Number theory

Paul Nelson has solved the subconvexity problem, bringing mathematicians one step closer to understanding the Riemann hypothesis and the distribution of prime numbers.

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.

Mathematicians and computer scientists answered major questions in topology, set theory and even physics, even as computers continued to grow more capable.

The Chinese remainder theorem is an ancient and powerful extension of the simple math of least common multiples.

Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.

New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs.

Legend says the Chinese military once used a mathematical ruse to conceal its troop numbers. The technique relates to many deep areas of modern math research.

Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.

Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program.