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Donald Knuth's Christmas Lecture: A Conjecture That Had To Be True [video] (stanford.edu)
284 points by taeric 7 months ago | hide | past | web | favorite | 25 comments



(Reposting comment from https://news.ycombinator.com/item?id=15882184 lightly edited.)

I attended this on Thursday. Knuth started with a problem about rectangles inside rectangles (https://imgur.com/faWRt2q — it's going to be an exercise in 7.2.2.1 of TAOCP when that's published, currently in the draft version of Pre-Fascicle 5C). He worked through some small cases, made a conjecture, showed a problem submitted to the Monthly, and lots of cool stuff with generating functions. The lecture was also peppered with jokes and cool stories, including a fascinating conjecture by Bill Gosper, who has a long history of coming up with these Ramanujan-like identities. He also showed a wonderful conjecture (involving queens on an infinite chessboard) that he thinks may never be proved, and showed a snippet of his CWEB program for the problem.

Knuth is turning 80 in about a month, and his talks seem to get better every year. (Though last year's lecture (https://www.youtube.com/watch?v=DjZB9HvddQk) on Hamiltonian Paths in Antiquity, which among other things covers Sanskrit poems that satisfy a “knight's tour” constraint, holds a special place in my heart — been planning to elaborate on it.)


Me too!

Another important thing to mention is that Knuth has a great sense of humor.


Indeed. I recently got my own copy of "The TeXbook" after having had it on long loan from my university library many years. It's simply a joy to read and surely one of the best software manuals ever published.


My apologies on not voting your submission up. I completely missed it.

Jealous of those that attended. Glad to see the recordings are easy to reach. I didn't realize they were in YouTube. So, I encourage everyone to see the article I missed, since it looks there.


This talk excited me as if I had learned a new programming paradigm. Sometimes I come up with little problems in the shower, not unlike this one, but then when I sit down with pen and paper, after working with a few examples, I hear a little voice saying like "what's the point on working on this? I'm no mathematician, and this is probably just a footnote on some 1000-year-old mathematics textbook anyway."

To see Knuth work methodically through this seemingly trivial problem and get something out of it was enlightening.


Indeed! He mentions something related at 5:00 in the video (https://youtu.be/BxQw4CdxLr8?t=300):

> 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.


For those of us that struggle with his cadence of speech, are transcripts available online?


Yes. It's difficult to listen to live. I'm (we're?) not knocking Knuth - he's brilliant; he's just hard to follow. Once he gets going, he gets tripped up with all that's going on in his head and the "uh uh um" throws off the flow.


Knuth's brilliance and eccentricity (or autism?) are a package deal. He's a guy who wanted to write mathematics papers, got side-tracked into creating a type-setting program (TeX), then got side-side-tracked into creating a font language (Metafont).


I think that's just how old people talk sometimes.


It's got nothing to do with his age, as far as I can tell Don Knuth has always spoken this way (though I suspect it may have gotten more pronounced [ no pun intended ] as he has gotten older).

I agree with what others have said. I think he just has 50 things going through his mind at any one moment, and the part of his brain that is controlling his speech just isn't always sure which of those 50 things it should be sharing at that moment.

I think any of us would be fortunate to be half as brilliant as he is. And the best part is, it is so obvious that he is one of the most humble and likeable people on the planet. Always generous, patient, and never arrogant. I personally would travel a great distance just to have lunch with the man, if ever given the opportunity.

A prime example in this video is the person who keeps interrupting him to tell him he had missed a line in his diagram. To be honest, my first reaction (after the guy had repeated it for like the 4th time or something) I was a little perturbed, and wished the guy would just shut up and let Don continue. But what was Don's reaction? After he finally understood what the guy was saying, he saw the error, corrected his mistake, and thanked the guy for "saving him 20 minutes".

Thank you Don Knuth! Not only are you brilliant, humble, hard-working and kind, you are a gentleman's gentleman, and the the world needs more men like you!


Have you tried speeding the video up? It still sounds choppy, but the earlier part of the sentence will still fit in your working memory.


For me, Knuth becomes far easier to comprehend (but still rough) at 1.6x speed. To put that into perspective, I like the majority of YouTube videos I watch at 1.25-1.33x --- it may seem like a surprising result, but ever since I started watching most videos sped-up, I've found it actually increases my understanding and enjoyment. As a side-effect, 1x now feels annoyingly slow. Perhaps it's indicative of the general information density (or lack thereof) in videos.


It's tangent time!

We're trained to absorb ideas at the pace of film and TV, which are super tightly scripted and edited. By comparison, regular speech has the density of a feather. Thank goodness for that ability to adjust the speed!

I just wish the algorithms used to speed up playback on Youtube, in browsers, etc were given a little more love. They sound really poor compared to the time stretching available in professional audio tools (or even something like Overcast). It's not even a quality vs perf tradeoff — high quality granular resynthesis is pretty darn cheap, computationally. Alas, I often need to listen strictly at 2x, since the artifacts from non-integer multiples are too distracting to me. Too bad speed adjustment is such a niche feature.


I've considered creating dubs of the (recent) Christmas Tree lectures, and I think I have the free time (and equipment) for it as of recent. I sometimes feel something akin to visceral anger when I have trouble understanding what somebody is saying, and I'd hate for that to get in the way of a good lecture for many more people.


I watched it with subtitles (hit the CC button).


Is the K in his name actually not silent? Huh. I've been calling him "Nooth" for ages. That's going to be hard to unlearn.


http://www-cs-faculty.stanford.edu/~knuth/faq.html

How do you pronounce your last name?

Ka-NOOTH.


Don't feel too bad. I never even thought about it for a long time after being introduced to his work, and I had made the same mistake.

I believe at some point I heard someone pronounce it correctly in a video lecture, and I thought the same thing "surely that can't be the correct pronunciation". Alas I did some searching and found the FAQ on his Stanford page and was proven wrong.

:D


Thank $DEITY for "youtube-dl". It's a bummer that Stanford can't afford to host its own videos, though.


This is tangential to the topic, but of you use TeX or any related system (latex, texinfo, cweb, metapost, etc.), please consider becoming a TUG (TeX User Group) member. They rely on membership and donations to keep going (and there are some tangible benefits to being a member, too).

https://tug.org/join.html


Anyone here know how I can get ahold of knuth without email? Hit my email in profile. I would like to help him finish his proof.


- See https://cs.stanford.edu/~knuth/email.html — just send a letter to his Stanford address.

- You may have misinterpreted the talk. There's already a proof (even for the closed form of the leading coefficient), by someone (I have the name written down somewhere but it's in the video). You might enjoy submitting a solution to the AMM problem instead (which only asks for the rate of growth, but if you have a fuller proof I'm sure that's good).


In the video Donald refers to Walter Stromquist.


I once sent him a letter (snail mail) addressed to Donald Knuth, c/o Stanford Computer Science Department (address at bottom of http://www-cs.stanford.edu/). He got back within a couple of weeks, so it seems to have reached him fairly efficiently.




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