I renewed my membership in the American Math Society for the nth year, wondering how many consecutive years I've been a member (it's got to be at least twenty). Supposing I'm struck by a lightning bolt and killed tomorrow, I'm wondering, would this merit a dry acknowledgement in the Math Notices: "He was a member of the Society for 20 years?"
Probably not.
The AMS online renewal system makes it easy to purchase Math books as you renew. Usually I can't resist the temptation, and this time I got a copy of a recent reprinting of I Martin Isaacs's 1976 book Character Theory of Finite Groups, a book that I struggled with as a non-math major (I was about to switch to it) ca 1982.
I think that Spyros Magliveras (perhaps David Klarner, but I doubt it) suggested this topic to me, and I got the Isaacs book out of the University of Nebraska math library, around 1982 or 83. Like in all math books (practically), the author begins by describing necessary Prerequisites & Preparations:
The reader will need to know some basic finite group theory: the Sylow theorems and how to use them and some elementary properties of permutation groups and solvable and nilpotent groups. A knowledge of additional topics such as transfer and the Schur-Zassenhaus theorem would be helpful at a few points but is not essential. The other prerequisites are Galois theory and some familiarity with rings. In summary, the content of a first-year graduate algebra course should provide sufficient preparation.
Now—I offer this text not because I consider it gobbledygook (in fact, I knew a little bit about all those subjects, even then). Instead, I offer it as an exemplar of a common rhetorical device of mathematical writers, the "depressing lead-in."
Mathematicians are always saying, "Ah—welcome! I'm only too delighted that you've decided to read this book! C'mon on in—but—you are in the wrong place, of course. Please leave immediately, put this book down, and go learn what you need to know before reading this book."
I can never be bothered to do that. Who wants to go read another book (or books) first? I've only just decided I want to read this book, and here's the author trying to check my ID. Instead, I think something along the lines of "Riigghht. What is it that's so hard, anyway?" I turn to the first page of the book and it's almost always possible to read the book anyway, looking up definitions only from other books.
Related situation: Someone says something like: "If you have a background in X, it's easy to see that Y." Fuck the background in "X". Tell me why Y, I think.
Anyway, I guess I'm not a good reader. I'm sure Mortimer Adler would say so.
Instead, I try to read things, and run into obstacles. If no solution to the obstacle presents itself in a few moments, I put the book down and consider something else instead (why thrash if there's nothing obvious to be done that might improve the situation)? I reread troublesome things again and again and again, just like I listen to the same Jazz music over and over again. Eventually I don't need to read it again, and I move on to the next random thing I'd like to be able to read. After I never have to read it again, I consider the book beneath contempt, something totally obvious to any breathing entity, no matter how many times I had to read it to understand it. These books I put into boxes and put into the garage.
The effect of this is that I'm always surrounded by books that are pissing me off in some way, or which I have to read again. They're inscrutable, they have introductions that piss me off, they have to be read. They're the books whose Necessary Prerequistes and Preparations I've not yet been able to sidestep.
This blog entry isn't making much sense, so I'll stop.
