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In the ‘Wild West’ of Geometry, Mathematicians Redefine the Sphere
High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible.
An Old Conjecture Falls, Making Spheres a Lot More Complicated
The telescope conjecture gave mathematicians a handle on ways to map one sphere to another. Now that it has been disproved, the universe of shapes has exploded.
How Quantum Physicists Explained Earth's Weather Patterns
By treating Earth as a topological insulator — a state of quantum matter — physicists found a powerful explanation for the movements of the planet’s air and seas.
Flow Proof Helps Mathematicians Find Stability in Chaos
A series of new papers describes how to fully characterize key dynamical systems with relatively little data.
Why the Brain’s Connections to the Body Are Crisscrossed
In all bilaterally symmetrical animals, from humans down to simple worms, nerves cross from one side of the body to the opposite side of the brain. Geometry may explain why.
Emmy Murphy Is a Mathematician Who Finds Beauty in Flexibility
The prize-winning geometer feels most fulfilled when exploring the fertile ground where constraint meets creation.