While "one-off" videos are obviously very popular with people because they're filling some of the massive holes in math and science pedagogy, I don't think they *scale* very well as a solution. Eventually there needs to be some sort of "pedagogical wikipedia" which both (a) presents the best version of every topic and (b) strings them together in a sort of curriculum or "tech tree" (like in the Civilization games). Imagine that there was an article on every concept in math and physics that opened up with the best high-level intuition for the subject with the most intuitive formulation and the best animations, and every concept had a link to an article that had the best presentation on *that* subject, and the whole thing had indexes that strung it together into a curriculum plus, like, problem sets, worked solutions, and ties to other formulations or abstractions of the same concepts. Sort of like Wikipedia meets Khan Academy meets 3b1b meets an actual textbook.
Obviously video explanations are great because they're easy to digest. But text explanations are also great because they can be exhaustive and easily used for reference. And in either case, what has been missing historically was consistently great *animations*; I think 3b1b's big pedagogical advancement was in solving the engineering problem of having good animations coupled with good explanations --- there are plenty of *bad explanations* and *bad* visuals out there, but nobody wants to look at those ever again once a good one exists.
So I imagine that what could happen is:
1. this pedagogical encyclopedia gets set up with stub articles for everything, with some sort of governing committee of editors that sets the tone and plans out the curriculum
2. the contest is about *producing content for it*, which can be writing articles, making explanatory video supplements, or making animations, visualization, or tools for making them which can be useful in the articles or videos after that.
3. people can also just edit and contribute to it all the time in general! I imagine most of the time people will just be writing articles because it's a lot easier to do, and the contest could serve to bolster the articles with labor-intensive videos and animations.
I'm also excited about a pedagogical encyclopedia that has an editorial committee, because I find myself wishing that Wikipedia was more *opinionated* about its presentations on technical subjects. It's not useful to have the article on e.g. Fourier transforms contain every subject under the sun that has to do with Fourier transforms --- it ends up being useless for learning the concept and difficult to use as a reference at the same time. So an opinionated resource could sort those various use-cases out into their own articles or sections in a more deliberate way that makes it better for everybody.
Anyway! That's my idea. Sounds like a lot of work, but maybe it'll inspire somebody who might be able to figure out how to do it?
For me, SoME was never really about the value of the information, nor the rigor of the lesson at hand. It's really easy to view mathematics education through the lens of a textbook, but I think it misses the point of independent math education.
When I was in 6th grade, I watched every single video on your youtube channel. Needless to say, the material was far above my head as an algebra student. The beauty of the math was the idea that intrigued me. The videos were not building a comprehensive web of say, fractals - but they were an introduction into a section of the expansive catalog of math.
The sad reality of our subject is that it's hard to create a passion for it in the classroom. It's almost a necessity to create that excitement through videos that build intrigue in a non-linear (read: non-textbook) way. I didn't need the background knowledge, and it was an almost motivating factor to understand how much there was to still discover.
For many, the value of online math exposition is not the perceived value in a textbook sense, but in the unlimited value of building a passion. I fear that passion is the factor that will be lost in a pivot to creating more traditionally effective videos.
Thank you, Grant, for your guidance, very wonderful clarification and enhancement of my comprehensive view of The Mathematical concepts.
Presently studying, reviewing the Theory of Infinities; being 75 years old, 50 years ago, I read a book in Jain Mathematics, where the description of Infinite had five definitions, I remember this: Infinite point, Infinite line, one dimension; Infinite area, two dimensions ; Infinite volume, three dimensions; Infinite perennial; Infinite forever… last two related to Time….I wonder if you can clarify the concept, with converging and diverging series, also the translation of the Origin, to all points of the Vector Field and a possible connections from the initial Origin describe in your Linear Algebra videos, like you said, pause and ponder…by the way, my likes is all in Physics… “ a Physicist asking a Mathematician… for a Theory of Infinites… respectfully admire your knowledge and how you teach your craft…
Hot takes:
While "one-off" videos are obviously very popular with people because they're filling some of the massive holes in math and science pedagogy, I don't think they *scale* very well as a solution. Eventually there needs to be some sort of "pedagogical wikipedia" which both (a) presents the best version of every topic and (b) strings them together in a sort of curriculum or "tech tree" (like in the Civilization games). Imagine that there was an article on every concept in math and physics that opened up with the best high-level intuition for the subject with the most intuitive formulation and the best animations, and every concept had a link to an article that had the best presentation on *that* subject, and the whole thing had indexes that strung it together into a curriculum plus, like, problem sets, worked solutions, and ties to other formulations or abstractions of the same concepts. Sort of like Wikipedia meets Khan Academy meets 3b1b meets an actual textbook.
