Richard Feynman described a decision-making problem and its solution in handwritten notes, but the meaning of the notes has been a mystery for almost 50 y. We decipher the problem and solution from Feynman’s notes, and prove that Feynman’s ...In the 1970s, physicist Richard Feynman turned lunch with a friend into a math problem—how to optimize dish selection over multiple meals—but his handwritten notes remained a mystery for decades. Here we present the fully deciphered problem and solution, ...

The Turing test asks whether a machine can imitate human behavior so well that another human cannot reliably tell the difference. It is not only the oldest and most discussed test of AI but can also provide insight into what cues people use to ...The Turing test has been widely discussed as a test of machine intelligence, but it also provides a measure of how humans distinguish other humans from machines. We evaluated 4 systems (ELIZA, GPT-4o, LLaMa-3.1-405B, and GPT-4.5) in two randomized, ...