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# Geometry

## Latest Articles

### An Old Conjecture Falls, Making Spheres a Lot More Complicated

The telescope conjecture gave mathematicians a handle on ways to map one sphere to another. Now that it has been disproved, the universe of shapes has exploded.

### Mathematicians Solve Long-Standing Coloring Problem

A new result shows how much of the plane can be colored by points that are never exactly one unit apart.

### New Proof Threads the Needle on a Sticky Geometry Problem

A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures.

### How Math Achieved Transcendence

Transcendental numbers include famous examples like e and π, but it took mathematicians centuries to understand them.

### The Simple Geometry That Predicts Molecular Mosaics

By treating molecules as geometric tessellations, scientists devised a new way to forecast how 2D materials might self-assemble.

### Math Patterns That Go On Forever but Never Repeat

Simple math can help explain the complexities of the newly discovered aperiodic monotile.

### Why the Brain’s Connections to the Body Are Crisscrossed

In all bilaterally symmetrical animals, from humans down to simple worms, nerves cross from one side of the body to the opposite side of the brain. Geometry may explain why.

### A New Kind of Symmetry Shakes Up Physics

So-called “higher symmetries” are illuminating everything from particle decays to the behavior of complex quantum systems.

### Hobbyist Finds Math’s Elusive ‘Einstein’ Tile

The surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’t be made to fill it in a repeating way.