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Kevin Hartnett

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    The Tricky Translation of Mathematical Ideas

    Big advances in math can happen when mathematicians move ideas into areas where they seem like they shouldn’t belong.

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    Cash for Math: The Erdős Prizes Live On

    Paul Erdős placed small bounties on hundreds of unsolved math problems. Over the past 20 years, only a handful have been claimed.

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    How to Use a Sphere to Talk to Mars

    To avoid garbled messages, mathematicians might translate them into geometric form.

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    A Simple Visual Proof of a Powerful Idea

    Ramsey’s theorem predicts a surprising (and useful) consistency in the organization of graphs. Here’s a simple visual proof of how it works.

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    The Almost-Proof of Fermat’s Last Theorem

    19th-century mathematicians thought the “roots of unity” were the key to solving Fermat’s Last Theorem. Then they discovered a fatal flaw.

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    The Hidden Twist to Making a Möbius Strip

    The simple Möbius strip illustrates a deep mathematical challenge that has long tormented the field of symplectic geometry.

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    How Curvature Makes a Shape a Shape

    The ancient study of an object’s curvature is guiding mathematicians toward a new understanding of simple equations.

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    Test Your Mathematical Sculpting Skills

    Can you turn a two-dimensional fractal into a 3-D object? Break out your scissors and tape for a chance to win a 3-D printed sculpture.

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    The Math That’s Too Difficult for Physics

    How do physicists reconstruct what really happened in a particle collision? Through calculations that are so challenging that, in some cases, they simply can’t be done. Yet.