Logical Dilemmas: The Life and Work of Kurt Gödel, published originally in 1997,was the first full-scale biography of its subject. It has now been reissued in paperback, and that is very good news for mathematical readers. This is a masterful biography that grapples with the life and ideas of a brilliant and complex man, both a true genius and a psychologically damaged recluse. As far as I know, this remains the only full-scale biography of Gödel. Other discussions in print of his life are incomplete and fragmentary. The recent book Incompleteness by Rebecca Goldstein touches somewhat on Gödel’s life and his mathematics, but does not pretend to be anything more than a sketch of his ideas and a snapshot of his life.
The author bases his account of Kurt Gödel’s life on primary documentation rather than interviews since Gödel’s circle of acquaintances was so small. The most important collection of documentation is the Nachlass (roughly, writings left behind). Gödel apparently kept virtually every piece of paper that crossed his desk, from luggage tags and library request slips to correspondence from cranks and requests for autographs. The author was cataloger of the Nachlass and co-editor of Gödel’s Collected Works, and he knows his subject well.
Gödel’s life can be broadly described in three phases: his childhood years in Brno , the years in Vienna as student and Dozent, and the period following his emigration to America . It was in the second phase, starting around 1930, that he arrived at his astonishing results on undecidability and incompleteness. In was also in this incredibly productive second phase of his life that Gödel worked on set theory and the theory of constructible sets. After emigrating to America, Gödel focused largely on philosophy and physics, although he did vet Paul Cohen’s proof of the independence of the continuum hypothesis during this period.
This is a biography for those who possess, in the author’s words, “a modicum of mathematical understanding” including an acquaintance with the structure of modern mathematics (e.g., the development of analysis in the nineteenth century with its more sharply defined concepts of function and real number) and its major figures. He does not however assume any familiarity with modern mathematical logic. The bulk of Chapter 3 provides a summary of the development of logic up to Gödel’s time, and a part of Chapter 6 is devoted to a similar discussion of set theory.
In Gödel’s life we see the sweep of great intellectual developments against a backdrop of the history of the twentieth century. Gödel often seemed curiously naïve about the great and terrible events going on around him. Karl Menger notes that one of Gödel’s letters in this vein established “a record for non-involvement on the threshold of … historic events.” The author presents a portrait of Kurt Gödel that captures the immensity of his contributions and sensitively explores his complicated personality but does not ignore his occasional deep strangeness.
Bill Satzer (firstname.lastname@example.org) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.