Traité des Substitutions et des Équations algébriques

JORDAN, Camille

Published by Gauthier-Villars, Paris, 1870

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THE FOUNDATION WORK OF MODERN GROUP THEORY. First edition, very rare, of "the book that established group theory as a subject in its own right in mathematics" (Gray, p. 149). "Jordan s monumental work, Traité des Substitutions et des Équations algébriques, published in 1870, is a masterpiece of mathematical architecture. The beauty of the edifice erected by Jordan is admirable" (Van der Waerden, A History of Algebra, p. 117). "In 1870, Jordan gathered all his results on permutation groups for the previous ten years in a huge volume, Traité des Substitutions, which for thirty years was to remain the bible of all specialists in group theory. His fame had spread beyond France, and foreign students were eager to attend his lectures; in particular Felix Klein and Sophus Lie came to Paris in 1870 to study with Jordan" (DSB)? "An instant classic, his Traité set a new research agenda of creating a theory of groups as opposed to the older agenda of devising ways to calculate the solutions of polynomial equations" (Katz & Parshall, p. 316). "The title of this comprehensive work of 667 quarto pages is excessively modest and therefore misleading. The work represents not only the definitive solution of the problem formulated by Galois, but also a review of the whole of contemporary mathematics from the standpoint of group-theoretic thinking" (Wussing, pp. 141-142). "Jordan s place in the tradition of French mathematics is exactly halfway between Hermite and Poincaré. Like them he was a universal mathematician who published papers in practically all branches of the mathematics of his time … [but] it is chiefly as an algebraist that he reached celebrity when he was barely thirty; and during the next forty years he was universally regarded as the undisputed master of group theory. When Jordan started his mathematical career, Galois s profound ideas and results (which had remained unknown to most mathematicians until 1846) were still very poorly understood, despite the efforts of Serret and Liouville to popularize them; and before 1860 Kronecker was probably the only first-rate mathematician who realized the power of these ideas and who succeeded in using them in his own algebraic research. Jordan was the first to embark on a systematic development of the theory of finite groups and of its applications in the directions opened by Galois … He also was the first to investigate the structure of the general linear group and of the classical groups over a prime finite field, and he very ingeniously applied his results to a great range of problems; in particular, he was able to determine the structure of the Galois group of equations having as roots the parameters of some well-known geometric configurations (the twenty-seven lines on a cubic surface, the twenty-eight double tangents to a quartic, the sixteen double points of a Kummer surface, and so on)" (ibid.). This is an extremely rare book on the market, and very uncommon even in institutional collections. ABPC/RBH list only the two copies in the Duarte sale in 1977. It has been suggested that most copies of the book were destroyed in a fire at the publisher s warehouse during the violent suppression of the Paris Commune early in 1871, and that the marginal browning seen in many of the surviving copies was caused by the heat of the fire. Évariste Galois (1811-32) published a few short papers in his lifetime, but his most important works were posthumous. He first set down his ideas on the relationship between what we call group theory and the solvability of polynomial equations in his most important work, Mémoire sur les conditions de résolubilité des équations par radicaux, usually called the Premier Mémoire, which he submitted to the Paris Académie des Sciences but which they rejected and returned to the author on 4 July 1831. He followed this with Des équations primitives qui sont solubles par radicaux, also known as the Second Mémoire. Both Mémoires were published for the first time. Seller Inventory # 4912

Bibliographic Details

Title: Traité des Substitutions et des Équations ...

Publisher: Gauthier-Villars, Paris

Publication Date: 1870

Edition: First edition.