GPT-5.4 Pro cracked a conjecture in number theory that had stumped generations of mathematicians, using a proof strategy that ...

Consider the numbers used - Even Numbers and Primes. Both groups have a common property - Digital Roots All Digital Roots have a common property - an infinite loop ...

A few months before the 2025 International Mathematical Olympiad (IMO) in July, a three-person team at OpenAI made a long bet that they could use the competition’s brutally tough problems to train an ...

A Mathematician with early access to XAI Grok 4.20, found a new Bellman function for one of the problems he had been working on with my student N. Alpay. Not an Erdős problem, but original research.

In a digital era plagued by growing privacy concerns and eroding institutional trust, the power to prove something without disclosing sensitive data is not merely an academic exercise—it's a ...

Kendra Pierre-Louis: For Scientific American’s Science Quickly, I’m Kendra Pierre-Louis, in for Rachel Feltman. In 1997, Deep Blue, a supercomputer built by IBM, did the unexpected: it defeated chess ...

A mathematician will turn a groundbreaking 100-page proof into computer code. The proof tool, Lean, lets users turn proofs written in prose into rules and logic for testing. Kevin Buzzard already uses ...

Michael Freedman’s momentous 1981 proof of the four-dimensional Poincaré conjecture was on the verge of being lost. The editors of a new book are trying to save it. One of the most important pieces of ...

Construct a convex octagon with four right angles. It probably says a lot about me as a teacher that I assign problems like this. I watch as students try to arrange the right angles consecutively.