Kevin Hartnett

Senior Writer

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.”

Animation showing two sets of tangrams cycling between identical squares and different shapes.

Mathematicians Cut Apart Shapes to Find Pieces of Equations

October 31, 2019

New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.

Photos of Google’s quantum computer system on the left, IMB’s supercomputer Summit on the right.
Abstractions blog

Google and IBM Clash Over Milestone Quantum Computing Experiment

October 23, 2019

Today Google announced that it achieved “quantum supremacy.” Its chief quantum computing rival, IBM, said it hasn’t. The disagreement hinges on what the term really means.

Photo of a yellow sunflower against a yellow background.
Abstractions blog

Mathematicians Begin to Tame Wild ‘Sunflower’ Problem

October 21, 2019

A major advance toward solving the 60-year-old sunflower conjecture is shedding light on how order begins to appear as random systems grow in size.

foundations of mathematics

With Category Theory, Mathematics Escapes From Equality

October 10, 2019

Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.

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.

Abstractions blog

Computers and Humans ‘See’ Differently. Does It Matter?

September 17, 2019

In some ways, machine vision is superior to human vision. In other ways, it may never catch up.

An illustration of eyeballs connected to many hands painting the Mona Lisa.
mathematical biology

A Mathematical Model Unlocks the Secrets of Vision

August 21, 2019

Mathematicians and neuroscientists have created the first anatomically accurate model that explains how vision is possible.