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Mathematics

geometry

Sphere Packing Solved in Higher Dimensions

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

number theory

Mathematicians Discover Prime Conspiracy

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

Q&A

Michael Atiyah’s Imaginative State of Mind

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.

Mathematics

Hope Rekindled for Perplexing Proof

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 Science

Landmark Algorithm Breaks 30-Year Impasse

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

Mathematics

Math Quartet Joins Forces on Unified Theory

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

Quantized Columns

Big Data’s Mathematical Mysteries

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

Mathematics

‘Outsiders’ Crack 50-Year-Old Math Problem

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

complex systems

Nature’s Critical Warning System

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?