Jordana Cepelewicz

Landmark results in geometry and number theory marked an exciting year for mathematics, at a time when advances in artificial intelligence are starting to transform the subject’s future.

Born poor in colonial India and dead at 32, Ramanujan had fantastical, out-of-nowhere visions that continue to shape the field today.

The proof creates stricter limits on potential exceptions to the famous Riemann hypothesis.

Number theorist Ken Ono is teaching Olympians to swim more efficiently.

Useful mathematical concepts, like the number line, can linger for millennia before they are rigorously defined.

The topologist Danny Calegari discusses the inevitability of disappointment in math, and how to learn from it.

Mathematicians have disproved a major conjecture about the relationship between curvature and shape.

Topologists prove two new results that bring some order to the confoundingly difficult study of four-dimensional shapes.

The French mathematician spent decades developing a set of tools now widely used for taming random processes.