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Elliptic Curve ‘Murmurations’ Found With AI Take Flight | Quanta Magazine

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Elliptic curves are among the more beguiling objects in modern mathematics. They don’t seem complicated, but they form an expressway between the math that many people learn in high school and research mathematics at its most abstruse. They were central to Andrew Wiles’ celebrated proof of Fermat’s Last Theorem in the 1990s. They are key tools in modern cryptography. And in 2000, the Clay Mathematics Institute named a conjecture about the statistics of elliptic curves one of seven “Millennium Prize Problems,” each of which carries a $1 million prize for its solution. That conjecture, first ventured by Bryan Birch and Peter Swinnerton-Dyer in the 1960s, still hasn’t been proved. Understanding elliptic curves is a high-stakes endeavor that has been central to math. So in 2022, when a transatlantic collaboration used statistical techniques and artificial intelligence to discover completely unexpected patterns in elliptic curves, it was a welcome, if unexpected, contribution. “It was just a

Elliptic Curve ‘Murmurations’ Found With AI Take Flight | Quanta Magazine Home Elliptic Curve ‘Murmurations’ Found With AI Take Flight Read Later Share Copied! Comments Read Later Read Later number theory Elliptic Curve ‘Murmurations’ Found With AI Take Flight By Lyndie Chiou March 5, 2024 Mathematicians are working to fully explain unusual behaviors uncovered using artificial intelligence. Read Later When viewed the right way, elliptic curves can flock like birds. Paul Chaikin for Quanta Magazine Introduction By Lyndie Chiou Contributing Writer March 5, 202

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