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Number theory

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How Can Infinitely Many Primes Be Infinitely Far Apart?

July 21, 2022

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?

July 13, 2022

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

July 5, 2022

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

July 5, 2022

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

June 6, 2022

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

April 21, 2022

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

March 30, 2022

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

March 9, 2022

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

February 3, 2022

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

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