>I can't help remember a quote from a friend that was taking a higher >level Real Analysis class. She was studying to become a college >professor. She came into my office following her class and we were >discussing the usefulness of some of the higher level, more abstract >math classes. I have never forgotten her final statement:
> "The only thing I will ever use this stuff for is to teach it to >people who will never use it."
Perhaps she was unaware of the utility of "higher level Real Analysis" -- or perhaps she was planning to do nothing but teach others who would go on to do nothing but teach -- but otherwise I find the statement unsupportable. Unless you have a 40 year research career planned out in some mathematical backwater and vow *never* to touch a measure or a linear operator, it's almost unimaginable that you won't use this stuff.
This isn't to say there isn't a lot of mathematics studied, published, and occasionally taught that isn't used -- but the usual foundations of a math PhD program (at Stanford they are Real Analysis, Complex Analysis and Algebra -- though the interpretation of these categories is a little flexible) really do seem pretty fundamental to an awful lot of applied and pure mathematics.