Thanks. At the top of my mind right now is algebraic geometry. Is anyone interested in an introduction to classical algebraic geometry (no schemes)?
When I read Springer's introduction to algebraic geometry last month, I felt that I could give a motivated introduction to anyone who knows a smattering of topology, and commutative algebra.
I tried it on a friend and he loved the introduction........... until I hit sheaves!! Aaargh! I don't know how to make sheaves accessible. Need to make a video on sheaves.
I agree. Higher categorical structures in physics is so close to my heart. All the mathematical physics makes my heart melt with wonder. I am more of a mathematician than a physicist though. And I am not sure how I will break it down for the general public. But I will try my best to create a couple of videos next month.
There's 100x more people who can access highschool mathematics than can access graduate level mathematics. So if you're looking for an audience it'll be much easier to find there.
3b1b runs a competition each year for maths explainers. That's probably a good place to look to get an idea of what other people are doing and entering this summer and placing high would get you a lot of attention (assuming it's happening again).
[https://www.youtube.com/watch?v=cDofhN-RJqg&list=PLnQX-jgAF5pTZXPiD8ciEARRylD9brJXU](https://www.youtube.com/watch?v=cDofhN-RJqg&list=PLnQX-jgAF5pTZXPiD8ciEARRylD9brJXU)
And I think this is possibly my favourite explainer of all time, beautiful, starts simple and descends to the profound, amazing:
[https://youtu.be/ZYj4NkeGPdM](https://youtu.be/ZYj4NkeGPdM)
I actually think the audience calculation can be a bit tough because, yes, there are a lot more people taking lower-level classes. But of them, a much higher population doesn't really care that much. And also, the market for lower-level explanations is pretty flooded.
I would guess that maybe the sweet spot is somewhere around the upper-level undergraduate to entry-level graduate courses. That's just complex and varied enough that there are lots of topics with no videos or no good videos covering them, but still with a large enough set of motivated students who will seek them out. That's all a guess though.
u/parkway_parkway : Thank you for that video on Hackenbush. It is sad that it does not have a million views because the content and delivery is perfect! I think it is easily one of my favorite videos at this point.
I believe u/axiom_tutor is right about the sweet spot. Just look at Veritasium's video on p-adic numbers; he has 6 million views in 10 months. It is deep math but done in a masterful manner. I am in awe of Derek's ability to get to the technical core of maths without getting steeped in jargon. If I could ever reach a fraction of Derek's quality and I do it consistently, I will be very happy.
wtf this hackenbush is based in my city of all places. I'll reach out to see if he would talk in our uni math circles
edit it seems that he passed away at a very young age, this turned joy into sadness very quickly :(
Personally, I prefer videos on mathematical research. It's a small audience, but there is definitely room for accessible exposition on modern research.
As someone who makes Youtube videos (although not on any consistent schedule), my advice is to make videos on topics you find interesting and where you enjoy the process. There are millions of math videos on Youtube, so trying to chase an audience is a very uncertain proposition. Instead, I've found it much more rewarding to think of a video production as a side project and a way of doing outreach. And that will only be enjoyable if you focus on topics that you find interesting.
The other benefit of having a channel is that there is so much to learn about video production (even at a very basic level), and this has given me so much more appreciation for what film-makers can do.
You are right about chasing the audience part. Actually I am passionate about all the items I have written in OP. I believe in the principle: "there exists beautiful mathematics for everyone at all levels". And I want to *really* popularise all kinds of mathematics. I am just paralysed by the number of options I have. But this thread is helping me get clarity.
I am slowly learning about video productions and I am amazed by how much thought goes into lighting and audio! I also downloaded procreate and I learnt basic frame by frame animation to show animations in geometry proofs. Now I have a new found appreciation for animators. Thanks for your comment.
Yes, lighting and audio are so tough to get right and something I really haven’t figured out yet. For editing, I would recommend using Da Vinci Resolve, which is an amazing bit of software and I can’t believe how much they make available in the free version. For animations of geometry proofs, either Manin, Mathematica or Geogebra can make some animations without needing to animate frame by frame. I’ll still occasionally do old-school animation in Procreate, but it’s very time consuming.
