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Mathematicians regard the Collatz conjecture as a quagmire and warn each other to stay away. But now Terence Tao has made more progress than anyone in decades.

Many of us are drawn to beauty in mathematics. But is that the way nature really works?

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

Readers’ modifications of a bean machine showed how deterministic laws are capable of producing random-seeming behavior.

Three physicists stumbled across an unexpected relationship between some of the most ubiquitous objects in math.

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

Looking for answers in infinite space is hard. High school math can help narrow your search.

New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.

Researchers have discovered a surprising mathematical relationship in the brain’s representations of sensory information, with possible applications to AI research.