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

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.

Art for "How Geometry, Data and Neighbors Predict Your Favorite Movies"
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How Geometry, Data and Neighbors Predict Your Favorite Movies

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

Art for "The Subtle Art of the Mathematical Conjecture"
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The Subtle Art of the Mathematical Conjecture

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

Art for "What the Sight of a Black Hole Means to a Black Hole Physicist"
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What the Sight of a Black Hole Means to a Black Hole Physicist

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

Art for "Usain Bolt’s Split Times and the Power of Calculus"
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Usain Bolt’s Split Times and the Power of Calculus

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.

Art for "Where Proof, Evidence and Imagination Intersect"
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Where Proof, Evidence and Imagination Intersect

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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The Double Life of Black Holes

Perfect black holes are versatile mathematical tools. Just don’t mistake them for the real thing.

Art for "Unscrambling the Hidden Secrets of Superpermutations"
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Unscrambling the Hidden Secrets of Superpermutations

A science fiction novelist and an internet commenter made breakthroughs on a longstanding problem about the number of ways you can arrange a set of items. What did they discover?

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The (Imaginary) Numbers at the Edge of Reality

Odd enough to potentially model the strangeness of the physical world, complex numbers with “imaginary” components are rooted in the familiar.

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