Dynamical systems

In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation for modern geometry and physics.

Earth’s climate is chaotic and volatile. Climate change is simple and predictable. How can both be true?

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

A simple, widely used mathematical technique can finally be applied to boundlessly complex problems.

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

Simple rules in simple settings continue to puzzle mathematicians, even as they devise intricate tools to analyze them.

The surprisingly subtle geometry of a familiar game shows how quickly math gets complicated.

For decades, a small group of mathematicians has patiently unraveled the mystery of what was once math’s most popular picture. Their story shows how technology transforms even the most abstract mathematical landscapes.

A series of new papers describes how to fully characterize key dynamical systems with relatively little data.