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Mathematics

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

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

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.

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

The Mathematics of Juggling

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

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

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.

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

How to Use a Sphere to Talk to Mars

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

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.