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The “Horgan Surface” and “The Death of Proof” (mathematics) - C C - Jul 15, 2024
https://johnhorgan.org/cross-check/the-horgan-surface-and-the-death-of-proof
INTRO (John Horgan): Decades ago, mathematicians named a geometric structure, or pseudo-structure, or something after me: the Horgan surface. They meant to insult me, not honor me. Here’s the backstory, which touches on disturbing trends in mathematics (and yeah, this column is an updated, free version of one on ScientificAmerican.com).
In 1993 my boss at Scientific American, excited by the news that a Princeton mathematician had proved Fermat’s last theorem, ordered me to write an in-depth report on mathematics. I resisted. My degrees were in literature and journalism, I whined; I could handle a quickie news story on Fermat's last theorem, but a major article would be too hard. My boss insisted.
I began interviewing prominent mathematicians, and eventually I came up with one of the biggest stories of my career, which goes as follows: For millennia the logical, step-by-step arguments known as proofs served as the gold standard for truth. What could be truer than the Pythagorean theorem? But mathematics was evolving in ways that undermined the status of conventional proofs.
First, mathematics kept growing more complex and specialized, making confirmation of some alleged proofs difficult... (MORE - details, no ads)