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# Langlands program

## Latest Articles

### Monumental Proof Settles Geometric Langlands Conjecture

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.

### What Are Sheaves?

These metaphorical gardens have become central objects in modern mathematics.

### A Rosetta Stone for 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.

### Elliptic Curve ‘Murmurations’ Found With AI Take Flight

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

### The Year in Math

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

### Echoes of Electromagnetism Found in Number Theory

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

### Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math

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

### Elliptic Curves Yield Their Secrets in a New Number System

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

### What Is the Langlands Program?

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