Collected Papers I: Contributions to Number Theory

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 manyof 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."