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 ...

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 ...

One of the biggest stories in science is quietly playing out in the world of abstract mathematics. Over the course of last year, researchers fulfilled a decades-old dream when they unveiled a proof of ...

It might come as a surprise to some people that this prediction hasn’t already come to pass. Given that mathematics is a subject of logic and precision, it would seem to be perfect territory for a ...

Despite multiple conferences dedicated to explicating Mochizuki’s proof, number theorists have struggled to come to grips with its underlying ideas. His series of papers, which total more than 500 ...