Mathematics

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.

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

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

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

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

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

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.

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