Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach. In 2012, the mathematician Shinichi Mochizuki claimed he had solved the abc conjecture ...

If pure math can teach us anything, it’s this: occasionally, your special interest might just change the world. For Joshua Zahl and Hong Wang, that special interest was the Kakeya conjecture. “I read ...

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 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 ...

The race is on to develop an artificial intelligence that can do pure mathematics, and top mathematicians just threw down the gauntlet with an exam of actual, unsolved problems that are relevant to ...

AI could soon spew out hundreds of mathematical proofs that look "right" but contain hidden flaws, or proofs so complex we can't verify them. How will we know if they're right? When you purchase ...

Peter Scholze wants to rebuild much of modern mathematics, starting from one of its cornerstones. Now, he has received validation for a proof at the heart of his quest from an unlikely source: a ...