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Kevin Hartnett

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    In Topology, When Are Two Shapes the Same?

    As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent.

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    Mathematicians Answer Old Question About Odd Graphs

    A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.

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    Undergraduate Math Student Pushes Frontier of Graph Theory

    At 21, Ashwin Sah has produced a body of work that senior mathematicians say is nearly unprecedented for a college student.

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    Inside the Secret Math Society Known Simply as Nicolas Bourbaki

    For almost a century, the anonymous members of Nicolas Bourbaki have written books intended as pure expressions of mathematical thought.

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    At the Math Olympiad, Computers Prepare to Go for the Gold

    Computer scientists are trying to build an AI system that can win a gold medal at the world’s premier math competition.

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    Computer Scientists Attempt to Corner the Collatz Conjecture

    A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot.

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    How Physics Found a Geometric Structure for Math to Play With

    Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about.

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    The Tricky Math of Herd Immunity for COVID-19

    Herd immunity differs from place to place, and many factors influence how it’s calculated.

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    The ‘Useless’ Perspective That Transformed Mathematics

    Representation theory was initially dismissed. Today, it’s central to much of mathematics.

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    In Mathematics, It Often Takes a Good Map to Find Answers

    Mathematicians try to figure out when problems can be solved using current knowledge—and when they have to chart a new path instead.