Book Review: Logical Dilemmas: The Life and Work of Kurt Godel and Godel: A Life of Logic, Volume 48, Number 8

In its March 29, 1999, issue TIME magazine provided its picks for the twenty greatest “scientists and thinkers” of the twentieth century. Kurt Gödel was on the list along with his good friend Albert Einstein. Alan Turing was the other mathematician among the twenty. Since we may agree that Einstein should be regarded primarily as a physicist, it turns out that the mathematicians TIME selected as the great thinkers of the past century were a pair of logicians! Whatever one may think about these two, the work of the overwhelming majority of mathematicians has been quite unaffected by what they accomplished. Turing’s main influence on most mathematicians, and indeed on the population at large, stems from his role as progenitor of the computer (see [1]), and it was for this role that TIME selected him. In Douglas Hofstadter’s TIME article on Gödel, John von Neumann is quoted proclaiming that Gödel’s “achievement...is singular and monumental...a landmark which will remain visible far in space and time....” Although Gödel did a number of other very important things, it is the “achievement” to which von Neumann referred, Gödel’s incompleteness theorem, that has caught the imagination of the educated public. Indeed, Hofstadter himself played an important part in bringing Gödel’s work to the attention of a general audience by writing his Pulitzer Prize-winning book [5], a whimsical, artful work, full of amusing dialogues and connections with music, art, and artificial intelligence. Kurt Gödel was a very strange man, and his life is as interesting as his scientific work. Both of the books under review bring the two together but are intended for quite different audiences. John Dawson explains in his preface that although he has not “presumed any acquaintance with modern mathematical logic,” he has assumed that his readers “possess a modicum of mathematical understanding.” In fact, his book would likely be tough going for anyone who had not studied mathematics at the graduate level. John L. Casti Book Review