Thread

1. paulpauper · 1791078403 · focus · HN ↗

   unpopular opinion: imho there is no substitute for deep learning and doing problems. Math is unlike other subjects, where you have to actually do it head on; you cannot just passively consume it like listening to a history podcast or watching a video.

   1. traes · 1791078822 · focus · HN ↗

      This is the single most popular opinion about learning math.

      1. lll-o-lll · 1791079221 · focus · HN ↗

         Learning nearly anything? You can’t learn to drive a car from YouTube. Or paint a house, or wash a dish, or code, or … Learning requires doing.

         Who thinks otherwise?

         1. mooglevich · 1791080322 · focus · HN ↗

            I think a lot of people, sadly, imply that they think this, even if they don't explicitly say it.

            I recently tried to obliquely bring this up to a friend and he asked out loud, "Sometimes I do wonder if it's better to watch YouTube videos or do problems. I'm not sure."

            This has been one piece of acedata representing an aggravating trend in my personal life. It could just be my attracting these types (which I've been fretting about since I'm thinking wtf is wrong with me then), but other examples are family members even expressing this bad habit with something as dumb as Marvel. They read forums about comics without ever reading them and feel possessive enough about the genre to get pissed when I, who...does read comics..., criticize the Disney Marvel movies.

            I'm hoping it's just me over indexing for it since it bothers me, but yeah - I have found that there are certainly people who just consume content without practicing or implementing the thing they're supposedly learning about, and then think they've actually learned.

            ofc ymmv - it could just be my strange social circles.

         2. socializer · 1791093578 · focus · HN ↗

            The insane popularity of channels such as 3Blue1Brown suggests that a lot of people do. Learning by watching is many orders more popular than learning by doing. Probably because it makes you feel smart without having to put that knowledge to the test, so it seems like a better way to master new concepts.

            There are many folks on HN who watched a YouTube video or read a Quanta article about some mathematical concept and run with that.

            1. traes · 1791101244 · focus · HN ↗

               > The insane popularity of channels such as 3Blue1Brown suggests that a lot of people do.

               I don't think this is true.

               First of all, the fact that watching videos is not a sufficient way to learn math does not mean that videos cannot be an excellent supplement for learning math. 3B1B's linear algebra videos for example are wonderful tools for gaining geometric understanding and motivation behind why things are the way the are in linear algebra, but of course they won't teach you how to invert a matrix. (He even says something to this effect explicitly many times throughout the series, if I recall.) Not everyone who watches those videos is engaging shallowly with math just because they're watching videos about it, there's plenty of value for serious students as well.

               Your next argument might be that the sheer number of views indicates an unrealistic volume of serious students. This is true, but it still doesn't indicate that people think watching videos is a good way to learn math; in particular, nothing says they're watching those videos because they're trying to learn math. They're beautiful and interesting and well put together videos, and I'm sure many people enjoy watching them passively fully conscious of the fact that they aren't actually deeply learning math. I don't think there's anything wrong with that!

               I'm sure there is a subset of viewers who think they're actually learning math by merely watching videos, but I'm willing to bet it's a relatively small fraction.

            2. lgeorget · 1791102896 · focus · HN ↗

               Personnally, I watch 3Blue1Brown's videos because I find them very enlightening. They're are also very nice to watch and listen to, the production quality is very high. I don't pretend learning a lot of maths by simply watching them but I like watching them anyway for what they are: videos about maths problems and maths concepts.
            3. tgv · 1791105661 · focus · HN ↗

               > Learning by watching is many orders more popular than learning by doing.

               But you hardly learn anything from it. You forget. And you don't know how to apply the bits that stick. You only remember some of the words and concepts. You may repeat them to other people. For 99% (or more) of the viewers, that's enough, because there's never a need to apply probability theory or differential calculus. So it is entertainment. Intellectual, more interesting than most other content, sometimes stimulating, but still entertainment. The 1% that does want to apply that knowledge, really needs to practice, though.

            4. laweijfmvo · 1791118148 · focus · HN ↗

               a common comment i read is something like “if <youtuber> was my teacher/professor i would have learned so much better!”

               and no, i don’t think so. you would have been entertained, but your teacher was making you learn. ability to explain concepts is important but it’s only the first step on the pathway to learning.

               1. traes · 1791135461 · focus · HN ↗

                  Hmm, I'm not so sure. You may have never had a truly horrible math teacher. I distinctly remember learning matrix multiplication in high school for the first time. We were taught the algorithm without any motivation at all. Not a single picture was drawn, she just did some examples and then passed out a giant worksheet. I didn't learn linear algebra in that class. If Grant Sanderson had taught it I'm sure I would have.

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