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In math, sometimes the most common things are the hardest to find.

The 19th-century discovery of numbers called “quaternions” gave mathematicians a way to describe rotations in space, forever changing physics and math.

An upstart field that simplifies complex shapes is letting mathematicians understand how those shapes depend on the space in which you visualize them.

To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape.

The physicist-mathematician Miranda Cheng is working to harness a mysterious connection between string theory, algebra and number theory.

Greatness was always expected of Ken Ono. But as he struggled with his parents’ expectations, he found solace and inspiration in the life of two-time college dropout — and mathematical genius — Srinivasa Ramanujan, the subject of the film *The Man Who Knew Infinity*.

Researchers are on the trail of a mysterious connection between number theory, algebra and string theory.