Tuesday, September 20, 2011

Analytic Number Theory by Donald J. Newman

- This book is dedicated to Paul Erd˝os, the greatest mathematician I have ever known, whom it has been my rare privilege to consider colleague, collaborator, and dear friend. I like to think that Erd˝os, whose mathematics embodied the principles which have impressed themselves upon me as defining the true character of mathematics, would have appreciated this little book and heartily endorsed its philosophy. This book proffers the thesis that mathematics is actually an easy subject and many of the famous problems, even those in number theory itself, which have famously difficult solutions, can be resolved in simple and more direct terms. There is no doubt a certain presumptuousness in this claim. The great mathematicians of yesteryear, those working in number theory and related fields, did not necessarily strive to effect the simple solution. They may have felt that the status and importance of mathematics as an intellectual discipline entailed, perhaps indeed required, a weighty solution. Gauss was certainly a wordy master and Euler another. They belonged to a tradition that undoubtedly revered mathematics, but as a discipline at some considerable remove from the commonplace. In keeping with a more democratic concept of intelligence itself, contemporary mathematics diverges from this somewhat elitist view. The simple approach implies a mathematics generally available even to those who have not been favored with the natural endowments, nor the careful cultivation of an Euler or Gauss.

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