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Kevin Hartnett

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

    Reprinted with permission from Quanta Magazine‘s Abstractions blog. The 61st International Mathematical Olympiad, or IMO, began yesterday. It may go down in history for at least two reasons: Due to the COVID-19 pandemic it’s the first time the event has been held remotely, and it may also be the last time that artificial intelligence doesn’t compete. […]

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    In Quantum Games, There’s No Way to Play the Odds

    Reprinted with permission from Quanta Magazine’s Abstractions blog. In the 1950s, four mathematically minded U.S. Army soldiers used primitive electronic calculators to work out the optimal strategy for playing blackjack. Their results, later published in the Journal of the American Statistical Association, detailed the best decision a player could make for every situation encountered in the game. Yet that strategy—which would evolve into […]

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    Why Mathematicians Can’t Find the Hay in a Haystack

    Reprinted with permission from Quanta Magazine‘s Abstractions blog. The first time I heard a mathematician use the phrase, I was sure he’d misspoken. We were on the phone, talking about the search for shapes with certain properties, and he said, “It’s like looking for hay in a haystack.” “Don’t you mean a needle?” I almost interjected. Then he […]

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    What Makes the Hardest Equations in Physics So Difficult?

    Reprinted with permission from Quanta Magazine‘s Abstractions blog. Physics contains equations that describe everything from the stretching of space-time to the flitter of photons. Yet only one set of equations is considered so mathematically challenging that it’s been chosen as one of seven “Millennium Prize Problems” endowed by the Clay Mathematics Institute with a $1 million reward: […]

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    A Simple Visual Proof of a Powerful Idea in Graph Theory

    Ramsey’s theorem predicts a surprising (and useful) consistency in the organization of graphs. Here’s a simple visual proof of how it works.Image by Lucy Reading-Ikkanda/Quanta Magazine; Source: Jonathan Jedwab, Simon Fraser University Reprinted with permission from Quanta Abstractions A recent advance in geometry makes heavy use of Ramsey’s theorem, an important idea in another field—graph theory. […]