Langlands program

In work that has been 30 years in the making, mathematicians have proved a major part of a profound mathematical vision called the Langlands program.

These metaphorical gardens have become central objects in modern mathematics.

In 1940 André Weil wrote a letter to his sister, Simone, outlining his vision for translating between three distinct areas of mathematics. Eighty years later, it still animates many of the most exciting developments in the field.

Mathematicians are working to fully explain unusual behaviors uncovered using artificial intelligence.

Landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.

A new magnum opus posits the existence of a hidden mathematical link akin to the connection between electricity and magnetism.

Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?

Ana Caraiani and James Newton have extended an important result in number theory to the imaginary realm.

The Langlands program provides a beautifully intricate set of connections between various areas of mathematics, pointing the way toward novel solutions for old problems.