Obviously video explanations are great because they're easy to digest. But text explanations are also great because they can be exhaustive and easily used for reference. And in either case, what has been missing historically was consistently great *animations*; I think 3b1b's big pedagogical advancement was in solving the engineering problem of having good animations coupled with good explanations --- there are plenty of *bad explanations* and *bad* visuals out there, but nobody wants to look at those ever again once a good one exists.
So I imagine that what could happen is:
1. this pedagogical encyclopedia gets set up with stub articles for everything, with some sort of governing committee of editors that sets the tone and plans out the curriculum
2. the contest is about *producing content for it*, which can be writing articles, making explanatory video supplements, or making animations, visualization, or tools for making them which can be useful in the articles or videos after that.
3. people can also just edit and contribute to it all the time in general! I imagine most of the time people will just be writing articles because it's a lot easier to do, and the contest could serve to bolster the articles with labor-intensive videos and animations.
I'm also excited about a pedagogical encyclopedia that has an editorial committee, because I find myself wishing that Wikipedia was more *opinionated* about its presentations on technical subjects. It's not useful to have the article on e.g. Fourier transforms contain every subject under the sun that has to do with Fourier transforms --- it ends up being useless for learning the concept and difficult to use as a reference at the same time. So an opinionated resource could sort those various use-cases out into their own articles or sections in a more deliberate way that makes it better for everybody.
Anyway! That's my idea. Sounds like a lot of work, but maybe it'll inspire somebody who might be able to figure out how to do it?
For me, SoME was never really about the value of the information, nor the rigor of the lesson at hand. It's really easy to view mathematics education through the lens of a textbook, but I think it misses the point of independent math education.
When I was in 6th grade, I watched every single video on your youtube channel. Needless to say, the material was far above my head as an algebra student. The beauty of the math was the idea that intrigued me. The videos were not building a comprehensive web of say, fractals - but they were an introduction into a section of the expansive catalog of math.
The sad reality of our subject is that it's hard to create a passion for it in the classroom. It's almost a necessity to create that excitement through videos that build intrigue in a non-linear (read: non-textbook) way. I didn't need the background knowledge, and it was an almost motivating factor to understand how much there was to still discover.
For many, the value of online math exposition is not the perceived value in a textbook sense, but in the unlimited value of building a passion. I fear that passion is the factor that will be lost in a pivot to creating more traditionally effective videos.
Thank you, Grant, for your guidance, very wonderful clarification and enhancement of my comprehensive view of The Mathematical concepts.
Presently studying, reviewing the Theory of Infinities; being 75 years old, 50 years ago, I read a book in Jain Mathematics, where the description of Infinite had five definitions, I remember this: Infinite point, Infinite line, one dimension; Infinite area, two dimensions ; Infinite volume, three dimensions; Infinite perennial; Infinite forever… last two related to Time….I wonder if you can clarify the concept, with converging and diverging series, also the translation of the Origin, to all points of the Vector Field and a possible connections from the initial Origin describe in your Linear Algebra videos, like you said, pause and ponder…by the way, my likes is all in Physics… “ a Physicist asking a Mathematician… for a Theory of Infinites… respectfully admire your knowledge and how you teach your craft…
2025, that's when I may be finishing my first year in uni, studying Mathematics & Computer Science!