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The mathematician Svitlana Mayboroda and collaborators have figured out how to predict the behavior of electrons — a mathematical discovery that could have immediate practical effects.

An unexpected connection has emerged between the results of physics experiments and an important, seemingly unrelated set of numbers in pure mathematics.

String theory has so far failed to live up to its promise as a way to unite gravity and quantum mechanics. At the same time, it has blossomed into one of the most useful sets of tools in science.

Nima Arkani-Hamed is championing a campaign to build the world’s largest particle collider, even as he pursues a new vision of the laws of nature.

A 115-year effort to bridge the particle and fluid descriptions of nature has led mathematicians to an unexpected answer.

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

A potent theory has emerged explaining a mysterious statistical law that arises throughout physics and mathematics.

Martin Hairer was named a 2014 Fields medalist for an epic masterpiece in stochastic analysis that colleagues say “created a whole world.”

A conversation with the mathematical physicist Freeman Dyson on quantum electrodynamics, climate change and his latest pet project.