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prime numbers

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

A Number Theorist Who Solves the Hardest Easy Problems

July 1, 2020

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.


The Map of Mathematics

February 13, 2020

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

An illustration of a woman sitting in a field embroidering a flower pattern. Around her grow wildflowers that appear to be randomly distributed but whose colors reveal a hidden pattern.
number theory

Mathematicians Catch a Pattern by Figuring Out How to Avoid It

November 25, 2019

We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”

Colored spheres arranged in pairs.
prime numbers

Big Question About Primes Proved in Small Number Systems

September 26, 2019

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.

A dartboard with pi at its center.
number theory

New Proof Settles How to Approximate Numbers Like Pi

August 14, 2019

The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer.

Illustration of lock with polynomials surrounding it
Abstractions blog

Mathematicians Seal Back Door to Breaking RSA Encryption

December 17, 2018

Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.

Art for "In the Universe of Equations, Virtually All Are Prime"
number theory

In the Universe of Equations, Virtually All Are Prime

December 10, 2018

Equations, like numbers, cannot always be split into simpler elements.

Art for "The Universal Pattern Popping Up in Math, Physics and Biology"
In Theory

The Universal Pattern Popping Up in Math, Physics and Biology

August 23, 2018

Quanta’s In Theory video series returns with an exploration of a mysterious mathematical pattern found throughout nature.

Crystal diffraction art for "A Chemist Shines Light on a Surprising Prime Number Pattern"
prime numbers

A Chemist Shines Light on a Surprising Prime Number Pattern

May 14, 2018

When a crystallographer treated prime numbers as a system of particles, the resulting diffraction pattern created a new view of existing conjectures in number theory.