Thursday, July 15, 2010

Book Review: Number Theory

I've had this book on the "What I'm reading" section of my website for four years, and that's not because I haven't been updating. Never before have I been so humbled by a book. Well, a non-religious book anyway.

Having no formal training in number theory, or anyone to talk about these things with, I don't know if this book is really good, but I do know that I learned much about what numbers are, the relations between infinite series and infinite products, and that it is possible to understand a page that is mostly Greek letters and arrows. I think seeing the deep relationships between apparently unrelated numbers, especially when it comes to counting things, is a view of the infrastructure of the universe. Sort of like going backstage at a play.

Perhaps the material is a little advanced for the introductory student, however, as in the middle of one proof the author drops in a result from Ramanujan which he later describes as pulling a rabbit out of a hat. For the non-math types, this is essentially proof by graduate student, except using the most brilliant mathematician who ever lived.

At any rate, this is a fine text if you want to expand your mind, though I also recommend having four years to bang your head against a brick wall. Though now that I've finished it, perhaps I can help you and it will only take you a year or two. I have to start studying things with actual economic value.


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