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Gregory Barber

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Articles

  • New Proofs Probe the Limits of Mathematical Truth

    2 months ago | quantamagazine.org | Solomon Adams |Gregory Barber |Erica Klarreich

    Introduction The world of mathematics is full of unreachable corners, where unsolvable problems live. Now, yet another has been exposed. In 1900, the eminent mathematician David Hilbert announced a list of 23 key problems to guide the next century of mathematical research. His problems not only provided a road map for the field but reflected a more ambitious vision — to build a firm foundation from which all mathematical truths could be derived.

  • The Jagged, Monstrous Function That Broke Calculus

    Jan 23, 2025 | quantamagazine.org | Solomon Adams |Gregory Barber |Erica Klarreich |Jordana Cepelewicz

    Calculus is a powerful mathematical tool. But for hundreds of years after its invention in the 17th century, it stood on a shaky foundation. Its core concepts were rooted in intuition and informal arguments, rather than precise, formal definitions. Two schools of thought emerged in response, according to Michael Barany, a historian of math and science at the University of Edinburgh. French mathematicians were by and large content to keep going.

  • Mathematicians Discover New Way for Spheres to ‘Kiss’

    Jan 15, 2025 | quantamagazine.org | Gregory Barber |Erica Klarreich |Jordana Cepelewicz

    Introduction In May of 1694, in a lecture hall at the University of Cambridge, Isaac Newton and the astronomer David Gregory started to contemplate the nature of the stars, only to end up with a math puzzle that would persist for centuries. The details of their conversation were poorly recorded and are possibly apocryphal — it had something to do with how stars of varying sizes would orbit a central sun.

  • Rational or Not? This Basic Math Question Took Decades to Answer.

    Jan 8, 2025 | quantamagazine.org | Erica Klarreich |Jordana Cepelewicz |Gregory Barber

    In June 1978, the organizers of a large mathematics conference in Marseille, France, announced a last-minute addition to the program. During the lunch hour, the mathematician Roger Apéry would present a proof that one of the most famous numbers in mathematics — “zeta of 3,” or ζ(3), as mathematicians write it — could not be expressed as a fraction of two whole numbers. It was what mathematicians call “irrational.”Conference attendees were skeptical.

  • Big Advance on Simple-Sounding Math Problem Was a Century in the Making

    Oct 14, 2024 | quantamagazine.org | Erica Klarreich |Matt von Hippel |Gregory Barber |Leila Sloman

    A new proof about prime numbers illuminates the subtle relationship between addition and multiplication — and raises hopes for progress on the famous abc conjecture. Introduction One morning last November, the mathematician Hector Pasten finally solved the problem that had been dogging him for more than a decade by using a time-tested productivity hack: procrastination.

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