Geometry

So-called “higher symmetries” are illuminating everything from particle decays to the behavior of complex quantum systems.

The surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’t be made to fill it in a repeating way.

The prize-winning geometer feels most fulfilled when exploring the fertile ground where constraint meets creation.

Can mathematics handle things that are essentially the same without being exactly equal? Category theorist Eugenia Cheng and host Steven Strogatz discuss the power and pleasures of abstraction.

Lek-Heng Lim uses tools from algebra, geometry and topology to answer questions in machine learning.

Is it possible to fill space “cubically” with shapes that act like spheres? A proof at the intersection of geometry and theoretical computer science says yes.

Whether you’re passing secret notes in class or downloading images from a space probe, Reed-Solomon codes offer an ingenious way to embed information and correct for errors.

Four Fields Medals were awarded for major breakthroughs in geometry, combinatorics, statistical physics and number theory, even as mathematicians continued to wrestle with how computers are changing the discipline.

Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong.