Langlands program

Hidden correspondences hint at a deeper structure to the mathematical universe. Our columnist unpacks one of those connections and asks mathematicians what they might mean.

By extending the scope of the key insight behind Fermat’s Last Theorem, four mathematicians have made great strides toward building a “grand unified theory” of math.

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.

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.