Kevin Hartnett

Senior Writer

Art for "With Ruler and Compass, Amateur Mathematician Tames Fiendish Problem"
geometry

Amateur Mathematician Finds Smallest Universal Cover

Through exacting geometric calculations, Philip Gibbs has found the smallest known cover for any possible shape.

abstractions blog

New Proof Shows Infinite Curves Come in Two Types

Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.

number theory

Without a Proof, Mathematicians Wonder How Much Evidence Is Enough

A new statistical model appears to undermine long-held assumptions in number theory. How much should it be trusted when all that really matters is proof?

Art for "A Proof About Where Symmetries Can’t Exist"
geometry

A Proof About Where Symmetries Can’t Exist

In a major mathematical achievement, a small team of researchers has proven Zimmer’s conjecture.

Art for "Machine Learning Confronts the Elephant in the Room"
artificial intelligence

Machine Learning Confronts the Elephant in the Room

A visual prank exposes an Achilles’ heel of computer vision systems: Unlike humans, they can’t do a double take.

Art for "Why Mathematicians Can’t Find the Hay in a Haystack"
Abstractions blog

Why Mathematicians Can’t Find the Hay in a Haystack

In math, sometimes the most common things are the hardest to find.

Illustration of a complex shape casting a shadow
geometry

Tinkertoy Models Produce New Geometric Insights

An upstart field that simplifies complex shapes is letting mathematicians understand how those shapes depend on the space in which you visualize them.

algorithms

Universal Method to Sort Complex Information Found

The nearest neighbor problem asks where a new point fits into an existing data set. A few researchers set out to prove that there was no universal way to solve it. Instead, they found such a way.

Photo illustration of Caucher Birkar
2018 Fields Medal and Nevanlinna Prize Winners

An Innovator Who Brings Order to an Infinitude of Equations

The mathematician Caucher Birkar was born on a subsistence farm and raised in the middle of the brutal war between Iran and Iraq. After fleeing to England, he has gone on to impose order on a wild landscape of mathematical equations.

About the author

Kevin Hartnett is a senior writer at Quanta Magazine covering mathematics and computer science. His work has been collected in the “Best Writing on Mathematics” series in 2013, 2016 and 2017. From 2013-2016 he wrote “Brainiac,” a weekly column for the Boston Globe‘s Ideas section.