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algebraic geometry

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

Multimedia

The Map of Mathematics

By Kevin Hartnett
February 13, 2020
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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
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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
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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
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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.

Portrait of Carolina Araujo at IMPA in Brazil
Q&A

A Movement to Close the Gender Gap in Mathematics

By Siobhan Roberts
January 22, 2019
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The Brazilian mathematician Carolina Araujo, who calls herself “a bit of an anarchist,” is organizing meetings and building a support network to study and solve the problems women face in mathematics.

Abstractions blog

New Proof Shows Infinite Curves Come in Two Types

By Kevin Hartnett
November 7, 2018
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Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.


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