twin primes conjecture

In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers — strange entities that mimic the primes.

What makes a proof stronger than a guess? What does evidence look like in the realm of mathematical abstraction? Hear the mathematician Melanie Matchett Wood explain how probability helps to guide number theorists toward certainty.

On his way to winning a Fields Medal, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

Decades ago, a mathematician posed a warmup problem for some of the most difficult questions about prime numbers. It turned out to be just as difficult to solve, until now.

In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems.

In mathematics, where proofs are everything, evidence is important too. But evidence is only as good as the model, and modeling can be dangerous business. So how much evidence is enough?

An obscure number theorist who became an overnight sensation with a major proof about the gaps between prime numbers now finds quiet inspiration walking along the Pacific Coast.