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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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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.

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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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Black Hole Echoes Would Reveal Break With Einstein’s Theory

Gravitational waves have opened up new ways to test the properties of black holes — and Einstein’s theory of gravity along with them.

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Physicists Mourn Joe Polchinski, Developer of Deep Ideas and Paradoxes

The theoretical physicist Joe Polchinski, who died Feb. 2, left a tremendous professional and personal legacy, says a friend and collaborator.

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How Math (and Vaccines) Keep You Safe From the Flu

Simple math shows how widespread vaccination can disrupt the exponential spread of disease and prevent epidemics.

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