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 ...

Since the start of the 20th century, the heart of mathematics has been the proof — a rigorous, logical argument for whether a given statement is true or false. Mathematicians’ careers are measured by ...

Computers are extremely good with numbers, but they haven’t gotten many human mathematicians fired. Until recently, they could barely hold their own in high school-level math competitions. But now ...

Mathematicians explore ideas by proposing conjectures and proving them with theorems. For centuries, they built these proofs line by careful line, and most math researchers still work like that today.