Logic's lost genius : the life of Gerhard Gentzen
著者
書誌事項
Logic's lost genius : the life of Gerhard Gentzen
（History of mathematics, v. 33）
American Mathematical Society , London Mathematical Society, 2007
- タイトル別名
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Gentzens Problem
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注記
Translation of: Gentzens Problem. Basel : Birkhäuser Verlag, c2001
Includes bibliographical references (p. 405-432) and index
内容説明・目次
内容説明
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 Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an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 Smorynski on Gentzen's proof theory; its relation to the ideas of Hilbert, Brouwer, Weyl, and Godel; and its development up to the present day. Smorynski 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. Information for our distributors: Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.
目次
Early youth and abitur 1928-1938--Weimar Republic and National Socialism in peace. From the beginning of studies to the extension of the unscheduled assistantship for another year with effect from 1 October 1938 1939-1942-From the beginning of the war to dismissal from the Wehrmacht and the wartime habilitation under Helmut Hasse The fight over "German logic" from 1940 to 1945: A battle between amateurs Recovery and docent position 1942 to 1944 Arrest, imprisonment, death and Nachlass Conclusion Tables of the life of Gerhard Gentzen Appendix A: Gentzen and geometry, by C. Smorynski Appendix B: Hilbert's programme, by C. Smorynski Appendix C: Three lectures, by Gerhard Gentzen Appendix D: From Hilbert's programme to Gentzen's programme, by Jan von Plato Bibliography Index.
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