Product Description
Most scholars think of David Hilbert's program as the most demanding and ideologically motivated attempt to provide a foundation for mathematics, and because they see technical obstacles in the way of realizing the program's goals, they regard it as a failure. Against this view, Curtis Franks argues that Hilbert's deepest and most central insight was that mathematical techniques and practices do not need grounding in any philosophical principles. He weaves together an original historical account, philosophical analysis, and his own development of the meta-mathematics of weak systems of arithmetic to show that the true philosophical significance of Hilbert's program is that it makes the autonomy of mathematics evident. The result is a vision of the early history of modern logic that highlights the rich interaction between its conceptual problems and technical development. ... Read more

Customer Reviews (2)

An explanation of the value of Hilbert's program of axiomatic completeness
There are two broad categories of major players in any field of intellectual human endeavor; the people that pose the problems and the ones that (re)solve them. Unfortunately, history often allocates greater praise to the solvers rather than the equally essential proposers. In the 1920's, the great German mathematician David Hilbert proposed an approach that would place mathematics on a sound axiomatic foundation. The goal was to prove the consistency of mathematics, in other words that it is not possible to ever properly deduce a contradiction. Like so many such programs, it was one whose time had come as there were several earlier discoveries and issues that pointed the way. In this book, Franks explains the program, some of the work done on it and the primary consequences of what Hilbert initiated.
The program went to the very essence of what mathematics and proof are, in some ways it is one of the most complex areas of philosophy. Very few question the existence of physical matter and the laws that govern its' behavior, but in mathematics the objects can only be approximated, they are the product of thought. So too are the reasoning techniques used to manipulate them, the primary reason that so many people find mathematics difficult is that you are manipulating abstract ideas represented by unusual symbols. Hilbert's goal was to formalize these ideas as much as possible so that whenever an object was declared and processed, each step in the route was formally understood. Furthermore, the rules regarding what you could do were rigidly traced back to a solid foundation of understanding.
Franks does an excellent job in describing this process, giving Hilbert much deserved credit for putting forward the program. While Kurt Gödel's Incompleteness Theorems meant that there were some limits beyond which even mathematics could not cross, Hilbert helped initiate a mindset that drove the mathematical community towards those barriers.
Most mathematicians simply do their mathematics without regard to the deep metamathematics underlying their actions. In most cases, this really does not matter, yet it is something that all practitioners should consider from time to time. Franks does a sound job in revisiting what Hilbert started and with few exceptions it is a book that all mathematicians can understand and appreciate.

BIBLIOGRAPHIC FLAW
The author cites the 1956 first edition of Alfred Tarski's LOGIC, SEMANTICS, METAMATHEMATICS that has been out-of-print for nearly fifty years and that contains hundreds of errors since corrected by Tarski in the second edition.
Tarski, A. 1956/1983. LOGIC, SEMANTICS, METAMATHEMATICS, second edition revised and corrected by Tarski with new introduction and new analytic index by J. Corcoran, Hackett Publishing Company, Indianapolis (1983). Originally published by Oxford: Oxford University Press, 1956.MR85e:01065.
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Product Description
Since the first volume of this work came out in Germany in 1937, this book, together with its first volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's final revision of 1961. ... Read more

Customer Reviews (2)

classical math physics text
This two volume set is a classic rivaled only by Morse and Feshbach "Methods of Theoretical Physics", vol 1 and 2. It should be a part of the library of any serious student of physics or engineering.

state of the art in the 50's
Beware the german edition is the prewar edition, and the english edition is a
complete overhaul to include modern material at the time. This is not really a
textbook, but a sourcebook of "issues" in partial differential equations. Some
problems have been forgotten now due to the focussing on real, linear equations
and weak solutions (as described, for example, in the books by Hormander). It is
a gem for who wants some taste of the full breadth of theory of PDE's. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR’d book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR’d book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more