Mathematics

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.

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

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.

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

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