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Mathematics

Art for "Proof Finds That All Change Is a Mix of Order and Randomness"
dynamical systems

Proof Finds That All Change Is a Mix of Order and Randomness

March 27, 2019

All descriptions of change are a unique blend of chance and determinism, according to the sweeping mathematical proof of the “weak Pinsker conjecture.”

Abstractions blog

Sum-of-Three-Cubes Problem Solved for ‘Stubborn’ Number 33

March 26, 2019

A number theorist with programming prowess has found a solution to 33 = x³ + y³ + z³, a much-studied equation that went unsolved for 64 years.

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

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

March 19, 2019

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

March 14, 2019

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

March 12, 2019

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

March 5, 2019

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

February 20, 2019

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

February 11, 2019

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

February 6, 2019

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