Springer Collected Works in Mathematics
2 total works
From the reviews: "The broad lines of Kummer's number-theoretic ideas now form an essential part of our heritage: it is fascinating to follow the details of their evolution...Volume I consists of Kummer's number theory. It constitutes a unity of thought and spirit almost from first sentence to last. One of the joys of reading it is in the double spectacle: the steady train of mathematical content, unimpeded by lack of basic algebraic number theory; while here and there, to serve problems at hand, the deft, unobtrusive forging of pieces of present day technique. It is not hard to get into, even for those of us who have had little contact with the history of our subject. Cleft though one may think one is from historical sources, on reading Kummer one finds that the rift is jumpable, the jump pleasurable. The reader is greatly helped in this jump in two ways.
Firstly, included in the volume is a continuum of well-written, moving letters from Kummer to Kronecker giving the details of many of Kummer's important discoveries as they freshly occurred to him (these, together with some letters from Kummer to his mother, form part of a description of Kummer's work by Hensel on the occasion of the centenary of Kummer's birth, also included in the volume). Secondly, there is an excellent introduction, in which Weil describes the main lines of Kummer's work, and explains its relations to Kummer's contemporaries, and to us."
Firstly, included in the volume is a continuum of well-written, moving letters from Kummer to Kronecker giving the details of many of Kummer's important discoveries as they freshly occurred to him (these, together with some letters from Kummer to his mother, form part of a description of Kummer's work by Hensel on the occasion of the centenary of Kummer's birth, also included in the volume). Secondly, there is an excellent introduction, in which Weil describes the main lines of Kummer's work, and explains its relations to Kummer's contemporaries, and to us."
The collected works of Ernst Eduard Kummer form two volumes. Volume I is devoted to Kummer's work on number theory while Volume II, divided into four parts, focuses on his other research interests. Part 1 (Function theory) covers his work on the hypergeometric function, and on repeated integrals of rational functions. In Part 2 (Algebraic geometry) we see how the discovery of "Kummer surfaces" seems to have been an outgrowth of Kummer's interest in the optical properties of biaxial crystals, and in the "Cyclides" of Dupin. The relation between these quartic surfaces and quotients of abelian surfaces was discovered only much later. One also finds here a number of papers describing actual plaster models of particular "Kummer surfaces", with special symmetries in evidence. Part 3 concerns Aerodynamics and ballistics and, finally, Part 4 (Speeches and reviews) spans a broad range of topics, including a long retrospective on the life and work of Dirichlet.