For something I’m writing I looked up a newspaper article I was interviewed in in, from June 7, 1989. Here’s what I had to say:

Ellenberg on mathematics: “I always think of it — this is kind of crazy — as a zoo. There are a million different mathematical objects. They are like animals. Some are like each other and some are unalike, and they are all objects . . . . There are things in different guises. The amazing thing is, it all connects. Anything you prove with trig[onometry] is just as true if you do it with algebra . . . . I think it is kind of amazing actually, if you think of it from an emotional point of view.”

On learning math: “My feeling is that a lot of people expect not to be good at math. If you see calculus and trig, to a seventh-grader, they see it as something very difficult and very arcane, when maybe the trick is to relax a little bit . . . . Many things you can understand on two levels. If you look at a novel, a novel can be very hard to interpret, but you can still read it and see what happened. With math, there is no real surface level. It is already written in a sort of obscure language. You don’t have the comforting template. You only have the deep structure, and that can be very off-putting.”

On the practicality of math: “Why is it important to have read any Shakespeare for your everyday life? To tell the truth, I can get through the day without ever using a Shakespeare quote, but I think Shakespeare is useful, and I think math is useful.”

What a strange experience, looking at this. In a way I seem very mentally disorganized. But at the same time this is recognizably me. Unsettling.

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Honestly, this was not so bad that your parents could have used this to gleefully embarrass you in front of a new girlfriend …

Still, are these records of our past always good things? I had two small triumphs in childhood that I sometimes recall. Early in what’s now called middle school I gave a presentation to my science class explaining in remarkable detail my thoughts on why the formula for the total resistance of two resisters in parallel is true, and had the class and teacher stunned into rapt attention, or perhaps in some cases, horror. In late middle school I gave a presentation on stage at a regional science competition and won first place, after having tripped over the microphone cord walking onto the stage. For records, I have only a small grainy newspaper photo of the latter event — no video or Super 8 film or sound recording or interview. Whenever I’ve bemoaned not having a better record of these “precious moments” I remind myself that I would probably feel a wee bit embarrassed and pained to come directly face to face with my much younger and immature self, and that maybe it’s best to leave some things to the softening gauze of aging and fading memory.

“If you look at a novel, a novel can be very hard to interpret, but you can still read it and see what happened. With math, there is no real surface level.”

There can be a surface level with math. For example, an equation like Euler’s e^{pi*i} + 1 = 0 can be beautiful even if the reader does not understand all the symbols. And some artists find commutative diagrams beautiful.

In what sense can that equation be said to be beautiful if you don’t know what the symbols mean?

An equation can be beautiful in the same way that a Kandinsky painting can be beautiful without knowing what its symbols mean.

I guess I can imagine that in principle, but I can’t say I see it in this equation, or any other I can think of.

Perhaps you can see it in the equations on my website.

Perhaps e^{pi*i} + 1 = 0 does look like a shiny bauble to some of the vast number of people who don’t know what it really means, but for them that’s like judging a book by its cover without even knowing the basic plot let alone any deeper meaning of the text. I think JSE is correct that most people can at least follow and enjoy the basic plot of most novels even if the deeper tangle of themes escapes them. With e^{pi*i} + 1 = 0, most see the cover but not even the plot.

I certainly get esthetic responses to mathematical texts (maybe not single formulas) even when I don’t understand them (or haven’t read them to see if I would understand). I think this is maybe similar to the reaction I can have to chinese or japanese calligraphy, even if I don’t understand anything of the written meaning. In particular, it is not so much the “abstract” platonic formula that I react to, but its typographical presentation.

If someone had shown me these quotes and told me that a mathematician I knew had said them at 17, I would have guessed JSE.

My former department chair claimed that the first time he went to a math talk, as an undergraduate who had not yet taken any topology (nor homological algebra), he saw the speaker write an exact sequence on the board and “it was like falling in love with a woman.” (Not coincidentally, he indeed went on to become a topologist.)