Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong. One of the oldest and simplest ...

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 ...