What's up in

# number theory

## Latest Articles

### Mathematical Trio Advances Centuries-Old Number Theory Problem

The work — the first-ever limit on how many whole numbers can be written as the sum of two cubed fractions — makes significant headway on “a recurring embarrassment for number theorists.”

### Teenager Solves Stubborn Riddle About Prime Number Look-Alikes

In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers — strange entities that mimic the primes.

### A Numerical Mystery From the 19th Century Finally Gets Solved

Two mathematicians have proven Patterson’s conjecture, which was designed to explain a strange pattern in sums involving prime numbers.

### Mathematicians Crack a Simple but Stubborn Class of Equations

Ever since Archimedes, mathematicians have been fascinated by equations that involve a difference between squares. Now two mathematicians have proven how often these equations have solutions, concluding a decades-old quest.

### A Question About a Rotating Line Helps Reveal What Makes Real Numbers Special

The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.

### How Can Infinitely Many Primes Be Infinitely Far Apart?

Mathematicians have been studying the distribution of prime numbers for thousands of years. Recent results about a curious kind of prime offer a new take on how spread out they can be.

### How Do Mathematicians Know Their Proofs Are Correct?

What makes a proof stronger than a guess? What does evidence look like in the realm of mathematical abstraction? Hear the mathematician Melanie Matchett Wood explain how probability helps to guide number theorists toward certainty.

### A Solver of the Hardest Easy Problems About Prime Numbers

On his way to winning a Fields Medal, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

### In Times of Scarcity, War and Peace, a Ukrainian Finds the Magic in Math

With her homeland mired in war, the sphere-packing number theorist Maryna Viazovska has become the second woman to win a Fields Medal in the award’s 86-year history.