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Symmetry, Algebra and the Monster

To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape.

Maryam Mirzakhani
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The Beautiful Mathematical Explorations of Maryam Mirzakhani

After her untimely death, Maryam Mirzakhani’s life is best remembered through her work.

Illustration: diver searching for new math
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Quantum Questions Inspire New Math

In order to fully understand the quantum world, we may have to develop a new realm of mathematics.

2D knots illustration by James O'Brien
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Inside the Knotty World of ‘Anyon’ Particles

A new class of quantum particle is about to emerge from the tangled considerations of quantum statistics.

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Using Mathematics to Repair a Masterpiece

The author shows how new mathematical techniques can be used to revitalize a 650-year-old work of art.

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How Feynman Diagrams Almost Saved Space

Richard Feynman’s famous diagrams weren’t just a way to do calculations. They represented a deep shift in thinking about how the universe is put together.

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Entanglement Made Simple

How quantum entanglement connects with the “many worlds” of quantum theory.

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Is AlphaGo Really Such a Big Deal?

The Go-playing program teaches itself to replicate something very much like human intuition, an advance that promises far-reaching consequences.

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Deep Secrets and the Thrill of Discovery

The biologist Sean B. Carroll rediscovers the scientific thrill of an unexpected revelation.