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mathematics

Art for "Möbius Strips Defy a Link With Infinity"
topology

Möbius Strips Defy a Link With Infinity

A new proof shows why an uncountably infinite number of Möbius strips will never fit into a three-dimensional space.

Art for "How to Find Simple Treasures in Complex Numbers"
insights puzzle

How to Find Simple Treasures in Complex Numbers

In spite of their name, “imaginary” numbers are as real as any other numbers, especially when it comes to hunting for lost treasure.

Art for "Smaller Is Better: Why Finite Number Systems Pack More Punch"
Abstractions blog

Smaller Is Better: Why Finite Number Systems Pack More Punch

Recent progress on the “sum product” problem recalls a celebrated mathematical result that revealed the power of miniature number systems.

number theory

How a Strange Grid Reveals Hidden Connections Between Simple Numbers

A graduate student has helped illuminate a long-suspected connection between addition and multiplication.

artificial intelligence

Foundations Built for a General Theory of Neural Networks

Neural networks can be as unpredictable as they are powerful. Now mathematicians are beginning to reveal how a neural network’s form will influence its function.

Art for "The Trouble With Turbulence"
In Theory

The Trouble With Turbulence

Turbulence is everywhere, yet it is one of the most difficult concepts for physicists to understand.

Portrait of Carolina Araujo at IMPA in Brazil
Q&A

A Movement to Close the Gender Gap in Mathematics

The Brazilian mathematician Carolina Araujo, who calls herself “a bit of an anarchist,” is organizing meetings and building a support network to study and solve the problems women face in mathematics.

Art for "Unscrambling the Hidden Secrets of Superpermutations"
Quantized Academy

Unscrambling the Hidden Secrets of Superpermutations

A science fiction novelist and an internet commenter made breakthroughs on a longstanding problem about the number of ways you can arrange a set of items. What did they discover?

Mathematics - abstract illustration
2018 in Review

The Year in Math and Computer Science

Several mathematicians under the age of 30 left their marks all over the field, and amateur problem-solvers of all ages made significant contributions to long-dormant puzzles.