Budding Mathematician

After we moved to Fort Devens my parents started leaving me with the teenage daughter of one of their friends. They'd drop me off at her house. I think her rate was a quarter an hour.

Once again, I had an age-inappropriate crush. I don't know if I had more of them than any other kid my age. But I have the feeling I did, and the rapes had something to do with it. I think I was looking for an attachment that could be a repository for all the uncomfortable feelings.

The baby-sitter's name was something odd. I think it was Sylvania. I remember having to ask what it meant and finding the answer a little hard to believe. Sylvania is a name like that -- who names their daughter "woods?" So let's say she was Syl.

She was a pretty brunette with glasses. She loved math and she was into computers. In 1955! I can't vouch for it, but I was told that for a science project she built some sort of calculator using coat-hangers. I think she was 16 in early 1955. Not having a picture of her, I've substituted Tina Fey, both on this post and in my thoughts.

Syl had a much younger little brother, Fred. He was a couple of years younger than I was. He was what we would call hyperactive today, and he'd be stuffed with Ritalin. To me, he was a super pain in the ass. I wanted him tied and gagged. Not having a picture of Freddy, I've substituted Eddie Munster, both on this post and in my thoughts. During my earliest visits, Syl would put him to bed early, so I'd get to be alone with her for a couple of hours, and she'd use the time to teach me whatever I was interested in. I was interested in math, mostly, and a little science.

At some point I asked her how much you could learn, and she said you could keep learning math forever if you wanted to. I liked the sound of that. She told me about the math she was studying then, called "calculus." I asked her to teach me some calculus, but she said I had to finish learning arithmetic first, and then I'd have to learn geometry, and then I'd have to learn trigo-something, and then I'd have to learn al-something.

I felt like I was close to finishing with arithmetic so I asked for a preview of geometry. She showed me some stuff from Euclid, like the Pythagorean theorem. The square of the hypotenuse of a right triangle equals the sum of the squares of the two sides. It didn't look like anything that could possibly be true, but she said that when you study geometry you learn how to prove things like that.

She didn't show me a proof of the Pythagorean Theorem or any other. It was enough that she just told me there were such things. I started to realize that even in arithmetic I was taking far too much on faith. I should be insisting on proofs. For example, my Mother had often said I could save trouble learning my times table by noticing that the order you multiply two numbers doesn't matter. So if you know 7 times 8, then you also know 8 times 7, because the answer is the same. But how do I really know that the answer is always the same? I would have to see a proof.

I came up with a proof in my head at home while sitting on the floor of the Play Porch. It wasn't rigorous by the standards of a 21st century mathematician, but you have to start somewhere. I just convinced myself that what multiplication did was count the total number of things you got when you arranged first-number rows of second-number things in each row, and that if you switched first-number and second-number the result was the same as turning the arrangement 90 degrees. The turning doesn't add or subtract anything. It was more of a persuasion than a proof, and it was hell making it work for fractions, which I'd just started learning, but, you know what? After getting a Ph.D. in math and picking up a hefty dose of Foundational Theory along the way, I've decided that persuasions are what proofs ought to be, screw overblown rigor.

The new-found need for proofs began to be felt in all matters. I started noticing how often flat statements by even my own parents turned out to be flat wrong. The more I noticed that people could be full of it, the more concerned I was to subject all claims to proof.

I might have decided in the midst of all this to become a mathematician when I grew up, except for one problem: I didn't know that mathematicians existed. I had an idea people could be paid to use mathematics. I certainly did not know that anyone could be paid to discover new mathematics and find new proofs for their discoveries.

I didn't even know at this time that science existed. I assumed that everything that needed to be known about the world was already written down in books somewhere. Probably anything I needed to know was somewhere in our set of Encyclopedia Britannica, and I could find it if I knew the word to look it up under.

The immediate effect of my obsession with proofs was that I pissed Dad off more than ever. "It's true because I say so, Dammit!"

[Below: Chinese-style Pythagorean Persuasion. c-squared = the area of the big square = the area of the four triangles plus that of the center square. The area of each right triangle is half a times b. So c-squared = 4(ab/2) + (b - a)-squared = 2ab + b-squared - 2ab + a-squared = a-squared + b-squared.]