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# Mathematics

## Latest Articles

### ‘Groups’ Underpin Modern Math. Here’s How They Work.

What do the integers have in common with the symmetries of a triangle? In the 19th century, mathematicians invented groups as an answer to this question.

### Perplexing the Web, One Probability Puzzle at a Time

The mathematician Daniel Litt has driven social media users to distraction with a series of simple-seeming but counterintuitive probability puzzles.

### Mathematicians Prove Hawking Wrong About the Most Extreme Black Holes

For decades, extremal black holes were considered mathematically impossible. A new proof reveals otherwise.

### The Geometric Tool That Solved Einstein’s Relativity Problem

Tensors are used all over math and science to reveal hidden geometric truths. What are they?

### 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.