During the seminar, I took a few notes, and as the piece of paper that they're on is liable to get lost and the notes will become increasingly more cryptic, I figured I'd transcribe them here in a bit clearer fashion. They're probably still cryptic; feel free to ask questions.
(A lj-cut is probably useful here.)
Someone asked him about the hardest question that he'd worked on that he'd solved. He said that this was a topic called the "giant component", which involved what happens with a set of points when one starts connecting them randomly -- there's a transition where at first one has lots of little connected independent bits, and then rather suddenly one has a large lump that connects most of the points, and the question he was looking at was how exactly the transition happened. The paper he ended up writing about this took up an entire issue of the journal it was published in (which I unfortunately didn't catch). He said it was rather like a Victor Hugo novel, with each chapter having a description of the fields nearby and the flowers in the fields and what they looked like and the clouds and so forth, and then a little bit at the end that actually advanced the plot -- in that he was trying to describe all of the interesting structures and such that he'd found while working through this.
The same questioner had also asked what the hardest question was that he'd worked on that he hadn't solved; this was a much more prosaic answer: the P=NP? problem.
I asked him about what he'd done to prepare for teaching classes when he was first starting out as a professor. His answer was to talk about the first year of his teaching at Caltech, where in addition to university classes he was also teaching some classes on how software works to the employees at one of the local computer companies -- the managers had the idea that if the people building hardware had a better understanding of what the hardware would end up doing, it would help them build better hardware. And so he was teaching this class, on a sort of split schedule because the managers wanted to have a separate session of the class that was a week ahead of the rank-and-file employees. And so he didn't really have that much time to prepare for these classes, which ultimately he thought was a good thing -- the teaching under adverse conditions brought a level of confidence quickly, which he thought was quite important.
Somewhere in there, it came up that he'd known Feynman fairly well at Caltech (which I hadn't known); he described one of his more vivid memories of him, when they'd both recieved the Presidental Medal of Honor (I think it was) from President Carter in the same year, and thus were sitting together waiting for their names to be called to receive the medal, and just as Knuth's name was called, Feynman elbowed him with a grin and said, "There you go, Don! It's your big chance!"
One of the best questions that got asked was what supporting habits he'd developed that enabled him to accomplish so much. He gave a couple of answers to this, and then sort of halfway-answered the next question and somewhat brought it back to being about this one since he'd thought of more that he wanted to say about it.
First, he mentioned being able to relax: to take time away from work and relax and enjoy the world around. (I'm finding that this is crucial for me, too -- too many years of "if I just push really hard for a few more months I'll be done with my dissertation", and finally I've realized that it doesn't matter; I still need to relax now too.)
Second, he said that he always started working on the thing he was ready to do that he most dreaded doing -- because otherwise it would keep sitting there and he'd keep dreading it. As he pointed out, this advice needs tempering, or he'd spend all his time doing things he dreaded, but it's useful as far as it goes. (Presumably, one doesn't do things that one dreads that one doesn't actually needs to do, and so forth.)
The next question brought up the fact that he had no idea how long writing TeX would take when he started doing it (it was just supposed to be a summer project!), or possibly that he had no idea how long the Art of Computer Programming would take to write, or perhaps both -- in any case, he said that one of the other answers (partly-in-jest, but only partly) to the supporting-habits question was to "be a bad estimator" of how long things would take; a lot of the big things that he'd done were things that he wouldn't have started if he'd known at the beginning how much work they'd be.
(I found that to be very comforting advice, even if not necessarily helpful -- one of the things I've been very frustrated with lately is that research things always seem to take a lot longer than I expect them to.)
As part of explaining why things take much more time than he expects, he said that he was always thinking of more questions as he went along, and added that as another "habit" to the list.
Near the end of the seminar, something came up about a set of problems called "The Millennium Problems", and what he would pose as a central challenge problem for computer science to work on, were he in a position to do so. His answer: to take one representative second of computer time of a standard PC sitting on a network, and to completely understand everything that that computer did in that one second.
This conversation then went on to a discussion of whether or not he thought computer predictions would ever be able to predict vast amounts of human behavior; his comment was that he didn't trust any programs that large to not contain crucial bugs -- with such programs, in his opinion, "The surprise is when you get an answer you can believe."
Unfortunately, that was the last question upon running out of time, or else I'd have asked him a question about whether this implied that it would be profitable to study the behavior of large programs in the presence of bugs, rather than studying programs with the assumption of no bugs, and whether anything had been done on that front.
So, that's pretty much all I remembered from the seminar, except that it was somewhat interesting watching Knuth's body language throughout the seminar. He started out looking very uncertain of himself and was somewhat halting and a bit unclear in forming his answers and was fairly hard to follow, but after ten or fifteen minutes that all seemed to have smoothed out and he seemed much more comfortable and the answers flowed nicely. Perhaps it's good to know that even people whose speaking abilities I very much look up to get nervous in front of audiences too.