Erica Klarreich

Contributing Writer

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.

Illustration of a salamander
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.

Illustration: boxing gloves
Abstractions blog

Graph Isomorphism Vanquished — Again

Just five days after posting a retraction, László Babai announced that he had fixed the error in his landmark graph isomorphism algorithm.

Illustration: boxing glove & graph
Abstractions blog

Complexity Theory Problem Strikes Back

The legendary graph isomorphism problem may be harder than a 2015 result seemed to suggest.

Abstractions blog

All Is Not Fair in Cake-Cutting and Math

When divvying something up, there’s more than one way to define what’s fair.

algorithms

How to Cut Cake Fairly and Finally Eat It Too

Computer scientists have come up with a bounded algorithm that can fairly divide a cake among any number of people.

profile

The Oracle of Arithmetic

At 28, Peter Scholze is uncovering deep connections between number theory and geometry.

combinatorics

Simple Set Game Proof Stuns Mathematicians

A new series of papers has settled a long-standing question related to the popular game in which players seek patterned sets of three cards.

geometry

Sphere Packing Solved in Higher Dimensions

The Ukrainian mathematician Maryna Viazovska has solved the centuries-old sphere-packing problem in dimensions eight and 24.