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# Mathematics

## Latest Articles

### 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.

### How Is Science Even Possible?

How are scientists able to crack fundamental questions about nature and life? How does math make the complex cosmos understandable? In this episode, the physicist Nigel Goldenfeld and co-host Steven Strogatz explore the deep foundations of the scientific process.

### In Highly Connected Networks, There’s Always a Loop

Mathematicians show that graphs of a certain common type must contain a route that visits each point exactly once.