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Mathematics

Art for "Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize"
Abel Prize

Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize

A founder of modern geometric analysis who produced “some of the most dramatic advances in mathematics in the last 40 years,” Uhlenbeck is the first woman to be awarded this top honor.

Art for "Where Proof, Evidence and Imagination Intersect"
Quantized Academy

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?

geometry

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.

Art for "The Universe’s Ultimate Complexity Revealed by Simple Quantum Games"
quantum information theory

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.

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.