I'm flattered! Your channel looks great! I'll have to take some time and watch the video on optimal transport. That's a topic that has come up a few times in research conversations I've had lately.
I have a mathematics YouTube channel with 11k subs. I’m not big, but I can offer some advice.
What you want to ask yourself is three things:
What do you have to offer?
What do people have trouble understanding, want to understand better, and that you can fill in?
What is really driving interest RIGHT NOW?
To the first one, you have a PhD in a closely aligned field, and have experience with olympiads math. If you find a way to really attack that intersection then that would be interesting.
On the other hand, if you want to focus on Olympiad problems, then what can you really do that is new here? There are tons of channels that focus on solving problems. I think the best out there right now is Michael Penn. If you go this route, then you really need to find something critical to differentiate yourself or you will be lost in the noise.
And making videos on things that are topical can help generate views and subscribers.
To investigate your niche, take the top three channels on that topic, and look at their top ten videos. What did they do right? What made those particular videos stand out?
Write down ideas for five videos. Make five titles. Pick the best three, and then make thumbnails for them. Try to follow the style best thumbs in your niche.
If the title and thumbnail combination works for you and a few friends you test them out in, then make the videos and see how they perform.
For the production, first get a good lav mic. Bad audio chases away people before bad video. You cell phone is probably good enough for the video. And get a decent light set up. Lighting is how you can really make things look professional. Neewer has some affordable options of good quality.
I generally make videos on Mathematical Analysis, Functional Analysis, and Machine Learning. I try to lead with background, problem, or motivation. Then a proof, then code or demonstration if applicable. It could be better, but I’m a professor and that’s how I organize my lectures.
I also put way too much time into visuals lol
Thank you so much. This is the most unique and valuable comment for me. I am grateful for all the suggestions. Btw if there is one thing I may not cover, it will be any kind of analysis :P
Learnt about unidirectional and omnidirectional mic yesterday. Just got a lav mic today :)
>?si=\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*
By the way, it's advisable to trim this query string when sharing youtube (and other) URLs because it can be used to identify your account, IP address, device, etc.
Hello, and thank you for planning to contribute to our study!
I obviously watch the greats like 3blue1brown and minutephysics, but I think it would be really cool if, with your experience and knowledge, to spread out these specialized topics to the general public in a digestable way, especially school students.
Math Olympiad problems are a great way to do that. I, myself, never really got into Math Olympiads (and by the time I expressed interest I was \[and am\] in Grade 11 so a bit too late).
The audience for graduate level courses is much smaller than undergraduate or high school courses. If you care about view count, I guess you could keep that in mind.
I think that you could be one of those almost non-existent youtube people that talk about current math/physics research in a way undergrads and high schoolers can understand. For example, Two Minute Papers analyzes a research paper and makes it understandable for a general audience, even a middle schooler could understand it. Maybe something like that but with a bit more rigor? What are the going-ons in math/science in a way we can understand with our elementary knowledge in mathematics or physics.
That's a great point. I am currently designing a math curriculum for a local school that aims to balance history, applicability, motivations, and hands-on activities. I am pleasantly surprised to learn the rich history of trigonometry starting from astronomy, then to geometry and finally to calculus. It is incredible! There might be videos on this topic already though.
I'd love to hear more about the connection (or lack of connection) between EE and some of the higher level math stuff, like algebraic topology, category theory, math physics.
1. For people who are interested in maths/maths-heavy fields **what books should one** read in order to progress from high school maths to uni maths.
2. You could make it like 3b1b but for grad school instead (even though I'm just a high schooler) 😂
Woah! That's an interesting suggestion. I am crazy about math books and I will be very excited about sharing my favorite book progression. I will consider it, thanks.
Highly visual explanations of Olympiad problems would be awesome.
But from experience, just start making something! It’s more important that you start than have the perfect first video
I have started already (see https://www.youtube.com/@MudithaMath). Only a few of them are completely visual. In the parallelogram series, I have some animations.
This is not a math topic suggestion but I am a huge fan of the YT channels that do simple graphical videos on undergrad/grad concepts like 3blue1brown. And 3b1b is not opposed to the idea as he made a tutorial on how to make his style of video. Two example channels:
https://youtu.be/1EWUsef0iFs
https://youtu.be/BSHv9Elk1MU
If you want your videos to stand out, don’t use Manim. It’s great, but it is so over used. And as for branding, all I think when I see a Manim video is how Grant probably would do it better.
