The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae: After C.F. Gauss's Disquisitiones Arithmeticae (Google eBook)
Catherine Goldstein, Norbert Schappacher, Joachim Schwermer
Springer, Feb 3, 2007 - Mathematics - 590 pages
The cultural historian Theodore Merz called it 'that 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 XIX th 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 18 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.
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Abel algebraic integers algebraic numbers analysis angewandte Mathematik arithmetic Berlin Bianchi Biermann binary quadratic forms Cantor Cauchy chap coefﬁcients complex numbers composition concept congruences coprime cyclotomic cyclotomy Dedekind deﬁned deﬁnition Dickson Dirichlet Disquisitiones Arithmeticae Disquisitiones generales divisor domain Eisenstein elliptic functions equations equivalent factors Fermat’s ﬁeld ﬁnally ﬁnd ﬁnite ﬁrst form f Galois Gauß Gauss sums Gaussian integers generales de congruentiis geometry Göttingen Hermite Hermite’s Hilbert Humboldt Hurwitz ideal numbers inﬁnite inﬂuence irreducible irreducible polynomial Jacobi Journal f¨ur Kronecker Kronecker’s Kummer Lagrange Legendre Leipzig Leopold Kronecker letter magnitudes mathematicians mathématiques Mathematische Minkowski modulo multiplication norm number ﬁelds number theory paper Paris polynomial prime number proof proved quadratic reciprocity law quadratic residue rational numbers reine und angewandte Repr residues Richard Dedekind roots of unity Schappacher sciences scientiﬁc speciﬁc Springer ternary forms Teubner theory of numbers transl Uber Weierstrass Werke Wissenschaften Zahlen Zahlentheorie Zolotarev