History of Mathematics
Volume: 33;
2007;
442 pp;
Softcover
MSC: Primary 01;
Print ISBN: 978-1-4704-2812-9
Product Code: HMATH/33.S
List Price: $97.00
AMS Member Price: $77.60
MAA Member Price: $87.30
Electronic ISBN: 978-1-4704-3899-9
Product Code: HMATH/33.E
List Price: $97.00
AMS Member Price: $77.60
MAA Member Price: $87.30
Supplemental Materials
Logic’s Lost Genius: The Life of Gerhard Gentzen
Share this pageEckart Menzler-Trott
A co-publication of the AMS and the London Mathematical Society
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unpublished sources, family documents, archival material, interviews,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.
Reviews & Endorsements
...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
Table of Contents
Table of Contents
Logic's Lost Genius: The Life of Gerhard Gentzen
- Cover Cover11
- Title page iii4
- Books v6
- Contents vii8
- Preface to the English edition xiii14
- Introduction xvii18
- Early youth and abitur 124
- 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 2144
- 1939-1942—From the beginning of the war to dismissal from the Wehrmacht and the wartime habilitation under Helmut Hasse 117140
- The fight over “German logic” from 1940 to 1945: A battle between amateurs 141164
- Recovery and docent position 1942 to 1944 233256
- Arrest, imprisonment, death and Nachlass 253276
- Conclusion 267290
- Tables of the life of Gerhard Gentzen 273296
- Appendix A: Gentzen and geometry, by C. Smoryński 283306
- Appendix B: Hilbert’s programme, by C. Smoryński 291314
- Appendix C: Three lectures, by Gerhard Gentzen 343366
- Appendix D: From Hilbert’s programme to Gentzen’s programme, by Jan von Plato 367390
- Bibliography 405428
- Index 433456
- Back Cover Back Cover1466