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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 "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.

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.

Illustration of lock with polynomials surrounding it
Abstractions blog

Mathematicians Seal Back Door to Breaking RSA Encryption

Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.

Art for "In the Universe of Equations, Virtually All Are Prime"
number theory

In the Universe of Equations, Virtually All Are Prime

Equations, like numbers, cannot always be split into simpler elements.