Lecture20

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Unformatted text preview: ral problems and consequences David Hilbert David Hilbert famous mathematician 23 problems founder of “metamathematics” goal to “mechanize” mathematics Kurt Gödel Kurt G Logician Proved in 1931…(age 25) “there are true propositions that there cannot be proved” (i.e., “no” to Hilbert’s program) Hilbert’s Shook the foundations of – – – – mathematics philosophy science everything Alan Turing Alan Turing British Mathematician Seminal work in Computation, AI, Cryptanalysis Subject of several books, movies A Halting Problem A Halting Problem x = input (“please enter a positive number) WHILE x > 1: IF x is even: x = x/2 ELSE: x = 3x + 1 The Halting Problem The Halting Problem Given: Program, Input to program Does the program on the input ever halt? Critical question that...
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This document was uploaded on 04/02/2014.

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