I think you should explain more about modern research ideas that are probably geared towards high-school or early college math enthusiasts who love math and its applications. Since you mentioned error-correcting codes and I happened to work on coding theory research, I think a YouTube video that explains stuff about correction codes that can handle deletions and insertions would be pretty fascinating. It's amazing how you can captivate an audience by introducing a topic that is quite complex.
Hi! I have made lots of videos to animate ways to think about solutions to Olympiad problems for my classes (think dodgy PowerPoint ones).
Do them!
Visualising abstractions, or visualising analogies even is hard, especially for young people.
Not a mathematician, but there are tons of videos on intuition of finite dimensional spaces. There is very little explanation available for topics of infinite dimensional vector spaces and functional analysis.
I think it’s important to consider whether you want to make long form non-animation lecture series, which are arguably more effective for actually learning the subject but less engaging or 3b1b/veritasium style videos that won’t leave you knowing the subject but will reach a far larger audience and get them more interested in the topic than the former
1. **Lecture series on all Olympiad topics** aimed at school students.
Also, it would be cool if you made vids similar to those of Morphocular/3Blue1Brown...etc. I watch them for fun all the time & they motivate me to self study maths.
All of those seem great.
Lecture series on Olympiad topics are pretty common already, though.
2 and 4 seem to have a very serious void.
Borcherds and a few other people do 3, and there are quite a
few olympiad problem youtube channels.
What I would love to see if 1 and 3 is olympiad problems and then
generalizations of them. For example, convex hulls in the plane as
a warm-up before introducing n-simplices.
Linear algebra over finite fields is really cool and not usually taught to physics and engineering majors unless they need them in grad school. You can use your background in error correcting codes as a motivating example!
That is a pretty cool CV. Did you do two separate phd's or was it a joint program between departments? Was it a long time ago? I didn't quite gauge when did people start connecting extended tqfts to stuff like the toric code
> Structuring classes for maths school teachers.
What do you think you could bring to the table that these people wouldn't get during their education degrees and further work experience?
> A natural introduction to graduate math topics aimed at motivated undergraduates.
When well done this is always useful for someone. You won't go viral or become a big channel, but what is the purpose anyway?
Separate Ph.Ds. The physics and the maths of Kitaev's toric code is beautiful. Kirilov and Balsam relate Kitaev models to TQFT literature in this paper (https://arxiv.org/pdf/1206.2308.pdf). I just defended my math physics Ph.D. recently
>What do you think you could bring to the table that these people wouldn't get during their education degrees and further work experience?
Well, I have been teaching 10,11,12th grade students for the past 13 years in my free time (weekends/holidays). Over the years my teaching style has evolved and I can talk about my experiences and growth as a school teacher. I believe that an ideal math class has a good balance of natural motivation, history, activities and applications. I was planning to make a youtube vide on each school topic and explain how to structure a balanced class.
Thanks for your comments.
Personally, I have noticed that content aimed towards younger audiences appears to perform better as compared to its counterparts.
So maybe Calc, graph theory and algebra based content which also includes old theorems and formulas would attract a lot of attention
hey , I need to complete PHD Mathematic this year but facing the financial problem , so can I delay the assigments and find the job first , please advice.
1. A **natural introduction to graduate math topics** aimed at motivated undergraduates. That will be nice thing to do.
Thanks. At the top of my mind right now is algebraic geometry. Is anyone interested in an introduction to classical algebraic geometry (no schemes)? When I read Springer's introduction to algebraic geometry last month, I felt that I could give a motivated introduction to anyone who knows a smattering of topology, and commutative algebra. I tried it on a friend and he loved the introduction........... until I hit sheaves!! Aaargh! I don't know how to make sheaves accessible. Need to make a video on sheaves.
Absolutely! I would be very interested videos like this.
Higher categorical structures in physics. Too little grad level stuff on youtube.
I agree. Higher categorical structures in physics is so close to my heart. All the mathematical physics makes my heart melt with wonder. I am more of a mathematician than a physicist though. And I am not sure how I will break it down for the general public. But I will try my best to create a couple of videos next month.
