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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.
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.

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

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

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.
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.

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.
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.

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.
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.

Powerful new quantitative tools are now available to combat partisan bias in the drawing of voting districts.
applied math

How to Quantify (and Fight) Gerrymandering

Powerful new quantitative tools are now available to combat partisan bias in the drawing of voting districts.

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

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

A Long-Sought Proof, Found and Almost Lost

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