Mathematics

Four mathematicians broke a 75-year-old record by finding a denser way to pack high-dimensional spheres.

Topologists prove two new results that bring some order to the confoundingly difficult study of four-dimensional shapes.

Mathematicians think abstract tools from a field called symplectic geometry might help with planning missions to far-off moons and planets.

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.

Mathematicians are using topological abstractions to find places where it’s hard to vote.

Recursion builds bridges between ideas from across different math classes and illustrates the power of creative mathematical thinking.

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.