The Theory of Algebraic Number Fields by David Hilbert

The Theory of Algebraic Number Fields by David Hilbert

Constance Reid, in Chapter VI of her book Hilbert, tells the story of the writing of the Zahlbericht, as his report entitled Die Theorie der algebra is- chen Zahlkorper has always been known. At its annual meeting in 1893 the Deutsche Mathematiker-Vereinigung (the German Mathematical Society) invited Hilbert and Minkowski to prepare a report on the current state of affairs in the theory of numbers, to be completed in two years. The two mathematicians agreed that Minkowski should write about rational number theory and Hilbert about algebraic number theory. Although Hilbert had almost completed his share of the report by the beginning of 1896 Minkowski had made much less progress and it was agreed that he should withdraw from his part of the project. Shortly afterwards Hilbert finished writing his report on algebraic number fields and the manuscript, carefully copied by his wife, was sent to the printers. The proofs were read by Minkowski, aided in part by Hurwitz, slowly and carefully, with close attention to the mathematical exposition as well as to the type-setting; at Minkowski's insistence Hilbert included a note of thanks to his wife. As Constance Reid writes, The report on algebraic number fields exceeded in every way the expectation of the members of the Mathemati- cal Society. They had asked for a summary of the current state of affairs in the theory. They received a masterpiece, which simply and clearly fitted all the difficult developments of recent times into an elegantly integrated theory.

David Hilbert was a German mathematician who lived from 1862 to 1943. He is regarded as one of the most prominent and all-encompassing mathematicians of the nineteenth and early twentieth century. In several domains, including invariant theory and the axiomatization of geometry, Hilbert discovered and developed a vast range of essential ideas. He also developed the Hilbert space theory, which is one of the basis of functional analysis. Georg Cantor's set theory and transfinite numbers were embraced and defended by Hilbert.

His 1900 presentation of a group of problems that set the route for most of twentieth-century mathematical research is a renowned example of his leadership in mathematics. Hilbert and his students made substantial contributions to the development of rigor and essential tools employed in modern mathematical physics. Hilbert is credited as being one of the first to distinguish between mathematics and meta/mathematics, as well as one of the creators of proof theory and mathematical logic. WELCOME TO THE INTRODUCTION.

Geometry, like arithmetic, requires only a few simple, foundational principles for its logical growth. The axioms of geometry are the fundamental principles of geometry. The selection of axioms and exploration of their interrelationships is a issue that has been treated in various great memoirs in the mathematical literature since Euclid's time. This dilemma is analogous to a logical study of our spatial intuition.

The following inquiry is a novel attempt to choose a simple and complete set of independent axioms for geometry and deduce the most important geometrical theorems from them in such a way that the relevance of the different groups of axioms and the breadth of the conclusions to be obtained from the individual axioms are brought out as clearly as possible.

SKU	Unavailable
ISBN 13	9783540627791
ISBN 10	3540627790
Title	The Theory of Algebraic Number Fields
Author	David Hilbert
Condition	Unavailable
Binding Type	Hardback
Publisher	Springer
Year published	1998-08-20
Number of pages	351
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note	Unavailable