WHO CARES ABOUT FIREFLIES?: STEVEN STROGATZ (p3) There's one other story about Mr. diCurcio that I like. At one time I was reading a biography of Einstein, and diCurcio treated me like I was a full-grown scientist—at 13 or 14. I mentioned to him that Einstein was very struck as a young high school student by Maxwell's equations, the laws of electricity and magnetism, and that they made a very deep impression on him. I said that I couldn't wait until I was old enough, or knew enough math, to know what Maxwell's equations were and to understand them. This being a boarding school we used to have family-style dinner sometimes, and so he and I were sitting around a big table with several other kids, his two daughters and his wife, and he was serving mashed potatoes. As soon as I said I would love to see Maxwell's equations sometime, he put down the mashed potatoes and said, "Would you like to see them right now?" And I said, "Yeah, fine." He started writing on a napkin with these very cryptic symbols, upside-down triangles and E's and B's and crosses and dots, and mumbled in what sounded like speaking in tongues—"the curl of a curl is grad div minus del squared. . . and from this we can get the wave equation. . . and now we see electricity and magnetism, and can explain what light is." It was one of these awesome moments and I looked at my teacher in a new way. Here was Mr. diCurcio, not just a high school teacher, but someone who knew Maxwell's equations off the top of his head. It gave me the sense that there was no limit to what I could learn from this man. There was also a Mr. Johnson at this same high school, who was my geometry teacher. Mr. Johnson was an MIT graduate, and seemed to know a lot about math. One day he happened to mention that there was a certain problem about triangles that he didn't know how to solve, even though it sounded like every other problem we were hearing about in trigonometry or geometry. The question was, if two angle bisectors of a triangle are the same length, does it have to be an isosceles triangle? That is, do those two angles at the bottom have to be the same? He said that he didn't know how to solve it, and that in 20 years of teaching he had never seen anyone do so either. I'd never heard a teacher say that there was a geometry problem that he didn't know how to do, so I became interested in it. I would be in gym class, and someone would throw the ball at me and I wouldn't be paying attention and would drop the ball, still thinking about the angle bisectors. This problem began to obsess me for several months, and I had things that were close to a solution but I could never get it. It was around that time that I learned what research was. I was doing research for the fun of it; there was no grade attached to this, and I didn't even tell anyone I was thinking about it—I just wanted to solve it. One day I thought I had. It was a Sunday morning, and I called up Mr. Johnson and asked him if I could come show him the proof. He said, "Yes, come to my house. Here's where I live." I walked down to his house, and he was still in his pajamas with his kids, and line by line he checked through this proof and said, "You've got it. That's it." He wasn't really smiling, but seemed pleased. He later wrote some special remark to the headmaster of the school that I had done this problem. I went from Loomis-Chaffee to Princeton, where the path was a little bit bumpy. I started as a freshman taking linear algebra—this is the whiz-kid math course for kids who had done well in high school. The first day a professor named John Mather walked in, and we couldn't tell if he was a professor or a grad student. He was so shy, had a big long red beard, and slithered along the wall. He didn't really stride into the room—he was practically invisible. Then he began, "The definition of a field, F, is. . ." That was all. He didn't say his name, not "Welcome to Princeton,"—nothing. He just began with the definition at the beginning of linear algebra. It was a dreadful experience for me. It was the first time in my life that I understood why people are terrified of math. He came really close to discouraging me from ever wanting to be a mathematician. The only reason that I went on to eventually become one was that my second course was with a great teacher, Eli Stein, who's still at Princeton. It was a course in complex variables, which was a lot like calculus. I always liked calculus in high school, and I suddenly felt like I could do math again, whereas that earlier course on linear algebra was a filter. It had a very fine mesh, and only certain students could get through the holes. What was supposedly being tested was your tendency to think abstractly. Could you come up with the sorts of rigorous proofs that a pure mathematician needs? That's the bread and butter of pure math. The truth probably is that I didn't really have that in me; that wasn't my natural strength. What I really like is math applied to nature—the math of the real world. At the time I didn't know there was a thing called applied math—I thought it was physics. Now this is what I do. I ended up majoring in math because of the good experience in my sophomore year with Stein. I'd always been encouraged to be a doctor, but always resisted, because I knew that I wanted to teach math. But in my junior year my parents encouraged me to take some pre-med courses, like biology and chemistry, and even though it was getting to be pretty late to become a doctor I agreed. My brother the lawyer convinced me with a persuasive argument that it was irrational to keep resisting: I wasn't committing to being a doctor, and it wouldn't hurt to learn biology and chemistry. I accepted that, and it made for a pretty hellish year because I was taking freshman biology, with its lab, freshman chemistry, with another, and organic chemistry, which supposedly depended on freshman chemistry. This is a lot for someone who's not good in the lab. Even though this pre-med year was a lot of work to be doing alongside a math major I actually liked the biology and chemistry courses, especially the idea that DNA was a double helix, and that this shape would immediately indicate its function. It explained how replication would work. I was perfectly content, and even took a pre-med Stanley Kaplan course to prepare for the MCATs. Still, when I got home for spring vacation my mother got a look at my face and said, "There's something wrong. Something's really bothering you. What's wrong? How do you like school?" I said, "I like it, it's fine, I'm learning good stuff." But she said, "You don't look right. You don't look happy. Something's wrong, what's wrong with you?" I didn't really know. I said, "Maybe I'm tired. I'm working a lot." But she said, "No, something else is really wrong. What are you going to take next year? You'll be a senior." I said, "That is bothering me because, being a pre-med so late, I'm going to have to take vertebrate physiology, some biochemistry, and all these pre-med courses. Plus I have a senior thesis in the math department, which means that my schedule is going to be so full that I'm not going to be able to take quantum mechanics." And she said, "Why does that matter to you?" I said, "I've been reading about Einstein since I was 12 years old. I love Heisenberg, Niels Bohr, Schrödinger—I could finally understand what they're really talking about. There are no more verbal analogies and metaphors; I can understand what Schrödinger did. I've worked my whole life to get to this point, and I'm ready to know what the Heisenberg uncertainty principle really says, and I'm going to be in medical school, cutting cadavers, and I'm never going to learn it." So she said, "What if you could just say right now, 'I want to do math. I want to do physics. I want to take quantum mechanics. I'm not going to be a doctor. I want to be the best math teacher and researcher I can be.'" And I just started crying. It was like a tremendous weight had been lifted. We were both laughing and crying. It was a moment of truth, and I never looked back. I'm very thankful I had such good parents, and that I was able to find a passion by denying it for awhile. Some people go their whole life and never really figure out what they want to do.
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