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Mathematician Disproves 80-Year-Old Algebra Conjecture
Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses.
The ‘Useless’ Perspective That Transformed Mathematics
Representation theory was initially dismissed. Today, it’s central to much of mathematics.
The Map of Mathematics
Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.
A Proof About Where Symmetries Can’t Exist
In a major mathematical achievement, a small team of researchers has proven Zimmer’s conjecture.
The Peculiar Math That Could Underlie the Laws of Nature
New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part numbers called “octonions.”
Mathematicians Find Moonshine Link for Pariah Symmetries
A type of symmetry so unusual that it was called a “pariah” turns out to have deep connections to number theory.
Symmetry, Algebra and the Monster
To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape.
New Number Systems Seek Their Lost Primes
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
The physicist-mathematician Miranda Cheng is working to harness a mysterious connection between string theory, algebra and number theory.