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# topology

## Latest Articles

### Unfolding the Mysteries of Polygonal Billiards

The surprisingly subtle geometry of a familiar game shows how quickly math gets complicated.

### What Makes for ‘Good’ Mathematics?

Terence Tao, who has been called the “Mozart of Mathematics,” wrote an essay in 2007 about the common ingredients in “good” mathematical research. In this episode, the Fields Medalist joins Steven Strogatz to revisit the topic.

### Mathematicians Identify the Best Versions of Iconic Shapes

Researchers are discovering the shortest knots and fattest Möbius strips, among other “optimal shapes.”

### In the ‘Wild West’ of Geometry, Mathematicians Redefine the Sphere

High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible.

### The Mathematician Who Sculpted the Shape of Space

Eugenio Calabi, who died on September 25, conceived of novel geometric objects that later became fundamental to string theory.

### 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.