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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

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.

Abstractions blog

The Mathematics of Juggling

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

Abstractions blog

A Simple Visual Proof of a Powerful Idea

Ramsey’s theorem predicts a surprising (and useful) consistency in the organization of graphs. Here’s a simple visual proof of how it works.

Abstractions blog

How to Use a Sphere to Talk to Mars

To avoid garbled messages, mathematicians might translate them into geometric form.


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.

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: diver searching for new math
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.

Thomas Royen at his home in Schwalbach am Taunus, Germany.

A Long-Sought Proof, Found and Almost Lost

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