The Shaping of Arithmetic - After C.F. Gauß's Disquisitiones Arithmeticae

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. They had served throughout the XIX th century as an ideal of exposition in matters of notation, problems and methods; as a model of organisation of the material and theory building; and last but not least as a source of mathematical inspiration. Various readings of the Disquisitiones Arithmeticae have left their marks on developments as different as Galois' theory of algebraic equations, Lucas' primalitytests, and Dedekind's theory of ideals.The present volume revisits successive periods in the reception of Gauss's book: it studies which parts were taken up when, which themes were further explored. It also focusses on how specific mathematicians reacted to the Disquisitiones Arithmeticae: Dirichlet and Hermite, Kummer and Genocchi, Dedekind and Zolotarev. An astounding variety of research programmes in the theory of numbers can be traced back toGauss's book. The 18 authors - mathematicians, historians, philosophers - who have collaborated for this volume, contribute in-depth studies on the various aspects of the bicentennary voyage of this mathematical text through history, and the way that the number theory we know today came into being and diversified.