Between inventing the concept of a universal computer in 1936
and breaking the German Enigma code during World War II, Alan
Turing (1912-1954), the British founder of computer science and
artificial intelligence, came to Princeton University to study
mathematical logic. Some of the greatest logicians in the
world--including Alonzo Church, Kurt Godel, John von Neumann, and
Stephen Kleene--were at Princeton in the 1930s, and they were
working on ideas that would lay the groundwork for what would
become known as computer science. This book presents a facsimile of
the original typescript of Turing's fascinating and influential
1938 Princeton PhD thesis, one of the key documents in the history
of mathematics and computer science. The book also features essays
by Andrew Appel and Solomon Feferman that explain the
still-unfolding significance of the ideas Turing developed at
Princeton.
A work of philosophy as well as mathematics, Turing's thesis
envisions a practical goal--a logical system to formalize
mathematical proofs so they can be checked mechanically. If every
step of a theorem could be verified mechanically, the burden on
intuition would be limited to the axioms. Turing's point, as Appel
writes, is that "mathematical reasoning can be done, and should be
done, in mechanizable formal logic." Turing's vision of
"constructive systems of logic for practical use" has become
reality: in the twenty-first century, automated "formal methods"
are now routine.
Presented here in its original form, this fascinating thesis is
one of the key documents in the history of mathematics and computer
science."
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