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

What’s easy for a computer to do, and what’s almost impossible? Those questions form the core of computational complexity. We present a map of the landscape.

If and when physicists are able to pin down the metal content of the sun, that number could upend much of what we thought we knew about the evolution and life span of stars.

A simple, step-by-step breakdown of two “perfect” math proofs.

The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge.

It’s “a definitive study for all time, like writing the final book,” says one researcher who’s mapping out new classes of geometric structures.

Big advances in math can happen when mathematicians move ideas into areas where they seem like they shouldn’t belong.

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