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The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae

After C.F. Gauss's Disquisitiones Arithmeticae

The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae by Catherine Goldstein
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The cultural historian, Theodore Merz called it the great book with seven seals, the mathematician Leopold Kronecker, "the book of all books": already one century after their publication, C.F. Gauss's "Disquisitiones Arithmeticae" (1801) had acquired an almost mythical reputation. It had served throughout the XIXth century and beyond as an ideal of exposition in matters of notation, problems and methods; as a model of organisation and theory building; and of course as a source of mathematical inspiration. Various readings of the "Disquisitiones Arithmeticae" have left their mark on developments as different as Galois's theory of algebraic equations, Lucas's primality tests, and Dedekind's theory of ideals. The present volume revisits successive periods in the reception of the Disquisitiones: it studies which parts were taken up and when, which themes were further explored. It also focuses on how specific mathematicians reacted to Gauss's book: Dirichlet and Hermite, Kummer and Genocchi, Dedekind and Zolotarev, Dickson and Emmy Noether, among others. An astounding variety of research programmes in the theory of numbers can be traced back to it.
Springer; February 2007
586 pages; ISBN 9783540347200
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Title: The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae
Author: Catherine Goldstein; Norbert Schappacher; Joachim Schwermer
 
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