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Ramsey theory

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.

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.

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.
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.

A surprising new proof is helping to connect the mathematics of infinity to the physical world.
foundations of mathematics

Mathematicians Bridge Finite-Infinite Divide

A surprising new proof is helping to connect the mathematics of infinity to the physical world.