Geometry

Mathematicians have struggled to prove Falconer’s Conjecture, a simple, but far-reaching, hypothesis about the distances between points. They’re finally getting close.

Mathematicians have illuminated what sets of points can look like if the distances between them are all whole numbers.

The French mathematician spent decades developing a set of tools now widely used for taming random processes.

The recipient of the 2024 Crafoord Prize in Mathematics discusses math as art, math as language, and math as abstract thought.

Two researchers have proved that Penrose tilings, famous patterns that never repeat, are mathematically equivalent to a kind of quantum error correction.

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.