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# geometry

## Latest Articles

### A Proof About Where Symmetries Can’t Exist

In a major mathematical achievement, a small team of researchers has proven Zimmer’s conjecture.

### Why Mathematicians Can’t Find the Hay in a Haystack

In math, sometimes the most common things are the hardest to find.

### Tinkertoy Models Produce New Geometric Insights

An upstart field that simplifies complex shapes is letting mathematicians understand how those shapes depend on the space in which you visualize them.

### A Master of Numbers and Shapes Who Is Rewriting Arithmetic

The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.”

### Three Decades Later, Mystery Numbers Explained

Zeta values seem to connect distant geometric worlds. In a new proof, mathematicians finally explain why.

### Mathematicians Explore Mirror Link Between Two Geometric Worlds

Decades after physicists happened upon a stunning mathematical coincidence, researchers are getting close to understanding the link between two seemingly unrelated geometric universes.

### The (Math) Problem With Pentagons

Triangles fit effortlessly together, as do squares. When it comes to pentagons, what gives?

### The Atomic Theory of Origami

By reimagining the kinks and folds of origami as atoms in a lattice, researchers are uncovering strange behavior hiding in simple structures.

### Why Mathematicians Like to Classify Things

It’s “a definitive study for all time, like writing the final book,” says one researcher who’s mapping out new classes of geometric structures.