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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.
The Mathematician Who Sculpted the Shape of Space
Eugenio Calabi, who died on September 25, conceived of novel geometric objects that later became fundamental to string theory.
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.
A New Symmetry Shakes Up Physics
So-called “higher symmetries” are illuminating everything from particle decays to the behavior of complex quantum systems.
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.
Is There Math Beyond the Equal Sign?
Can mathematics handle things that are essentially the same without being exactly equal? Category theorist Eugenia Cheng and host Steven Strogatz discuss the power and pleasures of abstraction.