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The Ukrainian mathematician Maryna Viazovska has solved the centuries-old sphere-packing problem in dimensions eight and 24.

A previously unnoticed property of prime numbers seems to violate a long-standing assumption about how they behave.

At 86, Britain’s preeminent mathematical matchmaker is still tackling the big questions and dreaming of a union between the quantum and the gravitational forces.

Three years ago, a solitary mathematician released an impenetrable proof of the famous *abc* conjecture. At a recent conference dedicated to the work, optimism mixed with bafflement.

Computer scientists are abuzz over a fast new algorithm for solving one of the central problems in the field.

A new breakthrough that bridges number theory and geometry is just the latest triumph for a close-knit group of mathematicians.

Machine learning works spectacularly well, but mathematicians aren’t quite sure why.

Three computer scientists have solved a problem central to a dozen far-flung mathematical fields.

Scientists are homing in on a warning signal that arises in complex systems like ecological food webs, the brain and the Earth’s climate. Could it help prevent future catastrophes?