#lee lady

At the beginning of the century, a college education was seen as a bauble for the rich, a finishing school for children of the upper class or a place where the youth of the nouveau riche could mingle with the upper class and acquire social graces and upward social mobility. (Upward economic mobility was not the issue for families that could afford to send their children to college.) A college education, which filled the minds of its students with esoteric knowledge and unrealistic theories, was looked on unfavorably by employers in such practical fields as journalism or engineering. But as the century got older, gradually college became seen as the means by which citizens could become above average, and it was regarded as unfair that this opportunity should be available only to the rich. By the Sixties, the construction of new colleges and a variety of scholarship programs (most notably the GI Bill) had resulted in a large mass of new college graduates. Discouragingly enough, though, many of these new graduates turned out to be only average after all.  It was then realized that we had underestimated what would be required to raise a person above the norm. For many, at least a Masters degree would be essential. Therefore money was poured into creating new graduate programs and expanding existing ones, and creating new graduate fellowships, such as those established by the National Defense Education Act. But by the end of the Sixties, it was becoming apparent that even a graduate degree was not adequate to make someone above average. It became common to find PhDs driving taxi-cabs and painting houses. Going to college has become the normal rite of passage for a moderately intelligent middle-class youth. Anyone who has the ability and the desire can now become educated, but the American dream of having a standard formula that any person can follow to become successful and above average is still unfulfilled.

There is a particular kind of open-ended idea which I call the blue-sky idea. Namely, someone sitting at his desk with his feet up and looking out the window has come up with some concept, and now hopes that he or someone he knows can come up with a good way of using that idea. At conferences one sometimes encounters mathematicians who specialize in this sort of idea, button-holing everyone who can't manage to avoid them and inflicting their most recent blue-sky idea on them. ... When one looks at the history of mathematics, it may seem that a lot of the most important developments have come out of blue-sky ideas. But in fact, from what I know, this is almost never the case. Good ideas always arise out of some existing line of thought, and it is only after when has put a lot of effort in that one realizes that there is some gradiose general concept that underlies all one's work. For instance, I am pretty sure that Eilenberg and Steenrod didn't sit down together over a beer one day and say, "Wouldn't it be neat to draw up a set of axioms for a thing called a category and then invent a concept called a functor, and then see if these would be useful for anything?" It's pretty clear that in fact they noticed that in algebraic topology the same sorts of situations keep coming up over and over again, and one keeps seeing different theorems with different subject matter, where somehow the proofs always turned out to be more or less the same. So they saw (I believe) the need for a vocabulary and a conceptual framework that would enable mathematicians to talk about all this in a unified way. Ergo: category theory.