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# Group theory

## Latest Articles

### The Simple Math Behind the Mighty Roots of Unity

Solutions to the simplest polynomial equations — called “roots of unity” — have an elegant structure that mathematicians still use to study some of math’s greatest open questions.

### Galois Groups and the Symmetries of Polynomials

By focusing on relationships between solutions to polynomial equations, rather than the exact solutions themselves, Évariste Galois changed the course of modern mathematics.

### New Shape Opens ‘Wormhole’ Between Numbers and Geometry

Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program.

### Amie Wilkinson Sees the Dynamic Chaos in Puff Pastry

To a dynamicist like Amie Wilkinson, understanding the universe is about knowing all the right moves.

### 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.”