Number theory

19th-century mathematicians thought the “roots of unity” were the key to solving Fermat’s Last Theorem. Then they discovered a fatal flaw.

For centuries, mathematicians tried to solve problems by adding new values to the usual numbers. Now they’re investigating the unintended consequences of that tinkering.

Peter Scholze is a favorite to win one of the highest honors in mathematics for his contributions in number theory and geometry.

At 28, Peter Scholze is uncovering deep connections between number theory and geometry.

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.