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

# Articles tagged number theory

### New Number Systems Seek Their Lost Primes

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.

### Handicapping the 2018 Fields Medal

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

### The Oracle of Arithmetic

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

### A Life Inspired by an Unexpected Genius

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*.

### Sphere Packing Solved in Higher Dimensions

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

### Mathematicians Discover Prime Conspiracy

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

### 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.

### 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.

### 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.