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In 1963 a mathematician, Paul Cohen, proved that this puzzle, the so-called continuum hypothesis, was neither provable nor disprovable, thanks to ��ö����’s incompleteness theorem.

Hofstadter is obsessed, I’d say it’s fair to say, with things that refer to, talk about or otherwise interact with themselves—notably ��ö����’s incompleteness theorem, a proof about the limits of proofs.

��ö����’s incompleteness theorem implies that both mathematics and physical reality will challenge us with “inexhaustible” problems.

��ö����’s “incompleteness theorem,” which he presented in 1930, when he was 24, upended his profession’s assumption that mathematics should be able to prove a mathematical statement that is true.

Human beings are some of the universe’s most energetic signal transmitters, and when Gleick isn’t explaining information’s relevance to Brownian motion and ��ö����’s incompleteness theorem, he’s deep in the more engaging stories of African talking drums, Ada Lovelace’s nascent computer programs, and how the telegram changed the world.