(Almost as old as the Web itself and in need of revision.)
We always had popular math books in the family. The first one I remember was a children’s book; what I remember is that in stressing the arbitrariness of the names of the numbers, this book suggested that in some primitive caveperson language, the names for “one”, “two”, and “three” might have been “oof”, “ba”, and “ick”. It became something of a family joke.
A little later on I looked at George Gamow’s One, Two, Three . . . Infinity. I didn’t understand much of this one but I liked the story near the beginning about the guy that invented chess claiming a prize from a foolish king: one grain on the first square, two grains on the second, four grains on the third, and so on (doubling each time). Like many another before me, I calculated out a lot of powers of two hoping to figure out how many grains would be on the sixtyfourth square but of course I gave up (and anyway there was a mistake in the calculation before I quit).
We also had a book about the house called
, I think, Mathematical Bafflers: tricky brainteasers with charming illustrations. It turns out to have been a collection of reprints from Litton Industries’ Problematical Recreations. Again, most of these were way over my head but I was able to understand a few, at least after reading the solutions. I think this was where I first learned about “four fours”. One attempts to write natural numbers using exactly four numeral 4’s: thus 1 = 44/44, 2 = 4/4 + 4/4, 3 = (4 + 4 + 4)/4, and so on. I’m quite sure that it was in the context of the “four fours” puzzle that I learned about the factorial function.
Meanwhile, of course, I was going to school (University Elementary) and learning arithmetic, but I don’t remember any of that very well until long division in fourth grade; probably because long division was the first thing that didn’t seem completely obvious and natural. This was in the “new math” sixties, so they told us about sets and so on. It made sense to me. I was lucky enough to have teachers that understood what was going on. I had also learned some compass-and-straightedge constructions by around this time.
My fifth grade math teacher was Donald Adair and he did a real good job. I remember his frequent exclamation: “Prove it!”.
In sixth grade, I had the great good fortune to be in Mary Ann DiBaggio’s class. She taught us about the stock market, the game of Go, and bases other than ten, along with some elementary geometry and algebra. Ms. (we still said “Miss” back then) DiBaggio was an inspiring teacher; this was my favorite class of all time.
By now, I knew I was “good at math”: I almost always caught on quicker than almost everybody else. There was one guy who was clearly even quicker than me: Peter Strickholm. He eventually got 800 on his math SAT — the highest possible score (I only had 750 which is still pretty good). Knowing Peter was another stroke of good luck for me and we spent lots of time talking about math and playing with mathematical games and toys. For example, I remember him explaining an impossibility proof for a certain configuration of Soma blocks.
Seventh grade brought Euclidean geometry and two-column proofs. Nothing could have seemed more natural. I wasn’t real impressed with the teacher and thought I could explain it more clearly so I frequently tried (in and out of class).
It was around this time that I first remember thinking of a career in mathematics. I’d seen IBM’s well-known timeline poster Men of Modern Mathematics and was duly awed.
So on through high school. I didn’t go out of my way to take on extra work — in fact, I made a point of not taking school seriously — but I got through a Calculus class. My instructor for Junior and Senior years was Greg Peters. One impressive thing he did that sticks in my mind was a fairly extensive presentation on symbolic logic. I believe this topic is sorely neglected in mathematics pedagogy and I was lucky to get this early exposure.
Most of the rest of the story is told in outline by my transcripts from Indiana U. (there’s also a verbose annotated version) and this abstract of my Ph.D. thesis). I went through college and grad school right there in my home town ( Bloomington Indiana). I showed an early bias for “pure” mathematics and took mostly algebra and topology classes when I had a choice.
I haven’t done much math since I got my doctorate. I taught for four years (at Ohio Dominican College) as an assistant professor and of course learned a certain amount as I went along. They fired me (for political reasons) and since then I’ve done even less. The class I taught most often was “Mathematical Concepts”. I wrote up an extensive set of lecture notes on elementary number theory and logic for this class, hoping to publish a textbook, but I haven’t been able to find a publisher.
My ex-chair went out of her way to see that I didn’t get to supervise student teachers in the public schools, but she messed up a couple times and I had a chance to see two of my students at work in the classroom. I enjoyed this immensely and had plenty to say to them about it. Teaching teachers is probably my real calling and it’s a god damn shame I’ll probably never have a chance to do it again.