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Communications of the ACM


A Proof from 'The Book'

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In 1637, the French mathematician Pierre de Fermat scribbled in a book that he had a proof for a theorem, which the margin was too small to contain. It seems likely that he was mistaken about his famous "last theorem," since no such proof was found for 358 years, and even then it required more than 100 pages and used mathematics that didn't exist in his time.

By contrast, the Boolean "sensitivity conjecture" is relatively recent, but after nearly 30 years and repeated failures it seemed likely that any proof would also be a long and difficult slog. In July, 2019, however, mathematician Hao Huang of Emory University in Atlanta posted a short paper that completed its proof in a couple of pages in a way that experts found very convincing. Indeed, they immediately described it as "from the book," a tome imagined by the great 20th-century mathematician Paul Erdös in which God records the shortest and most illuminating proof of each theorem.


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