Mathematical Notes

First, there's the problem of medium: the medium I'm working in, static HTML, is no good for presenting mathematical arguments. The symbols aren't there, and the typesetting isn't there. I have hopes that MathML will provide a solution, but as far as I know it isn't supported by browsers yet.

Second, there's the problem of time: I have a whole collection of one- and two-page notes about various mathematical trivia, and it would take a long time to turn the notes into essays, or indeed into anything useful to anyone else. I have more to say about time, but I think I'll save it for another essay.

By the way, the Risk odds I once mentioned are a perfect example of what I mean by trivia.

Finally, there's the problem of method: even if I turned all my notes into essays, the essays would still be just a big hodgepodge of mathematical trivia. Wouldn't it be better if there were a single, unified body of mathematical knowledge somewhere, to which I could contribute? Even so, there would be difficulties. For example, on the one hand, to be unified the system ought to store information in a single canonical form; on the other hand, different forms of the same idea can be useful, in that they provoke different ways of thinking.

To put it another way, the thing that I really enjoy, and would like to convey, is a particular mathematical way of thinking. The notes I have are merely a product (phenotype?) of the way of thinking, not the way itself. Making the products of thinking available isn't guaranteed to produce the same way of thinking; in fact, it's probably counterproductive, since it encourages looking things up instead of thinking about them. So, I might want to go through my notes and present only the problems, not the solutions. Or, since an essay can contain a train of thought, I might want to present only a few sets of notes, the ones that best illustrate the way of thinking.