Symmetry

Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space.

In a world seemingly filled with chaos, physicists have discovered new forms of synchronization and are learning how to predict and control them.

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

Zeta values seem to connect distant geometric worlds. In a new proof, mathematicians finally explain why.

Decades after physicists happened upon a stunning mathematical coincidence, researchers are getting close to understanding the link between two seemingly unrelated geometric universes.

A famously difficult mathematical problem resisted solution for over 40 years. Mathematicians have finally resolved it by following an intuition that links number theory to physics.

An eminent mathematician reveals that his advances in the study of millennia-old mathematical questions owe to concepts derived from physics.

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.