Logic's lost genius - The life of Gerhard Gentzen

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 Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an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. Cover -- Title page -- Books -- Contents -- Preface to the English edition -- Introduction -- 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. Smoryński -- Appendix B: Hilbert's programme, by C. Smoryński -- Appendix C: Three lectures, by Gerhard Gentzen -- Appendix D: From Hilbert's programme to Gentzen's programme, by Jan von Plato -- Bibliography -- Index -- Back Cover Cover 1 Contents 7 Preface to the English edition 13 Introduction 17 Early youth and abitur 23 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 43 1939-1942—From the beginning of the war to dismissal from the Wehrmacht and the wartime habilitation under Helmut Hasse 139 The fight over “German logic” from 1940 to 1945: A battle between amateurs 163 Recovery and docent position 1942 to 1944 255 Arrest, imprisonment, death and Nachlass 275 Conclusion 289 Tables of the life of Gerhard Gentzen 295 Appendix A: Gentzen and geometry, by C. Smoryński 305 Appendix B: Hilbert’s programme, by C. Smoryński 313 Appendix C: Three lectures, by Gerhard Gentzen 365 Appendix D: From Hilbert’s programme to Gentzen’s programme, by Jan von Plato 389 Bibliography 427 Index 455 Back Cover 465