Ernst Eduard Kummer – författare

From the reviews: "The broad lines of Kummer'snumber-theoretic ideas now form an essential part of our heritage: it isfascinating to follow the details of their evolution... Volume I consists of Kummer'snumber theory. It constitutes a unity of thought and spirit almost from firstsentence to last. One of the joys of reading it is in the double spectacle: thesteady train of mathematical content, unimpeded by lack of basic algebraicnumber 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 getinto, even for those of us who have had little contact with the history of oursubject. Cleft though one may think one is from historical sources, on readingKummer one finds that the rift is jumpable, the jump pleasurable. The readeris greatly helped in this jump in two ways. Firstly, included in the volume is acontinuum of well-written, moving letters from Kummer to Kronecker givingthe details of manyof Kummer's important discoveries as they freshlyoccurred to him (these, together with some letters from Kummer to his mother, form part of a description of Kummer's work by Hensel on theoccasion of the centenary of Kummer's birth, also included in the volume).Secondly, there is an excellent introduction, in which Weil describes the mainlines of Kummer's work, and explains its relations to Kummer's contemporaries,and to us."

Volume II of Ernst Kummer's Collected Papers can be divided into four different parts. The first part covers his work on the hypergeometric function, and on repeated integrals of rational functions. In the second part (Algebraic Geometry), we see how the discovery of Kummer surfaces seems to have been an outgrowth of the authors interest in optical properties of biaxial crystals, and in the "cyclides" of Dupin. The relation between Kummer surfaces and quotients of abelian surfaces was discovered only much later. In this section, one also finds a number of papers describing actual plaster models of particular Kummer surfaces with symmetries. The third part is devoted to his work on aerodynamics and ballistics. Finally, the fourth part (Speeches and Reviews) spans a broad range of topics, including a long retrospective on the life and work of Dirichlet.