Customer Reviews

History of the Theory of Numbers (AMS Chelsea Publishing) Volumes I; II; III. THREE VOLUME SET (Vol. 2)

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The author was himself an expert in number theory and modern algebra (as it was) in his day. These volumes were published in 1919-23 so don't expect the latest results. In fact, the terminology won't even be the same since much of the theory has undergone a great deal of mollycoddling and reformulation...publish or perish, you know.

If you plan to do original research in the theory of numbers, these volumes are a must (even with the heavy price tag). Why? There is so much work constantly being done, results are often lost with time - what seems like something new is probably not. Like the constant rediscovery of Bernoulli and Striling numbers.

The volumes are probably not what you expect. They're really just a large annotated bibliography without detailed proofs or much immediate historic motivation (long-term history is the over-riding theme). Dickson catalogs near-misses as well as sometime pointless generalizations, so the text is not all meat. (Perhaps he's being more journalist here, than editor). In fact, it can become quite tiresome. You may be content to read these in a library, as any results will probably require you to look up the original source for more details. You'd better take notes and write down the page numbers while perusing. It's hard to find your way back, so many papers, so many authors, and the index is not optimal.

Andre Weil's "Number Theory: An approach through history" is a more literary and biographical account, but less comprehensive in the excruciating details.

5 stars for being an indispensable reference (if only for the historically-minded). Not without shortcomings.

This long book is sort of the equivalent of an extremely long review paper, with innumerable references. It is the only work of its kind on Theory of Numbers. Written in the early 1920s, it is still the only place where one can find information on who did what in various topics of number theory, and many of those topics are still fertile ground for further research. So if one wants to do research on any topic in theory of numbers, or on related aspects of algebra, topology, Ramsey Theory, theory of graphs, etc. one *must* have Dickson's book handy. It's expensive; if you're lucky, a colleague or your departmental library may have a copy handy for you, but if not, go ahead and spend the money to buy it. It has been of great use to me.