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.

Computers make it possible for a mathematical proof to run as long as several thousand full-length novels combined. But human beings alone cannot verify such immense proofs. That, according to Ian ...

As he was brushing his teeth on the morning of July 17, 2014, Thomas Royen, a little-known retired German statistician, suddenly lit upon the proof of a famous conjecture at the intersection of ...

Whole numbers, addition and multiplication are among the first things schoolchildren learn, but a new mathematical proof shows that even the world’s best minds have plenty more to learn about these ...