Number theory

Greatness was always expected of Ken Ono. But as he struggled with his parents’ expectations, he found solace and inspiration in the life of two-time college dropout — and mathematical genius — Srinivasa Ramanujan, the subject of the film The Man Who Knew Infinity.

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.

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.

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

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

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?

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

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.