 | Eckart Menzler-Trott:
Logic’s Lost Genius - The Life of Gerhard Gentzen.
Translated from the German by Craig Smorynski and Edward Griffor. With appendices and two essays by Craig Smorynski and Jan von Plato. American Mathematical Society: Providence, Rhode Island (USA)and the London Mathematical Society: London (U.K.) Series: History of Mathematics, vol. 33. ISBN-10: 0-8218-3550-5 ISBN-13: 978-0-8218-3550-0 November 2007. 438 pages. Hardcover. US $ 89.- (Member Price: US $ 71.-) |
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 indispensable 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 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 Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen’s lectures for the mathematical public, make this book an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 Gödel; 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. Table of Contents:· 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 Place your order please: http://www.ams.org/bookstore?fn=20&arg1=hmathseries&item=HMATH-33ORDER CODE: HMATH/33
About the first, somehow outdated German edition ‚Gentzens Problem’ (2001) :
“(...) a diligently detailed biography (…) As with many other events in his life, this biography is able to provide details concerning the circumstances of Gentzen's last days that add substantially to what has appeared in print previously. (…) a significant counterweight to the overly-broad historical generalizations (…)”.
Prof. Albert C. Lewis, PhD. im “Zentralblatt für Mathematik und ihre Grenzgebiete” 2002
“ (…) There is much to praise in this book, and the research behind it, which includes extensive use of archives and some oral history. (…)”.
Prof. Ivor Grattan-Guinness, PhD. in “History and Philosophy of Logic”, July 2002, 313
This is a really valuable book.
(jfi) European Mathematical Society, Newsletter No. 47, March 2003, p. 44
De grote verdienste van dit boek is dat het enerzijds recht doet aan de genialiteit van Gentzen en anderzijds de ogen opent voor het drama dat zich aan deze verdoolde man heeft voltrokken. Zijn leven was vervuld van de schoonheid van de structuren en bewijzen die hij had gevonden en hij wilde niets liever dan daarover vertellen.
This is a really valuable book. De grote verdienste van dit boek is dat het enerzijds recht doet aan de genialiteit van Gentzen en anderzijds de ogen opent voor het drama dat zich aan deze verdoolde man heeft voltrokken. Zijn leven was vervuld van de schoonheid van de structuren en bewijzen die hij had gevonden en hij wilde niets liever dan daarover vertellen. Leo Steenvorden, in: Tijdschrift voor Geschiedenis, 116e jaargang, 2003 – 1, p. 158
The book (...) is a detailed biography of Gerhard Gentzen and at the same time a deep analysis of the situation of mathematical logic ( and of mathematics) in Nazi Germany. (...) The book is an enourmous source of information. (...) The book under review is an extremely praise-worthy work, Gentzen belongs and will belong to giants of mathematical logic. (...)
Prof. RNDr. Dr.Sc. Petr Hajek (Akademie der Wissenschaften, Prag) in Pokroky matematiky, fyziky a astronomie, rocnik 48 (2003) c. 3, p. 263 f.
(...) an indispensible source for everyone interested in Gentzen. Nevertheless it evokes mixed impressions especially in respect to its scholarly qualities. (...) written in love for its subject, and with deep disgust for the circumstances which made Gentzen's tragic end possible. (...) In the biographical parts an impressive wealth of material is presented, besides published sources hitherto unpublished material, family documents, archival sources, interviews etc. (...) For the present edition the summarizing comment is: it’s a pity!
Prof. Dr. Volker Peckhaus (Universität Paderborn) in: Bulletin of Symbolic Logic Vol. 9, December 2003
(...) The author’s intention is to tell the story of Gentzen’s life to those interested in or already familiar with his fundamental contributions to mathematics and logic, and to make clear his positions and circumstances as a mathematician under National Socialism. Above all, the author seeks to explain why the partisans of National Socialism promoted mathematical logic, specifically ist rationality, and to understand the political implications of their doing so. For example, Gentzen enjoyed the support of Bieberbach and Vahlen, who sought to use the rationality of mathematics and mathematical logic to advance „German Mathematics“. In order to understand how individuals fared under National Socialism, the biography of Gentzen serves as a case study. (...)
Joseph W. Dauben (Distiguished Professor of History and History of Science at Lehmann College) in Mathematical Reviews MR1997643 (2004e:01037)
The book under review is a detailed biography of Gerhard Gentzen and at the same time a penetrating analysis of the situation of mathematical logic (and of mathematics) in Nazi Germany. (...) The author offers us an impressive amount of historical information of Gentzen’s life and work, and none of it seems to hold any sinister details that hint at political motives or social resentment. (...) The author deserves credit for the enormous task of doing justice to the life and personality of one of our greatest logicians. It always is – and the more so in the case of a scholar who lived and died in uncertain times and circumstances – surprising how much evidence a clever researcher can find. Menzler-Trott has created a fitting monument to an introverted and naive scientist, who had so much to offer to science, but who utterly failed to grasp the problems and obligations of humanity. (...) If we can find any shortcoming, it is that the aesthetic aspect of Gentzen’s work does not the attention it deserves (...) Matters of this sort are, however, difficult to convey; one does not start to enjoy Beethoven’s music by reading reviews, one has to hear and play it oneself. (...) Summing up: Gentzens Problem is a valuable contribution to the history of an enigmatic logician and his work, and to the singularity in the history of science called Nazi mathematics. Menzler-Trott has provides a wealth of facts and details, and he has gone a long way towards their interpretation. (...) In particular, we may be certain that Gentzen belongs forever to the giants of mathematical logic.
Petr Hájek (Academy of Sciences of the Czech Republic, Institute of Computer Science) and Dirk van Dalen (Department of Philosophy, Utrecht University) in: Mathematical Intelligencer, Fall 2004, Vol. 26, No. 4)
This is a really valuable book. De grote verdienste van dit boek is dat het enerzijds recht doet aan de genialiteit van Gentzen en anderzijds de ogen opent voor het drama dat zich aan deze verdoolde man heeft voltrokken. Zijn leven was vervuld van de schoonheid van de structuren en bewijzen die hij had gevonden en hij wilde niets liever dan daarover vertellen. This is a really valuable book. De grote verdienste van dit boek is dat het enerzijds recht doet aan de genialiteit van Gentzen en anderzijds de ogen opent voor het drama dat zich aan deze verdoolde man heeft voltrokken. Zijn leven was vervuld van de schoonheid van de structuren en bewijzen die hij had gevonden en hij wilde niets liever dan daarover vertellen. This is a really valuable book. De grote verdienste van dit boek is dat het enerzijds recht doet aan de genialiteit van Gentzen en anderzijds de ogen opent voor het drama dat zich aan deze verdoolde man heeft voltrokken. Zijn leven was vervuld van de schoonheid van de structuren en bewijzen die hij had gevonden en hij wilde niets liever dan daarover vertellen. |
