This book gives the first English, detailed scientific biography of Ernst Zermelo (1871-1953), a German mathematician best known for a formulation of the axiom of choice and for an axiomatization of set theory. He is considered to be one of the greatest logicians in the first half of the 20th century. In five chapters, the author describes Zermelo's life and his scientific achievements from his youth through his studies, works, teaching and scientific activities. The author also analyses Zermelo's conditions for scientific study and research before, during and after World War II, his isolation during the war and his activities after the war. Zermelo's major scientific contributions (in set theory, the calculus of variations, the theory of games, the theory of rating systems, applied mathematics) are discussed without assuming a detailed mathematical knowledge of the field in question.

The presentation of Zermelo's works explores his motivations, aims, acceptance and influence on the development of mathematics. The book is based on a study of unknown and unpublished sources, archival materials, private letters, family documents, previously unpublished notes, interviews and memoirs. The main text is followed by a schematic curriculum vitae of Ernst Zermelo summarizing the most important events of his life. The book concludes with an appendix containing a German version of Zermelo's unpublished ideas and parts of his works (for example selected proofs), his original letters, notes and samples of his literary activities. The book contains more than 40 photos and facsimiles, a large list of references and an index. It gives new light to all facets of Zermelo's life and mathematical achievements and it can be recommended to a wide audience. The book is suitable for mathematicians, historians of mathematics and science, students and teachers.

Reviewer:

mbec