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

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

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

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

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

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.

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

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.

Researchers are on the trail of a mysterious connection between number theory, algebra and string theory.