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number theory

Black and white photo of John Conway against a black background
Abstractions blog

John Conway Solved Mathematical Problems With His Bare Hands

April 20, 2020

The legendary mathematician, who died on April 11, was curious, colorful and one of the greatest problem-solvers of his generation.

Langlands program

‘Amazing’ Math Bridge Extended Beyond Fermat’s Last Theorem

April 6, 2020

Mathematicians have figured out how to expand the reach of a mysterious bridge connecting two distant continents in the mathematical world.

Quantized Academy

How Rational Math Catches Slippery Irrational Numbers

March 10, 2020

Finding the best way to approximate the ever-elusive irrational numbers pits the infinitely large against the infinitely small.

Multimedia

The Map of Mathematics

February 13, 2020

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

Art for "Quanta’s Year in Math and Computer Science (2019)"
2019 in Review

The Year in Math and Computer Science

December 23, 2019

Mathematicians and computer scientists made big progress in number theory, graph theory, machine learning and quantum computing, even as they reexamined our fundamental understanding of mathematics and neural networks.

Animated graphic showing different ways many numbers can arrive at 1 via the Collatz process
number theory

Mathematician Proves Huge Result on ‘Dangerous’ Problem

December 11, 2019

Mathematicians regard the Collatz conjecture as a quagmire and warn each other to stay away. But now Terence Tao has made more progress than anyone in decades.

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.”

An illustration of a mathematician staring up at an infinite pile of cubes of varying sizes and colors.
Quantized Academy

Why the Sum of Three Cubes Is a Hard Math Problem

November 5, 2019

Looking for answers in infinite space is hard. High school math can help narrow your search.

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.