Logic's Lost Genius: The Life of Gerhard GentzenAmerican Mathematical Soc., 1 janv. 2007 - 440 pages 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 Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an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. |
Table des matières
1 | |
19281938Weimar Republic and National Socialism in Peace | 21 |
What Do Gentzens Intellectual Interests and Attitude in 1931 | 33 |
Gerhard Gentzens Dissertation Untersuchungen über das logische | 41 |
Why Did Gentzen Join the | 52 |
Widerspruchsfreiheit der reinen Zahlentheorie Mirrored in | 58 |
Revising the Proof of the Widerspruchsfreiheit der reinen | 64 |
The Correspondence between Bernays and Gentzen Merrily Continues | 75 |
Attempts to Rescue the Nachlass | 263 |
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 SMORYŃSKI | 283 |
32 | 82 |
Neue Fassung des Widerspruchsfreiheitsbeweises der reinen | 88 |
vii | 99 |
19391942From the Beginning of the War to Dismissal from | 117 |
A Battle | 141 |
NS Ideology in Mathematics through Bieberbach Receives Negative | 152 |
Johann L Schmidt | 159 |
Mathematical Foundational Research Remains Unmolested | 167 |
Heinrich Scholz 18841956 | 176 |
Bieberbach Max Steck and Jænsch | 186 |
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 |
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 |
Appendix B Hilberts Programme C SMORYŃSKI | 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 |
Gödels 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 |
405 | |
433 | |
Autres éditions - Tout afficher
Expressions et termes fréquents
Ackermann already analysis appeared applied arithmetic attempt axioms Berlin Bernays Bieberbach Brouwer calculus called carried classical complete concept connection consider consistency proof constructive correct correspondence derivation Deutsche Dingler discussion example existence expression extended fact finite formal formula foundations function further Gentzen geometry Gerhard Gentzen German give given Gödel Göttingen Heinrich Hilbert ideas induction inference infinite Institute intuitionistic intuitionistic logic later lecture letter logic March Math mathematicians mathematics Mathematik means mentioned methods natural Nazi number theory objects original Paul philosophy physics political position possible present problem Professor programme proof theory propositional provable prove publication published pure question reason received referred remains remarks respected result rules Scholz scientific sequent shows Steck student theorem thought transfinite University wanted Weyl wrote