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Mathematics

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.

Paul Erdős
Abstractions blog

Cash for Math: The Erdős Prizes Live On

Paul Erdős placed small bounties on hundreds of unsolved math problems. Over the past 20 years, only a handful have been claimed.

Combinatorics and constellations
combinatorics

A Puzzle of Clever Connections Nears a Happy End

The three young friends who devised the “happy ending” problem would become some of the most influential mathematicians of the 20th century, but were never able to solve their own puzzle. Now it receives its first big breakthrough.

Juggler
Abstractions blog

The Mathematics of Juggling

Juggling has advanced enormously in recent decades, thanks in part to the mathematical study of possible patterns.