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 ...

After an eight-year struggle, embattled Japanese mathematician Shinichi Mochizuki has finally received some validation. His 600-page proof of the abc conjecture, one of the biggest open problems in ...

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 ...

A mathematical proof has finally debunked the idea that we live in a simulation, according to a group of international researchers. The theory that the universe could be a computer programme has been ...

Much of mathematics is driven by intuition, by a deep-rooted sense of what should be true. But sometimes instinct can lead a mathematician astray. Early evidence might not represent the bigger picture ...

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.