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

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

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 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.

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.

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