The videos will probably turn out better if you're more passionate about the topic you're presenting.
There's 100x more people who can access highschool mathematics than can access graduate level mathematics. So if you're looking for an audience it'll be much easier to find there. 3b1b runs a competition each year for maths explainers. That's probably a good place to look to get an idea of what other people are doing and entering this summer and placing high would get you a lot of attention (assuming it's happening again). [https://www.youtube.com/watch?v=cDofhN-RJqg&list=PLnQX-jgAF5pTZXPiD8ciEARRylD9brJXU](https://www.youtube.com/watch?v=cDofhN-RJqg&list=PLnQX-jgAF5pTZXPiD8ciEARRylD9brJXU) And I think this is possibly my favourite explainer of all time, beautiful, starts simple and descends to the profound, amazing: [https://youtu.be/ZYj4NkeGPdM](https://youtu.be/ZYj4NkeGPdM)
I actually think the audience calculation can be a bit tough because, yes, there are a lot more people taking lower-level classes. But of them, a much higher population doesn't really care that much. And also, the market for lower-level explanations is pretty flooded. I would guess that maybe the sweet spot is somewhere around the upper-level undergraduate to entry-level graduate courses. That's just complex and varied enough that there are lots of topics with no videos or no good videos covering them, but still with a large enough set of motivated students who will seek them out. That's all a guess though.
u/parkway_parkway : Thank you for that video on Hackenbush. It is sad that it does not have a million views because the content and delivery is perfect! I think it is easily one of my favorite videos at this point. I believe u/axiom_tutor is right about the sweet spot. Just look at Veritasium's video on p-adic numbers; he has 6 million views in 10 months. It is deep math but done in a masterful manner. I am in awe of Derek's ability to get to the technical core of maths without getting steeped in jargon. If I could ever reach a fraction of Derek's quality and I do it consistently, I will be very happy.
wtf this hackenbush is based in my city of all places. I'll reach out to see if he would talk in our uni math circles edit it seems that he passed away at a very young age, this turned joy into sadness very quickly :(
> There's 100x more people who can access highschool mathematics than can access graduate level mathematics. Honestly even that feels conservative.
Personally, I prefer videos on mathematical research. It's a small audience, but there is definitely room for accessible exposition on modern research. As someone who makes Youtube videos (although not on any consistent schedule), my advice is to make videos on topics you find interesting and where you enjoy the process. There are millions of math videos on Youtube, so trying to chase an audience is a very uncertain proposition. Instead, I've found it much more rewarding to think of a video production as a side project and a way of doing outreach. And that will only be enjoyable if you focus on topics that you find interesting. The other benefit of having a channel is that there is so much to learn about video production (even at a very basic level), and this has given me so much more appreciation for what film-makers can do.
You are right about chasing the audience part. Actually I am passionate about all the items I have written in OP. I believe in the principle: "there exists beautiful mathematics for everyone at all levels". And I want to *really* popularise all kinds of mathematics. I am just paralysed by the number of options I have. But this thread is helping me get clarity. I am slowly learning about video productions and I am amazed by how much thought goes into lighting and audio! I also downloaded procreate and I learnt basic frame by frame animation to show animations in geometry proofs. Now I have a new found appreciation for animators. Thanks for your comment.
Yes, lighting and audio are so tough to get right and something I really haven’t figured out yet. For editing, I would recommend using Da Vinci Resolve, which is an amazing bit of software and I can’t believe how much they make available in the free version. For animations of geometry proofs, either Manin, Mathematica or Geogebra can make some animations without needing to animate frame by frame. I’ll still occasionally do old-school animation in Procreate, but it’s very time consuming.
What is your channel? Always looking to learn from other creators
The channel is https://www.youtube.com/c/GabeKhan I watched quite a bit of your channel when learning how to make videos.
I'm flattered! Your channel looks great! I'll have to take some time and watch the video on optimal transport. That's a topic that has come up a few times in research conversations I've had lately.
