Probability & dynamics2014
Changing scale to understand repeated motion
A simple repeated rule can produce stability or chaos; renormalization compares its behavior at different scales to uncover the deeper organization.
The storyAn award edition
2014
Different contributions. A shared moment in mathematics.
4 medalists — explore each contribution below.
Number theory2014
Counting arithmetic through geometric representations
Integer equations can look unrelated one by one; organizing them as geometric objects makes it possible to study their average behavior.
The storyAnalysis & PDEs2014
Giving meaning to equations driven by rough noise
Some random-growth equations contain products too irregular for ordinary calculus; regularity structures provide a precise language for making them meaningful.
The storyGeometry & topology2014
Counting loops by exploring the space of surfaces
A curved surface contains infinitely many closed geodesics; understanding the family of all surface geometries reveals a surprising law for simple loops.
The story