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 ...

Math students may not blink at calculating probabilities, measuring the area beneath curves or evaluating matrices, yet they often find themselves at sea when first confronted with writing proofs. But ...

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 ...

Marijn Heule turns mathematical statements into something like Sudoku puzzles, then has computers go to work on them. His proofs have been called “disgusting,” but they go beyond what any human can do ...

There’s a curious contradiction at the heart of today’s most capable AI models that purport to “reason”: They can solve routine math problems with accuracy, yet when faced with formulating deeper ...

Proof is a way to show a statement is always true by using worded or algebraic reasoning. Higher tier – There are algebraic ways to describe odd, even and consecutive integers, which are needed for ...

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 ...

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 ...