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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.”

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.

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.

Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.