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# topology

## Latest Articles

### An Old Conjecture Falls, Making Spheres a Lot More Complicated

The telescope conjecture gave mathematicians a handle on ways to map one sphere to another. Now that it has been disproved, the universe of shapes has exploded.

### How Quantum Physicists Explained Earth's Weather Patterns

By treating Earth as a topological insulator — a state of quantum matter — physicists found a powerful explanation for the movements of the planet’s air and seas.

### Flow Proof Helps Mathematicians Find Stability in Chaos

A series of new papers describes how to fully characterize key dynamical systems with relatively little data.

### Why the Brain’s Connections to the Body Are Crisscrossed

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.

### A New Symmetry Shakes Up Physics

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

### Emmy Murphy Is a Mathematician Who Finds Beauty in Flexibility

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

### Is There Math Beyond the Equal Sign?

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.

### An Applied Mathematician With an Unexpected Toolbox

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

### Quantum Field Theory Pries Open Mathematical Puzzle

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