Geometry

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.”

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

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

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

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

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.

Two “rare jewels” have illuminated a mysterious multidimensional object that connects a huge variety of mathematical work.

After her untimely death, Maryam Mirzakhani’s life is best remembered through her work.

A California housewife who in the 1970s discovered four new types of tessellating pentagons is dead at 94.