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An illustration of a pink hand reaching for quantum dice.
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Where Quantum Probability Comes From

September 9, 2019

There are many different ways to think about probability. Quantum mechanics embodies them all.

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Ann Nelson Took On the Biggest Problems in Physics

August 22, 2019

The theoretical particle physicist Ann Nelson, who died on August 4 at age 61, was a font of brilliant ideas and a champion of ending discrimination in the field.

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Color Me Polynomial

August 13, 2019

Polynomials aren’t just exercises in abstraction. They’re good at illuminating structure in surprising places.

Illustration of Fermat's Last Theorem
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Why the Proof of Fermat’s Last Theorem Doesn’t Need to Be Enhanced

June 3, 2019

Decades after the landmark proof of Fermat’s Last Theorem, ideas abound for how to make it even more reliable. But such efforts reflect a deep misunderstanding of what makes the proof so important.

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How Geometry, Data and Neighbors Predict Your Favorite Movies

May 22, 2019

A little high school geometry can help you understand the basic math behind movie recommendation engines.

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The Subtle Art of the Mathematical Conjecture

May 7, 2019

It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown.

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What the Sight of a Black Hole Means to a Black Hole Physicist

April 10, 2019

The astrophysicist Janna Levin reflects on the newly unveiled, first-ever photograph of a black hole.

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Usain Bolt’s Split Times and the Power of Calculus

April 3, 2019

Just how fast can the fastest human run? This adapted book excerpt from Infinite Powers reveals how calculus helps us investigate the nature of motion and change.

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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?

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A regular column in which top researchers explore the process of discovery.