## Latest Articles

### ‘Groups’ Underpin Modern Math. Here’s How They Work.

What do the integers have in common with the symmetries of a triangle? In the 19th century, mathematicians invented groups as an answer to this question.

### Grad Students Find Inevitable Patterns in Big Sets of Numbers

A new proof marks the first progress in decades on a problem about how order emerges from disorder.

### In Highly Connected Networks, There’s Always a Loop

Mathematicians show that graphs of a certain common type must contain a route that visits each point exactly once.

### Geometers Engineer New Tools to Wrangle Spacecraft Orbits

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

### 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.

### Maze Proof Establishes a ‘Backbone’ for Statistical Mechanics

Four mathematicians have estimated the chances that there’s a clear path through a random maze.

### The Mathematician Who Finds the Poetry in Math and the Math in Poetry

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

### ‘A-Team’ of Math Proves a Critical Link Between Addition and Sets

A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.”

### In the ‘Wild West’ of Geometry, Mathematicians Redefine the Sphere

High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible.