Partial differential equations

Focus, commitment, and insight resulted in a “once in a century” proof. Hong Wang is now just the third woman to win 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.

Mathematicians finally understand the behavior of an important class of differential equations that describe everything from water pressure to oxygen levels in human tissues.

Mathematicians have broken through a long-standing barrier in the study of “minimizing surfaces,” which play an important role in both math and physics.

The math of even the simplest ocean waves is notoriously uncooperative. A team of Italian mathematicians has made major advances toward understanding it.

Tipping points in our climate predictions are both wildly dramatic and wildly uncertain. Can mathematicians make them useful?

The proof, known to be so hard that a mathematician once offered 10 martinis to whoever could figure it out, connects quantum mechanics to infinitely intricate mathematical structures.

A team of mathematicians based in Vienna is developing tools to extend the scope of general relativity.

By mathematically proving how individual molecules create the complex motion of fluids, three mathematicians have illuminated why time can’t flow in reverse.