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Neuron drawings by Santiago Ramón y Cajal
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Why the First Drawings of Neurons Were Defaced

Every exquisite drawing by Santiago Ramón y Cajal, the founder of modern neuroscience, is marred by a curious mark. Here is the little-known story behind it.

Emergent reductionism flower
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To Solve the Biggest Mystery in Physics, Join Two Kinds of Law

Reductionism breaks the world into elementary building blocks. Emergence finds the simple laws that arise out of complexity. These two complementary ways of viewing the universe come together in modern theories of quantum gravity.

fidget spinners
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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.