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group theory

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

The ‘Useless’ Perspective That Transformed Mathematics

June 9, 2020

Representation theory was initially dismissed. Today, it’s central to much of mathematics.


The Map of Mathematics

February 13, 2020

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

Art for "A Proof About Where Symmetries Can’t Exist"

A Proof About Where Symmetries Can’t Exist

October 23, 2018

In a major mathematical achievement, a small team of researchers has proven Zimmer’s conjecture.

Photo of Cohl Furey
fundamental physics

The Peculiar Math That Could Underlie the Laws of Nature

July 20, 2018

New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part numbers called “octonions.”

Pariah moonshine
number theory

Mathematicians Find Moonshine Link for Pariah Symmetries

September 22, 2017

A type of symmetry so unusual that it was called a “pariah” turns out to have deep connections to number theory.

fidget spinners
Quantized Academy

Symmetry, Algebra and the Monster

August 17, 2017

To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape.

Colorful illustration of 5 plants with their roots exposed. Each plant forms the shape of a number,
number theory

New Number Systems Seek Their Lost Primes

March 2, 2017

For centuries, mathematicians tried to solve problems by adding new values to the usual numbers. Now they’re investigating the unintended consequences of that tinkering.


Moonshine Master Toys With String Theory

August 4, 2016

The physicist-mathematician Miranda Cheng is working to harness a mysterious connection between string theory, algebra and number theory.


A Life in Games

August 28, 2015

The mathematician John Horton Conway’s myriad accomplishments — including the Game of Life, sprouts and the surreal numbers — are the product of a mind at play.