Kevin Hartnett

Senior Writer

Abstractions blog

The Almost-Proof of Fermat’s Last Theorem

19th-century mathematicians thought the “roots of unity” were the key to solving Fermat’s Last Theorem. Then they discovered a fatal flaw.

Colorful illustration of 5 plants with their roots exposed. Each plant forms the shape of a number,
number theory

New Number Systems Seek Their Lost Primes

For centuries, mathematicians tried to solve problems by adding new values to the usual numbers. Now they’re investigating the unintended consequences of that tinkering.

Mobius strip illustration
Abstractions blog

The Hidden Twist to Making a Möbius Strip

The simple Möbius strip illustrates a deep mathematical challenge that has long tormented the field of symplectic geometry.


A Fight to Fix Geometry’s Foundations

When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry.

Francis Su

To Live Your Best Life, Do Mathematics

The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them.

Hyperbolic Crochet
Abstractions blog

How Curvature Makes a Shape a Shape

The ancient study of an object’s curvature is guiding mathematicians toward a new understanding of simple equations.

Julia Set Contest
Abstractions blog

Test Your Mathematical Sculpting Skills

Can you turn a two-dimensional fractal into a 3-D object? Break out your scissors and tape for a chance to win a 3-D printed sculpture.

3D "Basilica" Julia set

3-D Fractals Offer Clues to Complex Systems

By folding fractals into 3-D objects, a mathematical duo hopes to gain new insight into simple equations.


How to Force Our Machines to Play Fair

The computer scientist Cynthia Dwork takes abstract concepts like privacy and fairness and adapts them into machine code for the algorithmic age.