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# number theory

## 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.

## 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.

## 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.”

## 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.

## 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.

## On Your Mark, Get Set, Multiply

September 23, 2019

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

## 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.

## 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.

## 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.