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# Mathematics

## Latest Articles

### Grad Students Find Inevitable Patterns in Big Sets of Numbers

A new proof marks the first progress in decades on a problem about how order emerges from disorder.

### How Does Math Keep Secrets?

Cryptography is the thread that connects Julius Caesar, World War II and quantum computing, and it now lies under nearly every part of modern life. In this week’s episode, computer scientist Boaz Barak and co-host Janna Levin discuss the past and future of secrecy.

### Monumental Proof Settles Geometric Langlands Conjecture

In work that has been 30 years in the making, mathematicians have proved a major part of a profound mathematical vision called the Langlands program.

### What Are Sheaves?

These metaphorical gardens have become central objects in modern mathematics.

### ‘Sensational’ Proof Delivers New Insights Into Prime Numbers

The proof creates stricter limits on potential exceptions to the famous Riemann hypothesis.

### How America’s Fastest Swimmers Use Math to Win Gold

Number theorist Ken Ono is teaching Olympians to swim more efficiently.

### What Can Tiling Patterns Teach Us?

If you cover a surface with tiles, repetitive patterns always emerge — or do they? In this week’s episode, mathematician Natalie Priebe Frank and co-host Janna Levin discuss how recent breakthroughs in tiling can unlock structural secrets in the natural world.

### Why Is This Shape So Terrible to Pack?

Two mathematicians have proved a long-standing conjecture that is a step on the way toward finding the worst shape for packing the plane.

### How the Square Root of 2 Became a Number

Useful mathematical concepts, like the number line, can linger for millennia before they are rigorously defined.