Mathematics

John Pardon sees connections between different areas of math that others don’t. For that vision, he’s now been awarded a Fields Medal.

Before he won a Fields Medal for his pioneering work balancing randomness and order, Yu Deng first had to achieve equilibrium in his own life.

Decades ago, Paul Erdős used randomness to illuminate the vast and weird world of networks. Now mathematicians are making his technique even more powerful.

Lauren Williams tells 'The Joy of Why' how studying a fundamental object in algebraic combinatorics led to a career full of surprises.

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.

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.