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The Map of Mathematics

February 13, 2020

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

An illustration of a woman sitting in a field embroidering a flower pattern. Around her grow wildflowers that appear to be randomly distributed but whose colors reveal a hidden pattern.
number theory

Mathematicians Catch a Pattern by Figuring Out How to Avoid It

November 25, 2019

We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”

Art for "Color Me Polynomial"
Quantized Academy

Color Me Polynomial

August 13, 2019

Polynomials aren’t just exercises in abstraction. They’re good at illuminating structure in surprising places.

Illustration of lock with polynomials surrounding it
Abstractions blog

Mathematicians Seal Back Door to Breaking RSA Encryption

December 17, 2018

Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.

Art for "In the Universe of Equations, Virtually All Are Prime"
number theory

In the Universe of Equations, Virtually All Are Prime

December 10, 2018

Equations, like numbers, cannot always be split into simpler elements.

Photo of Dr. Peter Scholze
2018 Fields Medal and Nevanlinna Prize

A Master of Numbers and Shapes Who Is Rewriting Arithmetic

August 1, 2018

The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.”

Art for "A Classical Math Problem Gets Pulled Into the Modern World"

A Classical Math Problem Gets Pulled Into the Modern World

May 23, 2018

A century ago, the great mathematician David Hilbert posed a probing question in pure mathematics. A recent advance in optimization theory is bringing Hilbert’s work into a world of self-driving cars.

June Huh at the Institute for Advanced Study in Princeton, N.J.
algebraic geometry

A Path Less Taken to the Peak of the Math World

June 27, 2017

June Huh thought he had no talent for math until a chance meeting with a legendary mind. A decade later, his unorthodox approach to mathematical thinking has led to major breakthroughs.

Illustration: boxing gloves
Abstractions blog

Graph Isomorphism Vanquished — Again

January 14, 2017

Just five days after posting a retraction, László Babai announced that he had fixed the error in his landmark graph isomorphism algorithm.