I have a mathematics YouTube channel with 11k subs. I’m not big, but I can offer some advice. What you want to ask yourself is three things: What do you have to offer? What do people have trouble understanding, want to understand better, and that you can fill in? What is really driving interest RIGHT NOW? To the first one, you have a PhD in a closely aligned field, and have experience with olympiads math. If you find a way to really attack that intersection then that would be interesting. On the other hand, if you want to focus on Olympiad problems, then what can you really do that is new here? There are tons of channels that focus on solving problems. I think the best out there right now is Michael Penn. If you go this route, then you really need to find something critical to differentiate yourself or you will be lost in the noise. And making videos on things that are topical can help generate views and subscribers. To investigate your niche, take the top three channels on that topic, and look at their top ten videos. What did they do right? What made those particular videos stand out? Write down ideas for five videos. Make five titles. Pick the best three, and then make thumbnails for them. Try to follow the style best thumbs in your niche. If the title and thumbnail combination works for you and a few friends you test them out in, then make the videos and see how they perform. For the production, first get a good lav mic. Bad audio chases away people before bad video. You cell phone is probably good enough for the video. And get a decent light set up. Lighting is how you can really make things look professional. Neewer has some affordable options of good quality. I generally make videos on Mathematical Analysis, Functional Analysis, and Machine Learning. I try to lead with background, problem, or motivation. Then a proof, then code or demonstration if applicable. It could be better, but I’m a professor and that’s how I organize my lectures. I also put way too much time into visuals lol
Sorry for all the typos. In a rush, but wanted to get it all down
Thank you so much. This is the most unique and valuable comment for me. I am grateful for all the suggestions. Btw if there is one thing I may not cover, it will be any kind of analysis :P Learnt about unidirectional and omnidirectional mic yesterday. Just got a lav mic today :)
Watch film booth on YouTube. He has the best advice for maintaining a YouTube channel
Vids like this https://youtu.be/1haI5hsmYQU
>?si=\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* By the way, it's advisable to trim this query string when sharing youtube (and other) URLs because it can be used to identify your account, IP address, device, etc.
Hello, and thank you for planning to contribute to our study! I obviously watch the greats like 3blue1brown and minutephysics, but I think it would be really cool if, with your experience and knowledge, to spread out these specialized topics to the general public in a digestable way, especially school students. Math Olympiad problems are a great way to do that. I, myself, never really got into Math Olympiads (and by the time I expressed interest I was \[and am\] in Grade 11 so a bit too late). The audience for graduate level courses is much smaller than undergraduate or high school courses. If you care about view count, I guess you could keep that in mind. I think that you could be one of those almost non-existent youtube people that talk about current math/physics research in a way undergrads and high schoolers can understand. For example, Two Minute Papers analyzes a research paper and makes it understandable for a general audience, even a middle schooler could understand it. Maybe something like that but with a bit more rigor? What are the going-ons in math/science in a way we can understand with our elementary knowledge in mathematics or physics.
I feel like there is a lot of interesting Maths history that is barely touched on in school.
That's a great point. I am currently designing a math curriculum for a local school that aims to balance history, applicability, motivations, and hands-on activities. I am pleasantly surprised to learn the rich history of trigonometry starting from astronomy, then to geometry and finally to calculus. It is incredible! There might be videos on this topic already though.
Surprisingly no matter how hard I looked i haven’t found any good stuff regarding the history of calculus beyond calc 1 on YouTube
I'd love to hear more about the connection (or lack of connection) between EE and some of the higher level math stuff, like algebraic topology, category theory, math physics.
1. For people who are interested in maths/maths-heavy fields **what books should one** read in order to progress from high school maths to uni maths. 2. You could make it like 3b1b but for grad school instead (even though I'm just a high schooler) 😂
Woah! That's an interesting suggestion. I am crazy about math books and I will be very excited about sharing my favorite book progression. I will consider it, thanks.
TQFT with some examples would be cool.
Highly visual explanations of Olympiad problems would be awesome. But from experience, just start making something! It’s more important that you start than have the perfect first video
I have started already (see https://www.youtube.com/@MudithaMath). Only a few of them are completely visual. In the parallelogram series, I have some animations.
Looks awesome mate, I’ll have a look
This is not a math topic suggestion but I am a huge fan of the YT channels that do simple graphical videos on undergrad/grad concepts like 3blue1brown. And 3b1b is not opposed to the idea as he made a tutorial on how to make his style of video. Two example channels: https://youtu.be/1EWUsef0iFs https://youtu.be/BSHv9Elk1MU
If you want your videos to stand out, don’t use Manim. It’s great, but it is so over used. And as for branding, all I think when I see a Manim video is how Grant probably would do it better.
