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 Mathematics' Shortcoming? (Kurt Godel)

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PostSubject: Mathematics' Shortcoming? (Kurt Godel)   Wed 18 May 2011, 7:37 pm

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By the 1928 international congress of mathematicians Hilbert "made his questions quite precise.
http://en.wikipedia.org/wiki/Turing_machine

+ First, was mathematics complete ...

+ Second, was mathematics consistent ...

+ And thirdly, was mathematics decidable?"
(Hodges p. 91, Hawking p. 1121).


The first two questions were answered in 1930 by Kurt Gödel at the very same meeting where Hilbert delivered his retirement speech (much to the chagrin of Hilbert); the third "the Entscheidungs problem" had to wait until the mid-1930s.

Emil Post developed his definition of a worker moving from room to room writing and erasing marks per a list of instructions (Post 1936), as did Princeton professor Church and his two students Stephen Kleene and J. B. Rosser by use of Church's lambda-calculus and Gödel's recursion theory (1934). Church's paper (published 15 April 1936) showed that the Entscheidungs problem was indeed "undecidable" and beat Turing to the punch by almost a year (Turing's paper submitted 28 May 1936, published January 1937).

Hence, the answer to all three of the above questions is "NO". Funny we didn't learn this in school

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PostSubject: Re: Mathematics' Shortcoming? (Kurt Godel)   Mon 10 Dec 2012, 4:11 pm


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