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geometry

Art for "Three Decades Later, Mystery Numbers Explained"
Abstractions blog

Three Decades Later, Mystery Numbers Explained

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

Illustration for "Mathematicians Explore Mirror Link Between Two Geometric Worlds"
geometry

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.

Illustration of pentagon tiling
Quantized Academy

The (Math) Problem With Pentagons

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

Michael Assis folding a large, beige sheet or Miura-ori
statistical physics

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.

Classes of geometric structures
Abstractions blog

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.

Heavenly billiards
geometry

New Shapes Solve Infinite Pool-Table Problem

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

Maryam Mirzakhani
Quantized Columns

The Beautiful Mathematical Explorations of Maryam Mirzakhani

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

Marjorie Rice
Abstractions blog

Marjorie Rice’s Secret Pentagons

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

15 pentagon tessellations
geometry

Pentagon Tiling Proof Solves Century-Old Math Problem

A French mathematician has completed the classification of all convex pentagons, and therefore all convex polygons, that tile the plane.