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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
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– 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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