topology

In all bilaterally symmetrical animals, from humans down to simple worms, nerves cross from one side of the body to the opposite side of the brain. Geometry may explain why.

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

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.

Mathematicians have struggled to understand the moduli space of graphs. A new paper uses tools from physics to peek inside.

A new proof shows that a knot some thought would contradict the famed slice-ribbon conjecture doesn’t.

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.

A quantum approach to data analysis that relies on the study of shapes will likely remain an example of a quantum advantage — albeit for increasingly unlikely scenarios.