Stanford Lecture: Don Knuth—"A Conjecture That Had To Be True" (2017)

What people said

svat · 2023-03 · Strong recommendation

I was going to post this on another thread (the Neal Stephenson one [LINK] ), but it also fits here: Donald Knuth does all his writing (even coding!) by hand with pencil on notepad, going through several rounds of editing before anything reaches a computer, and his stated reason is that he can type faster than he can think. (Somewhere a typing speed of 80 wpm is mentioned, which is not even all that fast.) So he says that writing by hand, being slower, perfectly matches the speed at which he can think. In other words, he describes himself as a slow thinker. (We can actually get some glimpses of the way he thinks from his public lectures, e.g. I love the 2017 Christmas lecture [VIDEO] or maybe—I haven't watched much—the 1985 problem-solving seminar course [LINK] .) And if Knuth describes himself as a slow thinker, it is a lesson to us all.

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svat · 2017-12 · Strong recommendation

Indeed! He mentions something related at 5:00 in the video ( [VIDEO] ): > You know, people think that mathematicians have been working for hundreds of years and now there's tens of thousands or hundreds of thousands of mathematicians all spending every day working on problems so how could you possibly still find a simple down-to-earth problem that hasn't already been studied, you know, way too much? And the answer is: those problems aren't rare at all, they keep coming up several times a year, and this is an example where even this very basic problem of rectangle into rectangles has all kinds of, sort of, stones not yet turned. And the other thing you mentioned is one of the reasons it's always a pleasure for me to see Knuth's talks or read his work — he is one of the mathematicians (like Euler and unlike Gauss) who make it seem simple: we get the impression that we could do it too, if we spent enough time on it, that things are within reach for us, just barely. This is so inspiring. And then of course when you step back and look at his body of work, it's staggering! (Something like this talk may account for about half a page of Knuth's published output, and he has thousands of them…) That's additionally inspiring.

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svat · 2021-04 · Recommendation

The best description of the OEIS I've heard is by Donald Knuth in this fun talk ( [VIDEO] ) where at 19:50 he says how it lets you "compute your way into the literature": > For the last 30 years or more, there has been a wonderful tool for all kinds of problems of this form and it's been online for a long time: we have the Online Encyclopedia of Integer Sequences. And this is just the nicest thing since sliced bread for mathematics because you can compute your way into the literature. [audience laughter] If you want to know if anybody else has ever studied a problem, all you have to do is evaluate the first few cases of it and then you look it up and there it is. The hit rate is incredible, and all kinds of mathematicians have discovered each other through the OEIS. […] I donate to Wikipedia and the Internet Archive and the OEIS. (Aside: A good blog post about that lecture: [LINK] ) Indeed I've used it this way many times; the most recent example is that I became curious about how many polynomial functions there are mod n (after posting this comment: [LINK] ), and by computing the answers for n up to 10, I was able to look up up those numbers in the OEIS and find the general formula, and also the relevant papers. (Asked a question about it here: [LINK] but ended up answering it myself…) I don't think I'd have even known where to look (as I'm not a professional mathematician), if not for the OEIS. And this happens again and again.

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