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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.

Art for "How Network Math Can Help You Make Friends"
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The End of Theoretical Physics As We Know It

Computer simulations and custom-built quantum analogues are changing what it means to search for the laws of nature.

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How Network Math Can Help You Make Friends

Studying the structure of existing friendships in your community can help you forge the best connections when forming a new circle of friends.

Illustration for "Four Is Not Enough"
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Four Is Not Enough

How many colors do you need to color an infinite plane so that no points 1 unit apart are the same color?

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There Are No Laws of Physics. There’s Only the Landscape.

Scientists seek a single description of reality. But modern physics allows for many different descriptions, many equivalent to one another, connected through a vast landscape of mathematical possibility.

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Why Winning in Rock-Paper-Scissors (and in Life) Isn’t Everything

What does John Nash’s game theory equilibrium concept look like in Rock-Paper-Scissors?

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