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geometry

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.

Abstractions blog

How to Use a Sphere to Talk to Mars

To avoid garbled messages, mathematicians might translate them into geometric form.

Icosahedron
geometry

A New Path to Equal-Angle Lines

Equiangular lines are an elemental part of geometry. Mathematicians have discovered a tighter limit on the number of such lines that exist in every dimension.

Illustration: diver searching for new math
Quantized Columns

Quantum Questions Inspire New Math

In order to fully understand the quantum world, we may have to develop a new realm of mathematics.

Thomas Royen at his home in Schwalbach am Taunus, Germany.
statistics

A Long-Sought Proof, Found and Almost Lost

When a German retiree proved a famous long-standing mathematical conjecture, the response was underwhelming.