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Mathematics

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.

Kaisa Matomäki
Q&A

Kaisa Matomäki Dreams of Primes

Kaisa Matomäki has proved that properties of prime numbers over long intervals hold over short intervals as well. The techniques she uses have transformed the study of these elusive numbers.

Nash equilibrium maze
Game Theory

In Game Theory, No Clear Path to Equilibrium

John Nash’s notion of equilibrium is ubiquitous in economic theory, but a new study shows that it is often impossible to reach efficiently.

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.

Graph
Abstractions blog

The Tricky Translation of Mathematical Ideas

Big advances in math can happen when mathematicians move ideas into areas where they seem like they shouldn’t belong.

June Huh at the Institute for Advanced Study in Princeton, N.J.
algebraic geometry

A Path Less Taken to the Peak of the Math World

June Huh thought he had no talent for math until a chance meeting with a legendary mind. A decade later, his unorthodox approach to mathematical thinking has led to major breakthroughs.