**History of Mathematics** 2007; 442 pp; hardcover Volume: 33 ISBN-10: 0-8218-3550-5 ISBN-13: 978-0-8218-3550-0 List Price: US$92 Member Price: US$73.60 Order Code: HMATH/33
| Gerhard Gentzen (1909-1945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called "proof theory" but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today. The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945. Particular emphasis in the book is put on the conditions of scientific research, in this case mathematical logic, in National Socialist Germany, the ideological fight for "German logic", and their mutual protagonists. Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an indispensable source of information on this important mathematician, his work, and his time. The volume is completed by two deep substantial essays by Jan von Plato and Craig Smoryński on Gentzen's proof theory; its relation to the ideas of Hilbert, Brouwer, Weyl, and Gödel; and its development up to the present day. Smoryński explains the Hilbert program in more than the usual slogan form and shows why consistency is important. Von Plato shows in detail the benefits of Gentzen's program. This important book is a self-contained starting point for any work on Gentzen and his logic. The book is accessible to a wide audience with different backgrounds and is suitable for general readers, researchers, students, and teachers. Readership Mathematicians, scientists, and all others interested in the history of mathematics, the history of mathematical logic, and history in general. Reviews "...the book is a mine of information, and those interested in the history of logic in Gentzen's time are greatly in the author's debt." *-- Isis, An International Review Devoted to the History of Society and Its Cultural Influences* "...a book for all libraries..." *-- The Australasian Journal of Logic* "The mathematical logic is taken care of with equal meticulousness and accordingly the work serves two audiences very well, historians (of mathematics) and logicians (with a historical bent). ...of great value to specialists." *-- MAA Reviews* |