This weekend the latter half of my last Amazon order came. I now have a copy of Mathematical Writing (Knuth) and Approximation Theory (Cheney). The former was much less intriguing than I thought it would be; but Teacher in America (Barzun) was part of the same order, and it was better than I expected, so in the mean I think I was pleasantly surprised. Anyhow, most of Mathematical Writing consists of scribe notes and handouts from a class on mathematical writing that Knuth taught at Stanford. The introduction ends with the following comment:
Caveat: These are transcripts of lectures, not a polished set of essays on the subject. Some of the later lectures refer to mistakes in the notes of earlier lectures; we have decided to correct some (but not all) of those mistakes before printing this report. References to such no-longer-existent blunders might be hard to understand. Understand?
Unpolished though the book may be -- perhaps I should just call it a bound report? -- it does include interesting exercises and handouts, some references to books that sound intriguing. And between sometimes-dull transcripts of the highlights of class conversations, there are a few very interesting comments. In one such comment, Knuth noted that he usually writes his first drafts in long hand, because the speed at which he writes is almost perfectly matched to the speed at which he thinks. When he types, he types too fast for his thoughts to keep up. I'm glad I'm not alone in this.
Knuth's comment quickly came to mind this evening when I started to
type out a response to a paper I'm helping to edit (I'm the third
author, I think). The current draft had enough errors of notation
and syntax that I got lost easily, and somewhere in the middle I
just lost the thread of it. Frustrated, I sat down with pen and
pad and started to write a letter to a friend about how confused and
irate I was, and how I thought the exposition should
proceed; and seven pages and a few hours later, I had a clear
picture in my mind of where I think the paper gets lost, and how I
think the problem can be fixed. I think I'll have to make a copy of
this letter before I send it. I've had technical inspirations
while writing letters before, and regretted not keeping a copy to
re-read later. There is a proverb that says
the palest ink is
better than the best memory; and while my memory is good enough
that I remember the technical ideas that come out of such
inspirations, it is not so good that I can always recover the path
of thought that led me to a fruitful perspective.
- Currently drinking: Golden Monkey tea