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Langlands program

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What Is the Langlands Program?

By Alex Kontorovich
June 1, 2022
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The Langlands program provides a beautifully intricate set of connections between various areas of mathematics, pointing the way toward novel solutions for old problems.

2021 in Review

The Year in Math and Computer Science

By Bill Andrews
December 23, 2021
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Mathematicians and computer scientists answered major questions in topology, set theory and even physics, even as computers continued to grow more capable.

Color photo of Ana Caraiani in a black coat standing on a bridge
Q&A

The Mathematician Who Delights in Building Bridges

By Steve Nadis
November 17, 2021
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Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.

Animated illustration showing multiple permutations of colorful letters
group theory

Galois Groups and the Symmetries of Polynomials

By Allison Whitten
August 3, 2021
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By focusing on relationships between solutions to polynomial equations, rather than the exact solutions themselves, Évariste Galois changed the course of modern mathematics.

Illustration showing geometric figures at left connected via wormhole to numbers at right.
Langlands program

New Shape Opens ‘Wormhole’ Between Numbers and Geometry

By Kevin Hartnett
July 19, 2021
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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.

2020 in Review

The Year in Math and Computer Science

By Bill Andrews
December 23, 2020
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Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

A visualization of the tower formed by the 3-adic numbers
Abstractions blog

An Infinite Universe of Number Systems

By Kelsey Houston-Edwards
October 19, 2020
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The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory.

Diagram showing a colorful visualization of the simple Lie group
Abstractions blog

The ‘Useless’ Perspective That Transformed Mathematics

By Kevin Hartnett
June 9, 2020
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Representation theory was initially dismissed. Today, it’s central to much of mathematics.

Langlands program

‘Amazing’ Math Bridge Extended Beyond Fermat’s Last Theorem

By Erica Klarreich
April 6, 2020
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Mathematicians have figured out how to expand the reach of a mysterious bridge connecting two distant continents in the mathematical world.


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