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algebraic geometry

June Huh with a polyhedron.
2022 Fields and Abacus Medals

He Dropped Out to Become a Poet. Now He’s Won a Fields Medal.

By Jordana Cepelewicz
July 5, 2022
Read Later

June Huh wasn’t interested in mathematics until a chance encounter during his sixth year of college. Now his profound insights connecting combinatorics and geometry have led to math’s highest honor.

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
Read Later

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.

Mathematician Lauren Williams standing in front of a whiteboard that has mathematics written on it.
combinatorics

A Mathematician’s Unanticipated Journey Through the Physical World

By Kevin Hartnett
December 16, 2020
Read Later

Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.

Q&A

Conducting the Mathematical Orchestra From the Middle

By Rachel Crowell
September 2, 2020
Read Later

Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.

Visualization of the distribution of prime numbers in the shape of colorful dots in a hexagonal pattern
Abstractions blog

Mathematicians Will Never Stop Proving the Prime Number Theorem

By Susan D'Agostino
July 22, 2020
Read Later

Why do mathematicians enjoy proving the same results in different ways?

Multimedia

The Map of Mathematics

By Kevin Hartnett
February 13, 2020
Read Later

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

Animation showing two sets of tangrams cycling between identical squares and different shapes.
geometry

Mathematicians Cut Apart Shapes to Find Pieces of Equations

By Kevin Hartnett
October 31, 2019
Read Later

New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.

foundations of mathematics

With Category Theory, Mathematics Escapes From Equality

By Kevin Hartnett
October 10, 2019
Read Later

Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.

Colored spheres arranged in pairs.
prime numbers

Big Question About Primes Proved in Small Number Systems

By Kevin Hartnett
September 26, 2019
Read Later

The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems.


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