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# geometry

## Latest Articles

### Number of Distances Separating Points Has a New Bound

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

### Merging Fields, Mathematicians Go the Distance on Old Problem

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

### Michel Talagrand Wins Abel Prize for Work Wrangling Randomness

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

### ‘The Rest of the World Disappears’: Claire Voisin on Mathematical Creativity

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

### Never-Repeating Tiles Can Safeguard Quantum Information

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

### A New Agenda for Low-Dimensional Topology

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.

### Unfolding the Mysteries of Polygonal Billiards

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

### What Makes for ‘Good’ Mathematics?

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.

### How to Build an Origami Computer

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