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Chapter 16
Computability
andIts Limitations
Until the mid 1930s the notion of computability had not yet been math-
ematically well established, which is natural since the rst electronic com-
puters were not constructed until the Colossus, ENIAC, and EDVAC were
built in the 1940s. It is quite interesting that the computational limita-
tions of these (as well as all future) computers had already been proven
mathematically in 1936.
16.1 GÖDEL’S INCOMPLETENESS THEOREM
At the turn of the 19th century, the German mathematician David Hilbert
(1862–1943) set out to nd an algorithm for determining the truth or false-
hood of any mathematical proposition. ...