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No one knows how to find the smallest shape that can cover all other shapes of a certain width. But high school geometry is getting us closer to an answer.

Mathematicians and computer scientists made big progress in number theory, graph theory, machine learning and quantum computing, even as they reexamined our fundamental understanding of mathematics and neural networks.

Researchers have spent centuries looking for a scenario in which the Euler fluid equations fail. Now a mathematician has finally found one.

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.