Logic's Lost Genius: The Life of Gerhard Gentzen
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 Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an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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19281938Weimar Republic and National Socialism in Peace
What Do Gentzens Intellectual Interests and Attitude in 1931 and 1932 Appear to Be?
Political Language in Mathematics in 1918
Whom Did Gentzen Know in Gottingen and What Did He Read?
Gentzens Life in the Early Nazi Period The Withdrawn Manuscript Uber das Verhaltnis zwischen intuitionistischer und klassischer Arithmetik of 15 ...
Gerhard Gentzens Dissertation Untersuchungen iiber das logische Schliefien of 12 July 1933
The Penetration of the Nazis into Mathematical Research at the University in Gottingen 1933 and 1934Or Vahlen and Bieberbach vs Weber and Weg...
Hans Rohrbachs Report on the Conditions in the Mathematical Institute in Prague
Why Did Gentzen Banish Any Thought of Flight?
Arrest Imprisonment Death and Nachlass
The Arrest of Gerhard Gentzen and the Awful Imprisonment
Gentzens Physical Death
Is Gentzens Death Understandable?
Attempts to Rescue the Nachlass
The State Examination with Elektronenbahnen in axialsymmetrischen Feldern unter Anwendung auf kosmische Probleme on 16 November
Why Did Gentzen Join the SA?
Gentzen in Financial Difficulties
Financial Straits and Job Hunting
Consistency Proof for Number Theory in Discussion with Paul Bernays
Widerspruchsfreiheit der reinen Zahlentheorie Mirrored in the Correspondence of Bernays and Weyl
Difficulties with the Widerspruchsfreiheit der reinen Zahlentheorie of 11 August 1935
Consistency of Type Theory
Revising the Proof of the Widerspruchsfreiheit der reinen Zahlentheorie
Die Widerspruchsfreiheit der reinen Zahlentheorie
Gentzen Was an Intellectual Independent
Gentzen Expresses His Thanks to Turing
Correspondence between Bernays and Ackermann 1936 to 1940
The Correspondence between Bernays and Gentzen Merrily Continues
Die gegenwärtige Lage in der mathematischen Grundlagenforschung The Extension of the Tenure of the Unscheduled Assistantship on 1 October 19...
Jean Cavailles and Gerhard Gentzen
Gentzen Becomes an Associate of the Publication of Scholzs Forschungen zur Logik und zur Grundlegung der exakten Wissenschafien
Die gegenwärtige Lage in der mathematischen Grundlagenforschung
Neue Fassung des Widerspruchsfreiheitsbeweises der reinen Zahlentheorie 1938
19391942From the Beginning of the War to Dismissal from
Stecks Attack on Hilbert Leads to Bieberbachs Commissioning a Defence of Mathematical Logic by H Scholz and Publishing It in Deutsche Mathema...
May and Dingler Provide Arguments for Steck
Steck and Scholz in Dispute
Max Steck as Denouncing Expert Witness and Publicist
The Dedicated National Socialist Logician and Historian of Mathematics Oskar Becker Remains Neutral
Resistance as a Mathematician Was Possible under National Social ism
Kurt Reidemeisters Additional Contemplations on PoliticoScientific Power Play in German Mathematics
Recovery and Docent Position 1942 to 1944
Hans Rohrbach Commandeers Gerhard Gentzen to Prague through the Osenberg Initiative
Keplers Laws of Planetary Motion
The First Courses in November 1943
The Last Known Scientific Letter of Gerhard Gentzen
Teaching Functions Computing Office and War
The Deciphering of the Stenographic Notes
Tables of the Life of Gerhard Gentzen
Contemporary Assessments of Gentzen
Publications of Gentzen
Appendix A Gentzen and Geometry C Smorynski
Appendix B Hilberts Programme C Smorynski
Problems in Paris
Hilbert and Geometry
Back to Hilbert
Weyl Stirs Things Up
More on Brouwer
Outbreak of Hostilities
The Formula Game
On the Infinite
A Fragile Truce
Hilberts Programme Is Born
Brouwer Takes Up Arms
Hilbert Finishes Off Brouwer
The Programme Expands
Three Lectures Gerhard Gentzen
The Concept of Infinity and the Consistency of Mathematics
The Current Situation in Research in the Foundations of Mathematics
From Hilberts Programme to Gentzens Programme Jan von Plato
Later Developments in Structural Proof Theory
Overige edities - Alles weergeven
Ackermann already analysis applied axiomatic axioms Berlin Bilharz Brouwer Cavailles classical complete consistency proof constructive derivation Deutsche Mathematik Dingler finitary finite finitistic formal formalisation formula foundational research foundations of mathematics Frege geometry Gerhard Gentzen German mathematics Godel Gottingen Grundlagen habilitation Hasse Heinrich Scholz Hellmuth Kneser Hermann Weyl Heyting Hilbert Hilbert's Programme Hugo Dingler in-itself conception infinite infinity intuitionism intuitionistic arithmetic intuitive Jean Cavailles Kneser Kurt lecture letter Logik Ludwig Bieberbach Math Mathematical Institute mathematical logic mathematicians means metamathematics methods Miinster modes of inference Munich Nachlass National Socialism National Socialist natural deduction natural numbers Nazi ordinal numbers paper Paul Bernays philosophy possible Prague predicate logic problem Prof proof theory propositional provable prove published pure number theory question real numbers reinen Zahlentheorie respected Herr Professor result Rohrbach rules scientific sequent calculus set theory standpoint student theorem transfinite induction type theory Uber University Verlag wrote