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Urmila Mahadev spent eight years in graduate school solving one of the most basic questions in quantum computation: How do you know whether a quantum computer has done anything quantum at all?

Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years.

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

How much stock should we put in mathematical models of evolution that have not been validated by rigorous empirical data?

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.

Quanta’s In Theory video series returns with an exploration of a mysterious mathematical pattern found throughout nature.

Studying the structure of existing friendships in your community can help you forge the best connections when forming a new circle of friends.

Evolutionary stories like the grandmother hypothesis are easy to construct from mathematical models, but how well do they reflect reality?