Geometry

This past October, dozens of mathematicians gathered in Pasadena to create the third version of “Kirby’s list” — a compendium of the most important unsolved problems in the field.

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

Terence Tao, who has been called the “Mozart of Mathematics,” wrote an essay in 2007 about the common ingredients in “good” mathematical research. In this episode, the Fields Medalist joins Steven Strogatz to revisit the topic.

Two mathematicians have shown that origami can, in principle, be used to perform any possible computation.

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.

The links between math, music and art have been explored for thousands of years. Sarah Hart is now turning a mathematical eye to literature.

Researchers are discovering the shortest knots and fattest Möbius strips, among other “optimal shapes.”

Landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.

Mathematicians prove a theorem that illuminates the geometry of universes with tiny amounts of mass.