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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

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.

svat 9y ago
Indeed! He mentions something related at 5:00 in the video (https://youtu.be/BxQw4CdxLr8?t=300 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.

svat 9y ago

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