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number theory

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2022 Fields and Abacus Medals

A Solver of the Hardest Easy Problems About Prime Numbers

By Erica Klarreich
July 5, 2022
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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.

Maryna Viazovska seated on the wooden steps of an amphitheater at the Swiss Federal Institute of Technology Lausanne.
2022 Fields and Abacus Medals

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

By Thomas Lin +1 authors
Erica Klarreich
July 5, 2022
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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.

number theory

Graduate Student’s Side Project Proves Prime Number Conjecture

By Jordana Cepelewicz
June 6, 2022
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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.”

A mathematical graph with plant roots.
number theory

New Proof Illuminates the Hidden Structure of Common Equations

By Leila Sloman
April 21, 2022
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Van der Waerden’s conjecture mystified mathematicians for 85 years. Its solution shows how polynomial roots relate to one another.

Q&A

In Music and Math, Lillian Pierce Builds Landscapes

By Jordana Cepelewicz
March 30, 2022
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Lillian Pierce wants to transform access to the world of mathematics, while making headway on problems that bridge the discrete and continuous.

A rectangle broken up into five fractions.
number theory

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

By Jordana Cepelewicz
March 9, 2022
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A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of unit fractions.

number theory

Mathematicians Prove 30-Year-Old André-Oort Conjecture

By Leila Sloman
February 3, 2022
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A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.

number theory

Mathematicians Clear Hurdle in Quest to Decode Primes

By Kevin Hartnett
January 13, 2022
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Paul Nelson has solved the subconvexity problem, bringing mathematicians one step closer to understanding the Riemann hypothesis and the distribution of prime numbers.

An illustration of a flashlight whose beam illuminates graphs and numbers.
number theory

Mathematicians Outwit Hidden Number Conspiracy

By Jordana Cepelewicz
January 3, 2022
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Decades ago, a mathematician posed a warmup problem for some of the most difficult questions about prime numbers. It turned out to be just as difficult to solve, until now.


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