, enabling beginners and advanced readers alike to learn and explore at their own pace--a bit and a byte at a time.

- Tim Chartier at the Huffington Post
- Tim on twitter
- Mime-matics on Vimeo
- Work with the ESPN show Sports Science and a podcast about it
- The list of national media interest in March Madness

Enjoy!

Chuck Adler grew up in the DC suburbs, and went to a very good public high school. He attended Brown University, where he got a bachelor of science in Physics, and then stayed there for graduate school, eventually getting a Ph. D. in laser physics. Dr. Adler has been a faculty member at St. Mary's College since 1997; his research area is atomic physics and light scattering, particularly atmospheric optics (rainbows, ice crystal halo displays and the like). He was the chair of the 10th international "Light and Color in the Open Air" conference in 2010. In addition to science fiction, he enjoys mysteries and historical novels, plus almost any technical book on almost any subject, particularly cookbooks, of which he owns several hundred. He enjoys cooking a great deal, particularly baking bread.

From teleportation and space elevators to alien contact and interstellar travel, science fiction and fantasy writers have come up with some brilliant and innovative ideas. Yet how plausible are these ideas--for instance, could Mr. Weasley's flying car in the Harry Potter books really exist? Which concepts might actually happen, and which ones wouldn't work at all? Wizards, Aliens, and Starships delves into the most extraordinary details in science fiction and fantasy--such as time warps, shape changing, rocket launches, and illumination by floating candle--and shows readers the physics and math behind the phenomena. More...

]]>What inspired to blog this afternoon was an email I received from Andrew S. DeSio, Director of Publicity for Princeton University Press. Andrew has asked me to help spread the word that Martin Gardner really did write his own autobiography. Here's an excerpt from Andrew's message.

"Since the book has released some critics of the bio have claimed the book was posthumously pieced together by friends of the famed math writer and that the new biography is a collaboration between the Press and friends of Gardner. This is simply not true. Prior to his death, Martin Gardner wrote a complete manuscript of his autobiography. While some of his dearest friends helped us fine tune the project, this book is absolutely his own. Our math editor Vickie Kearn and I would like the opportunity to refute this claim and so we are hoping your blog might be the perfect forum for us to post a “Letter” with our official statement on the book."

I have to say that in all of my numerous dealings with Princeton University Press I have never ever sensed any action that might be out of integrity. In particular, I've had a few email exchanges with their math editor Vickie Kearn and I even interviewed her for one of my podcasts and, if Vickie says that Martin Gardner wrote his autobiography himself, I believe her.

Here is Vickie's letter. And, here is an excerpt from Martin Gardner's original manuscript, courtesy of Princeton University Press.

By Vickie Kearn, Mathematics Editor, Princeton University Press

Once we began to promote Undiluted Hocus Pocus: The autobiography of Martin Gardner, a few people asked me “Who wrote the book?” I initially thought they were confusing a biography with an autobiography but now that I have read a few reviews on amazon, I understand why they asked the question. Some believe that Gardner’s friends put together bits and pieces of things that Martin Gardner wrote. So to clarify things, here is the back story about the publication of this book.

I never met Martin Gardner. I never talked with him on the phone. But, we did write letters to one another for almost 25 years. No one writes letters anymore so when I receive one, I always get excited—especially when it is from someone like Martin Gardner. His letters were always full of fun information and sometimes they concerned book projects we were working on. The letters were always written on a typewriter and corrected by hand in ink, often green. He wrote in small script and it sometimes took a while to sort out the handwriting but the letters were always a treasure trove and worth the effort to decipher.

When Martin’s son, Jim Gardner, contacted me and asked if Princeton University Press would be interested in publishing Martin’s autobiography, I was thrilled. I could not think of a book I would more like to publish. As with many people, Martin Gardner had a huge amount to do with my becoming a math major so being able to do something for him was a fantastic opportunity.

When Jim sent the manuscript I started laughing because it looked like an extremely long letter. It was written with the same typewriter and edited in the same way as his letters. I have attached a page from the manuscript in case you never corresponded with Martin Gardner.

Jim and I talked for a long time about Martin’s wishes for the manuscript and we decided that we would change as little as possible in the manuscript. We could not ask the author his opinion about any changes so we kept asking ourselves would Martin like any changes we planned before we made them. We did correct typos and filled in all the ??? he had sprinkled throughout the manuscript. We confirmed some dates and the order in which events took place.

There are a few places in the manuscript where there is some repetition. Martin had many interests and we knew some people would go only to the chapters that interested them. So, in cases where we thought that might happen, we allowed the repeated material to stand.

Some people ask why it took so long to publish the book after Martin’s death. He finished the manuscript a few months before he died and passed it to his son to decide what to do with it. With any large estate, there are lots of decisions to make and time passes quickly. People who knew Martin well have found some wonderful stories in the book that they never heard before. Other people wish there was more in the book about other things and wonder why he included what he did. We will never know the answer to that question but I do know the answer to:

Who wrote Martin Gardner’s autobiography? He did!