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number theory

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.

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.

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.

number theory

A Magical Answer to an 80-Year-Old Puzzle

Using crowd-sourced and traditional mathematics research, Terence Tao has devised a solution to a long-standing problem posed by the legendary Paul Erdős.

Q&A

After Prime Proof, an Unlikely Star Rises

Two years ago, Yitang Zhang was virtually unknown. Now his surprise solution to a major problem in number theory has catapulted him to mathematical stardom. Where does he go from here?

number theory

Mathematicians Chase Moonshine’s Shadow

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

Mathematics

Prime Gap Grows After Decades-Long Lull

A year after tackling how close together prime number pairs can stay, mathematicians have now made the first major advance in 76 years in understanding how far apart primes can be.

Manjul Bhargava video
2014 Fields Medal and Nevanlinna Prize Winners

The Musical, Magical Number Theorist

The search for artistic truth and beauty has led Manjul Bhargava to some of the most profound recent discoveries in number theory, which have helped earn him the Fields Medal.