It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown. Mountain climbing is a beloved metaphor for mathematical research.

Last week, Yitang “Tom” Zhang, a popular math professor at the University of New Hampshire, stunned the world of pure mathematics when he announced that he had proven the “bounded gaps” conjecture ...

The original version of this story appeared in Quanta Magazine. Much of mathematics is driven by intuition, by a deep-rooted sense of what should be true. But sometimes instinct can lead a ...

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 ...

Prime numbers just got less lonely. A proof announced this week claims to show that the number of primes with a near-neighbour that is also a prime number is infinite – although the “near-neighbour” ...

A Japanese mathematician claims to have solved one of the most important problems in his field. The trouble is, hardly anyone can work out whether he's right. Sometime on the morning of 30 August 2012 ...