Shaping of arithmetic.
Berlin : Springer, c2007
|提及的人：||Carl Friedrich Gauss|
Catherine Goldstein, (Mathematician); Norbert Schappacher; Joachim Schwermer
|ISBN:||9783540204411 3540204415 9783540347200 3540347208 1280804068 9781280804069|
|描述：||1 online resource (x, 578 p.) : 36 ill.|
|責任：||Catherine Goldstein, Norbert Schappacher, Joachim Schwermer, editors.|
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.; The 19 authors - mathematicians, historians, philosophers - who have collaborated on this volume contribute in-depth studies on the various aspects of the bicentennial voyage of this mathematical text through history, and the way that the number theory we know today came into being.