Summer of Math Exposition

The point of this video is to explain Euler’s Formula without using advanced math like Taylors Series. In order to do that, he used multiple tools including computer animation, hand drawings and even himself making a toy car. The diversity of the methoed he was trying to show to the viewer were very well balanced because for example if you only use animation the video gets monotonous most of the times. I can see that he put a lot of effort on this video. The editing, audio and overall atmosphere of the video were high quality. This video would be perfect for secondary schoolers who want to understand Euler’s formula without proper calculas. The only thing was that I felt like the intro was a bit long. He could’ve reduce the part where he explained the trigonometry. And it would even be greater if the car he made actually moved in the video.

You present the intuition clearly, and both the animation and the practical effects work well. But this is one of the most commonly explained math topics, and there are already plenty of great videos covering it from pretty much the same angle.

Overall, a very nice video.

I think the multimedia approach works well, such as a combination of Manim and Lego.

There are quite a few videos on this subject, including how multiplying by i leads to rotation, so I don’t believe this video has the same level of novelty as other entries.

However, I still think it is a valuable addition to online math exposition.

Overall, I thought this was a decent video. Clearly, the creator put forth a lot of effort and should be commended for this effort. That being said, I didn’t love the video. It was fine, but I have a number of complaints. For one, the introduction states that basic trigonometry and calculus are assumed, but the video incorporates differential equations and touches on Fourier series. I think a viewer who really only understands trigonometry and basic calculus would have a hard time understanding a lot of what’s in here. It also felt like there were several times in the video where there was a bit of a jump in logic. I’m not saying it was illogical, just that every once in a while a big leap would take place and I’m guessing that some viewers would not have been able to follow the logic.

Euler’s formula is certainly a great choice of subject matter. I would have liked to see you start with a definition of the exponential function. You did show many possible definitions of it, and later you settled on the differential equation. When I view math presentations, I get more out of them if the presenter defines objects before using them. This creates a solid foundation for the presentation to build on. The stop action segment of you building a Lego toy was amusing but I’d would have preferred it if you spent that time developing the mathematical explanation.

Solid video. Liked the color coding. Music and pacing reasonable. But it does feel like it’s a topic I’ve seen other videos about. Could slow down just a tad on the exposition depending on who you want the audience to be—I think for college students it’s fine, but for high school kids they might want some of it unpacked a bit more.

Everything after about 9:20 or so felt extraneous. Like I’d click away at that point if I weren’t trying to watch the whole thing to be a better reviewer. There’s nothing wrong with a video that makes it’s point in a tidy fashion and then finishes.

The lego thing looks fun, but I don’t know that for explanatory purposes it added that much, and it felt a little brief.

You have a great voice. You could be a voice actor.

Wonderful equation. I liked how it did something different with a well known concept… Explaining things from the very basics, without much higher level math concepts. I think it would have really made it nice, since basics was your theme, to also treat the idea of imaginary numbers and what rules having them in an exponent follows with a basic introduction. I think assuming all these things were something that the viewer is comfortable with undermined the theme of doing things in a not too far fetched way from the High School level mathematics.

Other than that, I think a primer to circular motion: of how for motion in a circle with a constant speed, the velocity vector is always perpendicular would be a great addition. But Your physical Lego model and explanation makes of for that. Greatly done!

This is a solid effort and your video is mostly well made and well paced. I want to like it but I feel it really lacks originality, to be honest it just seems like a less good version of the 3B1B video covering the same subject. Maybe if you would center it around how your explanation is different from that one, you could have brought across the specific value of your video more. But as it stands, this feels mostly like just another explanation of why e^(pi*1) = -1. I would really recommend you pick a more original subject next time.

It think you should not have marked it graduate level, as it is undergraduate level.

Not bad. Even knowing this concept well it grabbed my interest better than most of the entries I’ve seen so far. You have a good narration voice, maybe try modulating more and putting some energy into it. I think the editing could be slowed down just a bit - you often cut away just as I’m seeing what’s on the screen. Keep making videos!

The use of Lego was unexpected and nice. The video itself is solid, but it feels like most other typical videos on Euler’s Identity.

Very well made, competent video. Unfortunately, explaining e, the complex numbers, and their connections via rotations is more or less the standard in 2026. So, while Iook forward to see more of your work, it does not stand out much.

Your Video itself was definitely very good and you did a good job at explaining the core idea of “both functions trace out a circle at the exact same rate”. Maybe at 5:30 where you said that you can see that -b + ai is indeed a 90 degree counterclockwise rotation, you could have made the argument a bit more formal by saying “As both of the two basis vectors 1 and i get rotated by 90 degrees when being multiplied by i, also every linear combination of them so every complex number gets rotated by 90 degrees counter clockwise”

At 6:00 you could have also reminded the viewer of the fact that we move our derivative vector by 90 Degrees because as seen in the differential equation this is exactly how e^(ix) behaves and we want to depict that. I know to you and me it’s obvious but someone new to the topic won’t be able to immediately remember all connections which is why I’d suggest to remind them of such.

The only main reason I’ve “only” gave you a Score of 6.5 is that though I really like your method of teaching, especially with the physical lego part, you haven’t really explained something new. As you probably know, 3Blue1Brown already captured this idea of explaining eulers formula (or at least Euler’s identity) and also other videos like this one up to 7:30: https://www.youtube.com/watch?v=TLgZit1HTxA. That’s why “Better than most” would not be justified for your video but if your goal is simply to create intuitive, engaging explanations you can definitely be satisfied with you result.

Differential equations with legoes, what more can you ask for. Maybe a bit too quick at some points, but a great video overall. I really liked the mix of animation and video, physical board for the vector field, lego car for the demonstration.

It has what a lot of the videos have: good technical and graphical execution, but it also has something that most videos could use more of: an impactful, clear, narrative. You have a clear compelling question, you have a journey wherein one understands how you get from A to B, and you end not only answering the question but connecting it to bigger themes. It was executed well on the “PDF-level” i.e. the writing level which is usually the most important part.