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# Ramsey theory

## Latest Articles

### Disorder Persists in Larger Graphs, New Math Proof Finds

David Conlon and Asaf Ferber have raised the lower bound for multicolor “Ramsey numbers,” which quantify how big graphs can get before patterns inevitably emerge.

### ‘Rainbows’ Are a Mathematician’s Best Friend

“Rainbow colorings” recently led to a new proof. It’s not the first time they’ve come in handy.

### Rainbow Proof Shows Graphs Have Uniform Parts

Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones.

### Mathematicians Catch a Pattern by Figuring Out How to Avoid It

We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”

### Mathematicians Calculate How Randomness Creeps In

Mathematicians have figured out exactly how many moves it takes to randomize a 15 puzzle.

### Mathematicians Begin to Tame Wild ‘Sunflower’ Problem

A major advance toward solving the 60-year-old sunflower conjecture is shedding light on how order begins to appear as random systems grow in size.

### 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.

### 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.

### 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.