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Ramsey theory

An illustration of a woman sitting in a field embroidering a flower pattern. Around her grow wildflowers that appear to be randomly distributed but whose colors reveal a hidden pattern.
number theory

Mathematicians Catch a Pattern by Figuring Out How to Avoid It

November 25, 2019

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

Abstractions blog

Mathematicians Calculate How Randomness Creeps In

November 12, 2019

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

Photo of a yellow sunflower against a yellow background.
Abstractions blog

Mathematicians Begin to Tame Wild ‘Sunflower’ Problem

October 21, 2019

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.

Paul Erdős
Abstractions blog

Cash for Math: The Erdős Prizes Live On

June 5, 2017

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
combinatorics

A Puzzle of Clever Connections Nears a Happy End

May 30, 2017

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

A Simple Visual Proof of a Powerful Idea

April 13, 2017

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

combinatorics

Simple Set Game Proof Stuns Mathematicians

May 31, 2016

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.

foundations of mathematics

Mathematicians Bridge Finite-Infinite Divide

May 24, 2016

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