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number theory

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.

Two competitors are racing to solve the multiplication problem 25 times 63 in two separate lanes of a running track. One competitor is using the standard multiplication algorithm while the other is using Karatsuba method.
Quantized Academy

On Your Mark, Get Set, Multiply

September 23, 2019

The way you learned to multiply works, but computers employ a faster algorithm.

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 Fermat's Last Theorem
Quantized Columns

Why the Proof of Fermat’s Last Theorem Doesn’t Need to Be Enhanced

June 3, 2019

Decades after the landmark proof of Fermat’s Last Theorem, ideas abound for how to make it even more reliable. But such efforts reflect a deep misunderstanding of what makes the proof so important.

Art for "The Subtle Art of the Mathematical Conjecture"
Quantized Columns

The Subtle Art of the Mathematical Conjecture

May 7, 2019

It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown.

Art for "Mathematicians Discover the Perfect Way to Multiply"
number theory

Mathematicians Discover the Perfect Way to Multiply

April 11, 2019

By chopping up large numbers into smaller ones, researchers have rewritten a fundamental mathematical speed limit.