Logic's Lost Genius: The Life of Gerhard Gentzen

Voorkant
American Mathematical Soc., 1 jan. 2007 - 440 pagina's
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 Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an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.
 

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Inhoudsopgave

Early Youth and Abitur
1
19281938Weimar Republic and National Socialism in Peace
21
What Do Gentzens Intellectual Interests and Attitude in 1931 and 1932 Appear to Be?
33
Political Language in Mathematics in 1918
34
Whom Did Gentzen Know in Gottingen and What Did He Read?
37
Gentzens Life in the Early Nazi Period The Withdrawn Manuscript Uber das Verhaltnis zwischen intuitionistischer und klassischer Arithmetik of 15 ...
38
Gerhard Gentzens Dissertation Untersuchungen iiber das logische Schliefien of 12 July 1933
41
The Penetration of the Nazis into Mathematical Research at the University in Gottingen 1933 and 1934Or Vahlen and Bieberbach vs Weber and Weg...
46
Hans Rohrbachs Report on the Conditions in the Mathematical Institute in Prague
246
Why Did Gentzen Banish Any Thought of Flight?
247
Arrest Imprisonment Death and Nachlass
253
The Arrest of Gerhard Gentzen and the Awful Imprisonment
255
Gentzens Physical Death
257
Is Gentzens Death Understandable?
260
Rumours
261
Attempts to Rescue the Nachlass
263

The State Examination with Elektronenbahnen in axialsymmetrischen Feldern unter Anwendung auf kosmische Probleme on 16 November
51
Why Did Gentzen Join the SA?
52
A Conjecture
53
Gentzen in Financial Difficulties
54
Financial Straits and Job Hunting
55
Consistency Proof for Number Theory in Discussion with Paul Bernays
57
Widerspruchsfreiheit der reinen Zahlentheorie Mirrored in the Correspondence of Bernays and Weyl
58
Difficulties with the Widerspruchsfreiheit der reinen Zahlentheorie of 11 August 1935
59
Consistency of Type Theory
63
Revising the Proof of the Widerspruchsfreiheit der reinen Zahlentheorie
64
Die Widerspruchsfreiheit der reinen Zahlentheorie
65
Gentzen Was an Intellectual Independent
69
Gentzen Expresses His Thanks to Turing
71
Correspondence between Bernays and Ackermann 1936 to 1940
72
The Correspondence between Bernays and Gentzen Merrily Continues
75
Die gegenwärtige Lage in der mathematischen Grundlagenforschung The Extension of the Tenure of the Unscheduled Assistantship on 1 October 19...
77
Jean Cavailles and Gerhard Gentzen
82
Gentzen Becomes an Associate of the Publication of Scholzs Forschungen zur Logik und zur Grundlegung der exakten Wissenschafien
84
Die gegenwärtige Lage in der mathematischen Grundlagenforschung
86
Neue Fassung des Widerspruchsfreiheitsbeweises der reinen Zahlentheorie 1938
88
vii
99
19391942From the Beginning of the War to Dismissal from
117
A Battle
141
Stecks Attack on Hilbert Leads to Bieberbachs Commissioning a Defence of Mathematical Logic by H Scholz and Publishing It in Deutsche Mathema...
190
May and Dingler Provide Arguments for Steck
197
Steck and Scholz in Dispute
202
Max Steck as Denouncing Expert Witness and Publicist
208
The Dedicated National Socialist Logician and Historian of Mathematics Oskar Becker Remains Neutral
216
Resistance as a Mathematician Was Possible under National Social ism
218
Kurt Reidemeisters Additional Contemplations on PoliticoScientific Power Play in German Mathematics
219
Longer Notes
221
Recovery and Docent Position 1942 to 1944
233
Hans Rohrbach Commandeers Gerhard Gentzen to Prague through the Osenberg Initiative
234
Keplers Laws of Planetary Motion
236
The First Courses in November 1943
238
The Last Known Scientific Letter of Gerhard Gentzen
243
Teaching Functions Computing Office and War
244
The Deciphering of the Stenographic Notes
266
Conclusion
267
Upshot
269
Tables of the Life of Gerhard Gentzen
273
Contemporary Assessments of Gentzen
278
Publications of Gentzen
281
Appendix A Gentzen and Geometry C Smorynski
283
Appendix B Hilberts Programme C Smorynski
291
Problems in Paris
293
Hilbert and Geometry
296
First Steps
300
Enter Brouwer
301
Back to Hilbert
308
Weyl Stirs Things Up
310
Hilbert Responds
312
More on Brouwer
322
Outbreak of Hostilities
323
The Formula Game
324
On the Infinite
325
A Fragile Truce
327
Hilberts Programme Is Born
329
Brouwer Takes Up Arms
331
Hilbert Finishes Off Brouwer
332
The Programme Expands
334
Godels Theorem
335
Concluding Remarks
339
Three Lectures Gerhard Gentzen
343
The Concept of Infinity and the Consistency of Mathematics
350
The Current Situation in Research in the Foundations of Mathematics
353
From Hilberts Programme to Gentzens Programme Jan von Plato
367
Hilberts Programme
373
Gentzens Programme
383
Later Developments in Structural Proof Theory
396
References
401
Bibliography
405
Index
425
Copyright

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