Karen Uhlenbeck

MATHEMATICS
The Equations of Nature

Throw a ball in the air - where does it go? Put a pot on the stove - how does the heat spread? Blow a soap bubble - what shape will it take? Flip a switch and... a light turns on! All of these phenomena are governed by simple differential equations that have been known and studied for over 100 years. Nature at a small scale - electrons, protons, and other particles - is governed by more complicated laws; these also involve differential equations. Such equations lie at the heart of Karen Uhlenbeck's work. Her discoveries have shed light on the solutions to these equations and have found applications in both geometry and physics.

A soap film on a wire frame naturally assumes the form of a curved surface. This is what negative curvature looks like.