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A long story derived from going through old papers last weekend:

I was never cut out to be a math major, but it took over three years of increasingly frustrating college math for me to realize that.

I was really good at math up through 11th grade. In 3rd grade, I was doing 6th- and 7th-grade math. All through high school I entered and regularly won math contests. (Sometimes I came in second to my arch-rival. Yes, in those days I had an arch-rival. But only for math contests.) Granted, I was thrown off a little in 10th grade when I went away for a long weekend and missed the two days of class in which we covered the concept of proofs and about 80 pages in the geometry textbook, but I more or less recovered from that eventually.

Calculus, in 12th grade, was tough. There was a lot that I never quite understood about it, and I was having a good time with friends outside of school and not getting enough sleep, and I'd never really had any trouble with math so I was very slow figuring out that calculus was different. But I persevered, and somehow managed to ace the AP test. (I've always been really good at taking tests.) I also did extremely well on (both halves of) the SAT.

So it made sense that I would skip the intro classes and place into fast-track math at Swarthmore. Which meant I tumbled headlong into Linear Algebra.

I'd done some matrix math before. When I was, oh, maybe 10 or so, my father taught me a matrix-multiplication encryption technique that I still think is pretty cool. And for a little while I did well: I got the highest score in the class on the first test.

But I didn't keep up with the class. I didn't do enough of the homework (even though I had the incentive that a friend of mine was grading the homework); I didn't follow enough of what was going on in lectures; I didn't study enough. I got the lowest score in the class on the final. The blue book for the final, graded by the professor, gives my grades on the cover:

Homework: F

Class grade: C+ SHAME!!!

I'd gotten pretty much straight As all through school up 'til college, so that was kinda distressing. I don't think I ever actually looked inside the blue book until last weekend when I was going through papers, so I was spared comments from the professor like (regarding two questions I'd skipped) "Too bad; these were the easiest two questions on the test" and "Did you really do none of the work these last few weeks of class?" (I should note that the professor, call him Prof. M., was a really good teacher, whom I took several classes from and still admire. I assume that he was expressing his disappointment that such a promising student had fallen apart so badly. But reading those notes from him, even fifteen years later and with a lot more perspective, still made me cringe a little.)

Luckily (at least I thought it was lucky at the time, though perhaps I'd have been better off in the long run if this hadn't been true), all first-semester classes were pass/fail at Swarthmore (instead of a grade, you got a brief paragraph of written commentary by the teacher), and I passed, with a little note from the professor that said something like "I gather that Jed is a computer 'hacker'; perhaps that's what took up all of his time." I shrugged it off.

But things only got worse.

I took a bunch of other math classes; I had always known that I would be a math major, and would go on to graduate school in math. That was the obvious course for my life to follow. My father had majored in math; a close friend who had preceded me at Swarthmore had majored in math; I'd always been good at math. Of course I would major in it.

I took the intro Discrete Math class at some point, and relaxed a bit; this was the stuff I was good at. Nobody in high school had ever told me there was a difference between Discrete and Continuous math, but now that I understood the distinction, it made sense. Calculus was hard, but Discrete was where all the fun stuff was. Number theory. Game theory. Graph theory. Cool stuff.

I moved on to Combinatorics, which (being discrete) ought to have been easy for me. No such luck. I don't recall how well I did in that class, but it can't have been great. My only real memory of that class is running into Prof. M. in the hallway one day; he was looking tired, and asked me how I thought the class was going. He was concerned that the students didn't seem to be getting it. I did my best to reassure him that it wasn't his fault; we just weren't putting as much work into the class as it required. I know I wasn't.

And then, must've been junior year, I took Modern Algebra.

On the one hand, this was a terrible mistake. Almost everything in the class was way over my head, and I wasn't spending nearly enough time studying for it. If I recall aright, I spent every class session alternating between total lack of comprehension and trying desperately to stay awake (not from boredom (this was taught by a really great teacher, who also never seemed to quite know what to make of me); that must've been just another semester when I wasn't getting enough sleep).

On the other hand, I think this class was what finally pounded home the fact that math was not my subject, and that was a good result.

There was apparently a time when I knew what this meant (quoted from my notes):

The ideal A=(p(x)) in F[x] is a max. ideal iff p(x) is irreducible over F. Therefore, modding out by an irreducible produces a field.

In my notes there's a diagram showing the differences between a group, a ring, a division ring (or skew field), an integral domain, a field, and a finite field. I imagine it meant something to me at the time.

My recollection is that I got approximately a zero on the Honors exam in modern algebra.

(Digression to explain. Honors exams were exams administered by external examiners—professors from other schools, who wrote comprehensive and very difficult tests for Swarthmore Honors classes. Honors at Swarthmore at the time didn't actually mean "academically superior," it meant "student in a program that involves not getting grades, and instead taking extremely rigorous exams in your subject at the end of your college career." I didn't go Honors, because I had no interest in taking seminars (equivalent to two classes worth of credits) and being judged on them a year or two later; by then I'd figured out that I was a generalist, and Honors seemed aimed at specialists, or at least narrower-focus generalists than I. But I was also a little bitter that this meant I wouldn't get to have the word "Honors" attached to my degree. I still think that was a lousy term for it, and unlike many people, I was very pleased when the Honors program was heavily revamped in the mid-'90s. On the other hand, I was also just not a very good student; smart, good at taking tests, interested in lots of stuff, just not very good at being a student per se. So not only did I not get Honors, I also didn't end up getting Distinction in Course, which is what the really sharp non-Honors students got. End digression.)

I think everyone in the class was a little shell-shocked after that exam; I think it actually was harder than it should've been. But I, as the worst student in the class, was extremely demoralized, and didn't quite believe that others had had as hard a time with it. I don't really remember, but I don't think I completely answered a single question on that exam.

I'd been in over my head all semester, but was too damn stubborn to admit it. But it wasn't too long after that that I gave up being a math major. Thank goodness I gave up before trying to take the Topology seminar, which had a reputation for being extremely fun but also the hardest math class Swarthmore offered. I'd never have made it through that.

(Okay, so to be a good self-contained story about how Jed finally learned from experience, it should probably end there. But what I'm leaving out is the fact that I did originally try to double-major—in math and English—and was told that the powers-that-be didn't think I could handle that quantity of work. So instead I dropped math (which took more credits to major in than other departments) and ended up majoring in English and Computational Linguistics, the latter being a special major combining CS and Linguistics. I had asked to do English, CS, and Ling as a triple major, but the Committee on Academic Requirements said no can do, so I combined CS and Ling under one rubric. Anyway, my point in this closing aside is that I've probably munged the timeline in an attempt to tell a coherent story. I imagine you can deal with that.)