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 ...

New computer tools have the potential to revolutionize the practice of mathematics by providing more-reliable proofs of mathematical results than have ever been possible in the history of humankind.

Computer-assisted of mathematical proofs are not new. For example, computers were used to confirm the so-called 'four color theorem.' In a short release, 'Proof by computer,' the American Mathematical ...

The one source of truth is mathematics. Every statement is a pure logical deduction from foundational axioms, resulting in absolute certainty. Since Andrew Wiles proved Fermat’s Last Theorem, you’d be ...

In 2024, an AI entered the fray of the International Mathematical Olympiad (IMO). Google’s AlphaProof is part of the same Alpha group that also created AlphaFold and AlphaGo. It solved problems that ...

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 ...