What's up in

# Number theory

## Latest Articles

### 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.

### Graduate Student’s Side Project Proves Prime Number Conjecture

Jared Duker Lichtman, 26, has proved a longstanding conjecture relating prime numbers to a broad class of “primitive” sets. To his adviser, it came as a “complete shock.”

### New Proof Illuminates the Hidden Structure of Common Equations

Van der Waerden’s conjecture mystified mathematicians for 85 years. Its solution shows how polynomial roots relate to one another.

### In Music and Math, Lillian Pierce Builds Landscapes

Lillian Pierce wants to transform access to the world of mathematics, while making headway on problems that bridge the discrete and continuous.

### Math’s ‘Oldest Problem Ever’ Gets a New Answer

A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of unit fractions.

### Mathematicians Prove 30-Year-Old André-Oort Conjecture

A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.