Alan Turing's Systems of Logic: The Princeton Thesis

ed.: Alan Turing's Systems of Logic: The Princeton Thesis

Princeton Thesis | Mudd Manuscript Library Blog

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 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. 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.

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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 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. 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.

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In 1872, Princeton established the John C. Greene School of Science, which evidenced the germs of a graduate school by promising higher degrees to those who stayed on to study beyond the B.S. or B.A. degree. As President James McCosh told the Trustees, "It is absolutely necessary to have such an addition if we are to keep up with the other great colleges of the country." Though graduate students had inhabited Princeton since its earliest years, working informally with professors, the Board of Trustees did not approve of a tentative graduate program until 1877. This was also the year Princeton awarded its first advanced degree: Francis Robbins Upton received a masters in science. In 1879, eighteen years after Yale awarded the first American Ph.D., Princeton's graduate school officially opened, offering twelve courses (four philosophy, five literature and three science) to 42 students.

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