Mathematician Grigori Perelman solved the Poincaré conjecture, and then rejected the $1 million prize that came with it.

For close to 40 years, a simple little hypothesis has been quietly sitting in a corner of graph theory, minding its own business. Known as the “bunkbed conjecture”, it always seemed kind of ...

Quantum entanglement has a central role in many areas of physics. To grasp the essence of this phenomenon, it is fundamental to understand how different manifestations of entanglement relate to each ...

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 ...

Innocent-looking problems involving whole numbers can stymie even the most astute mathematicians. As in the case of Fermats last theorem, centuries of effort may go into proving such tantalizing, ...

The COLA method can help identify whether you're operating on speculation, belief, evidence, or principle—and respond ...

The “sensitivity” conjecture stumped many top computer scientists, yet the new proof is so simple that one researcher summed it up in a single tweet. A paper posted online this month has settled a ...