Systems of Logic Based on Ordinals(33 views)
Description: FIRST EDITION of Turing's groundbreaking PhD thesis, "one of the key documents in the history of mathematics and computer science." "Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing, 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 Gödel, 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." While at Princeton, Turing earned his PhD, and his "fascinating and influential 1938 Princeton PhD thesis [is] one of the key documents in the history of mathematics and computer science. "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 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" (Alan Turing's Systems of Logic: The Princeton Thesis, ed. Andrew W. Appel). IN: Proceedings of the London Mathematical Society, Series 2., Vol. 45., Part 3., 21 March, 1939, pp. 161-228. London: C.F. Hidgson & Son, 1939. Tall octavo, modern three quarter red cloth over linen boards, original wrappers bound-in. A beautiful, fine copy with full margins and no institutional stamps. RARE.
Artist or Maker: TURING, ALAN