Mathematics

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.

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

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

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

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

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.

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.

These metaphorical gardens have become central objects in modern mathematics.

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