Geometry

Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite.

Mathematicians have proved that a random process applied to a random surface will yield consistent patterns.

Amie Wilkinson searches for exotic examples of the mathematical structures that describe change.

A little high school geometry can help you understand the basic math behind movie recommendation engines.

Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space.

A founder of modern geometric analysis who produced “some of the most dramatic advances in mathematics in the last 40 years,” Uhlenbeck is the first woman to be awarded this top honor.

A pair of mathematicians has built on an obscure, 30-year-old mathematical theory to show that soap-filmlike minimal surfaces appear abundantly in a wide range of shapes.

A new proof shows why an uncountably infinite number of Möbius strips will never fit into a three-dimensional space.

Through exacting geometric calculations, Philip Gibbs has found the smallest known cover for any possible shape.