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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.

Sylvia Serfaty, Stefan Falke for Quanta Magazine

In Mathematics, ‘You Cannot Be Lied To’

For Sylvia Serfaty, mathematics is all about truth and beauty and building scientific and human connections.

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.

Illustration: boxing gloves
Abstractions blog

Graph Isomorphism Vanquished — Again

Just five days after posting a retraction, László Babai announced that he had fixed the error in his landmark graph isomorphism algorithm.

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.

Illustration: boxing glove & graph
Abstractions blog

Complexity Theory Problem Strikes Back

The legendary graph isomorphism problem may be harder than a 2015 result seemed to suggest.