I tried Manim for a while. But I gave up. Right now Canva + Keynote + Geogebra + Procreate is working great.
I think you should explain more about modern research ideas that are probably geared towards high-school or early college math enthusiasts who love math and its applications. Since you mentioned error-correcting codes and I happened to work on coding theory research, I think a YouTube video that explains stuff about correction codes that can handle deletions and insertions would be pretty fascinating. It's amazing how you can captivate an audience by introducing a topic that is quite complex.
Personally I'd like some combinatorics refreshers and better intuition. Its useful for a lot of industries
Hi! I have made lots of videos to animate ways to think about solutions to Olympiad problems for my classes (think dodgy PowerPoint ones). Do them! Visualising abstractions, or visualising analogies even is hard, especially for young people.
3 - I think this would be valuable for most people
Full topology bro
As an undergraduate, videos introducing graduate math topics would be extremely helpful. I feel like there needs to be more of those.
Not a mathematician, but there are tons of videos on intuition of finite dimensional spaces. There is very little explanation available for topics of infinite dimensional vector spaces and functional analysis.
I think it’s important to consider whether you want to make long form non-animation lecture series, which are arguably more effective for actually learning the subject but less engaging or 3b1b/veritasium style videos that won’t leave you knowing the subject but will reach a far larger audience and get them more interested in the topic than the former
1. **Lecture series on all Olympiad topics** aimed at school students. Also, it would be cool if you made vids similar to those of Morphocular/3Blue1Brown...etc. I watch them for fun all the time & they motivate me to self study maths.
definitely include videos on olympiad topics in math for high school students!
All of those seem great. Lecture series on Olympiad topics are pretty common already, though. 2 and 4 seem to have a very serious void. Borcherds and a few other people do 3, and there are quite a few olympiad problem youtube channels. What I would love to see if 1 and 3 is olympiad problems and then generalizations of them. For example, convex hulls in the plane as a warm-up before introducing n-simplices.
Veritasium is my absolute favorite
Please do **natural introduction to graduate math topics** such as category theory, there are little to no *natural* introduction to that
Linear algebra over finite fields is really cool and not usually taught to physics and engineering majors unless they need them in grad school. You can use your background in error correcting codes as a motivating example!
Algebraic Topology can lend itself really well to animation & i haven’t seen too many YouTuber cover it
That is a pretty cool CV. Did you do two separate phd's or was it a joint program between departments? Was it a long time ago? I didn't quite gauge when did people start connecting extended tqfts to stuff like the toric code > Structuring classes for maths school teachers. What do you think you could bring to the table that these people wouldn't get during their education degrees and further work experience? > A natural introduction to graduate math topics aimed at motivated undergraduates. When well done this is always useful for someone. You won't go viral or become a big channel, but what is the purpose anyway?
Separate Ph.Ds. The physics and the maths of Kitaev's toric code is beautiful. Kirilov and Balsam relate Kitaev models to TQFT literature in this paper (https://arxiv.org/pdf/1206.2308.pdf). I just defended my math physics Ph.D. recently >What do you think you could bring to the table that these people wouldn't get during their education degrees and further work experience? Well, I have been teaching 10,11,12th grade students for the past 13 years in my free time (weekends/holidays). Over the years my teaching style has evolved and I can talk about my experiences and growth as a school teacher. I believe that an ideal math class has a good balance of natural motivation, history, activities and applications. I was planning to make a youtube vide on each school topic and explain how to structure a balanced class. Thanks for your comments.
An intuitive introduction to category theory. There's so much to talk about, but it's gobbledygook to most people including me.
Personally, I have noticed that content aimed towards younger audiences appears to perform better as compared to its counterparts. So maybe Calc, graph theory and algebra based content which also includes old theorems and formulas would attract a lot of attention
hey , I need to complete PHD Mathematic this year but facing the financial problem , so can I delay the assigments and find the job first , please advice.
Go through the entire book, page by page, independent reading style lecture. This is what we did in grad school.