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Where Proof, Evidence and Imagination Intersect
In mathematics, where proofs are everything, evidence is important too. But evidence is only as good as the model, and modeling can be dangerous business. So how much evidence is enough?
Math Duo Maps the Infinite Terrain of Minimal Surfaces
A pair of mathematicians has built on an obscure, 30-year-old mathematical theory to show that soap-filmlike minimal surfaces appear abundantly in a wide range of shapes.
The Universe’s Ultimate Complexity Revealed by Simple Quantum Games
A two-player game can reveal whether the universe has an infinite amount of complexity.
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.
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.
How a Strange Grid Reveals Hidden Connections Between Simple Numbers
A graduate student has helped illuminate a long-suspected connection between addition and multiplication.
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.
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.
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?