The only course in which I took more than occasional or cursory notes was Lynn Loomis' Mathematics 12 (now 212). Professor Loomis' lectures were models of clarity and precision. Every week I would write an amplified version of my notes in a lined notebook with hard black covers edged in crimson.
It was the purest mathematics I'd encountered up until then, and while I had no difficulty working the problems or understanding the proofs, I began to worry about the motivation. What was the point of Lebesgue's way of defining an integral? Perhaps, I thought, Lebesgue himself could enlighten me.
So I went to the big card catalogue in Widener. Sure enough, there was what I'd been looking for: Lebesgue, H., Lecons sur l'Integration, a set of lectures directed at the very question I'd been asking myself. Lebesgue approached the question historically. He began by explaining how Archimedes, in the third century B.C., had been led to invent integration. Then he explained why 17th-century mathematicians had been forced to improve Archimedes' definition and what had led their successors to invent further improvements and generalizations. Now, finally, I understood the Lebesgue integral. More important, I had discovered that you need to know the history of an idea if you really want to understand it.
With a few exceptions--I've mentioned most of them--my courses didn't take up a large fraction of my time. I didn't feel comfortable being told what to read and when to do it. I never took a music appreciation course, but I spent hours each week listening to orchestral and chamber music with score in hand. I practiced my violin, played sonatas with my classmate Noel Lee '46-'48 and played in the Harvard-Radcliffe Orchestra. I spent many happy hours slowly working my way through the novels of Anatole France and the philosophical essays of Henri Bergson, without expert guidance or a firm grasp of the subjunctive.
Would I be able to spend so much time in these ways today? I doubt it. Harvard undergraduates have even more academic, athletic and artistic opportunities than we did. They are smarter, harder-working and much nicer to each other than we were.
But they have less time to read and reflect and try to make the connections that we did. Not enough time is left over from course work for self-education, for reading literature or history or philosophy that hasn't been assigned, for listening to music that you won't be tested on, for strolling around art museums just to look at the pictures, for writing essays or stories or poems that no instructor will get to grade and, above all, for thinking and talking about what it all means. That can be fixed, though it won't be easy. The first step will be to recognize that there's problem.