Mathematics

A decades-old proof showed that seven shuffles are enough to mix up a deck of cards. But it requires you to cut the deck with the precision of a professional magician. A new proof gets around that obstacle.

With automated proof-checkers, a problem can be broken up into small chunks, solved bit-by-bit, then reassembled with confidence that every piece is correct. For some, this heralds a new area in mathematical research.

The podcast returns with 12 all-new episodes that explore the biggest questions in basic science and mathematics.

By replacing the most fundamental concept in topology, Peter Scholze and Dustin Clausen are taking the first step in a far bigger program to understand why numbers behave the way they do.

Grothendieck is revered in the world of math; outside of it, he’s known for his unusual life, if he’s known at all. But what were his actual mathematical contributions?

At 25, Kurt Gödel proved there can never be a mathematical “theory of everything.” Columnist Natalie Wolchover explores the implications.

A graduate student recently harnessed the complexity of mathematical proofs to create a powerful new tool in cryptography.

Ultrafinitism, a philosophy that rejects the infinite, has long been dismissed as mathematical heresy. But it is also producing new insights in math and beyond.

Zermelo-Fraenkel set theory is so widely accepted that modern mathematicians hardly think about it. But believing in its core principles didn’t come easily.