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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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Why an Old Theory of Everything Is Gaining New Life

For decades, physicists have struggled to create a quantum theory of gravity. Now an approach that dates to the 1970s is attracting newfound attention.

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The (Math) Problem With Pentagons

Triangles fit effortlessly together, as do squares. When it comes to pentagons, what gives?

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What Bacteria Can Tell Us About Human Evolution

To discover our species’ deep history and to shape its future health, we should learn from the microbes that accompanied us on our evolutionary journey.

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