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.

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 ...