Book Review Ernst Zermelo: An Approach to His Life andWork

Ernst Zermelo is familiar to mathematicians as the creator of the controversial Axiom of Choice in 1904 and the theorem, based on the Axiom of Choice, that every set can be well ordered. Many will be aware that in 1908 he axiomatized set theory—in a form later modified by Abraham Fraenkel (1922) and then by Zermelo himself (1930). Some will know of Zermelo’s conflict with Ludwig Boltzmann over the Poincaré Recurrence Theorem and its role in understanding the Second Law of Thermodynamics. Fewer will know of the following: Zermelo’s work in the calculus of variations at the start of his career; his pioneering work in game theory before that of Emile Borel and John von Neumann; his conflict with Thoralf Skolem over whether axiomatic set theory should be formulated in first-order or second-order logic (and the resulting conflict over the Löwenheim–Skolem Theorem and the existence of a countable model of set theory); his contributions to infinitary logic; or finally his conflict with Gödel over the latter’s Incompleteness Theorems and Zermelo’s attempts to circumvent them. The book under review is the first full-length biography of Zermelo. It is based on a great deal of archival research, on the cooperation of Zermelo’s widow Gertrud (who outlived him by