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twin primes conjecture

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A teenager wearing a blue polo shirt and glasses.
number theory

Teenager Solves Stubborn Riddle About Prime Number Look-Alikes

By Jordana Cepelewicz
October 13, 2022
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In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers — strange entities that mimic the primes.

The Joy of Why

How Do Mathematicians Know Their Proofs Are Correct?

By Steven Strogatz
July 13, 2022
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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.

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.

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.

A photograph of the mathematician James Maynard outside his home in Oxford, England.
profiles

A Number Theorist Who Solves the Hardest Easy Problems

By Erica Klarreich
July 1, 2020
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In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

Multimedia

The Map of Mathematics

By Kevin Hartnett
February 13, 2020
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Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

Colored spheres arranged in pairs.
prime numbers

Big Question About Primes Proved in Small Number Systems

By Kevin Hartnett
September 26, 2019
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The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems.

Art for "Where Proof, Evidence and Imagination Intersect"
Quantized Academy

Where Proof, Evidence and Imagination Intersect

By Patrick Honner
March 14, 2019
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In mathematics, where proofs are everything, evidence is important too. But evidence is only as good as the model, and modeling can be dangerous business. So how much evidence is enough?

Yitang Zhang
Thinking Places

Yitang Zhang’s Santa Barbara Beach Walk

By Thomas Lin +2 authors
Olena Shmahalo
Lucy Reading-Ikkanda
June 15, 2017
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An obscure number theorist who became an overnight sensation with a major proof about the gaps between prime numbers now finds quiet inspiration walking along the Pacific Coast.


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