## Latest Articles

### 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.

### She 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.

### Mathematicians Cross the Line to Get to the Point

A new paper establishes a long-conjectured bound about the size of the overlap between sets of lines and points.

### The Biggest Smallest Triangle Just Got Smaller

A new proof breaks a decades-long drought of progress on the problem of estimating the size of triangles created by cramming points into a square.

### New Proof Shows That ‘Expander’ Graphs Synchronize

The proof establishes new conditions that cause connected oscillators to sway in sync.