Summer of Math Exposition

Why did the Basel problem and Wallice product relate to factoring sine? To me it seems jumping into the math on the next slide and just skip Basel and Wallice.

This is clearly the best of the five videos I’ve seen so far!

This video combines several strong advantages: A very interesting topic (IMHO), great presentation, very good pacing, and avoiding lots of assumptions or undefined terms.

The script is engaging and it shows not just the results, but also some motivation and how Euler arrived at his solution. I also like the timeline at the end to put this into the historic context.

The visuals are excellent.

This is the first time I’ve seen a video about factoring a function rather than finding its power series. For others that may not be a new thing, but for me it certainly was a really interesting new concept that I learned from this video.

Definitely one of the most clear, interesting, understandable, motivating and enjoyable math videos I’ve seen.

Bonus point for showing your face at least in the beginning. In the days of AI generated content, that little human touch goes a long way.

That was nice! In the end just a run-through of a bit of algebra. But it was well-paced and didn’t overstay its welcome.

Very good. not much to say besides what you already know. Keep up the good work!

I really enjoyed the video. The highly technical language is accompanied by simple but effective animations. I think the choice not to include music is nevertheless consistent with the video, which is similar to a traditional lecture. There are many formulas, but that is what one would expect from a video of this kind. You made the right choice in targeting an expert audience; a video like this would not work for high school students.

In short: a technical topic, not particularly complex, explained clearly.

For a pure math video this was quite good. I followed the logic easily (I’ve seen it before), and your narration was great. I made it to the end (more than I can say for most submissions). Very well paced too. I’d say if anything, I would try to make videos like this more visually interesting, with fewer stills that stay up on the screen for a longtime while you gesture with the mouse (feels very Powerpoint-y). More animation and more color always helps. Overall great job!

Clear

Flow of concepts was very smooth, the visuals were very helpful.

Very insightful and straight forward video. Enjoyed the algebra.

Nothing crazy to mention other than a well-done video with a concise and insightful video.

Well done!

The video was enjoyable and well-made. It was a good topic, which was quite interesting and memorable. I like the style of having LaTeX slides, but then talking and illustrating over them. I feel this is much clearer for this type of video than hand-writing everything.

The math was mostly well explained, taking clear steps to make everything understood. I did think, however, that while including the incorrect factorization itself was worthwhile, graphing it was superfluous. I felt there are a few more things like this that could be streamlined somewhat.

I think that the video would have benefitted from a little more animation, with better graphing tools than simply Desmos. This would add a bit more polish to an otherwise great video.

I believe that you should be able to use LaTeX markdown more effectively in the SoME description (this is a minor point).

Enthusiasm is the sine of a good video.

Good explanations. The visualization of the factorization was also quite helpful in understanding how each new factor influences the result. I think however that the second half of the video (the visualizations generally and the ‘proof’ of Eulers method) was a bit too long and could have been shortened. Especially how the Taylor expansion of sin works should be known to most undergrad math/physics students (which is the audience which you indicated that the video is for). A brief reminder of it of course doesn’t hurt, but this was too long in my opinion.

Interesting video on an interesting topic, which is well discussed. I really liked the clarity of the video, and the fact that it was explained how the basel was used as “evidence”. The audio quality is very good and the video quality is good: even though there are no animations the video still feels very well-crafted and the attention in the crafting of a clear script is evident and appreciated.

I think that video is a bit longer than it needs too, and I found some explanations unnecessary. For instance, the part where you show the desmos plots is in my opinion too much of a “chapter” on its own, while I would have liked it better if you would have presented the plots while writing the product or very fast instead. Similarly, I think it’s not necessary to go through the computations that slowly, while a fast display of the computation on the screen and talking about the result would have been equally good at presenting the topic.

I have a positive comment that I first thought as negative. This video left me with many questions: what is this equivalent condition on convergence theorem? Ok but you said you would say how to prove the product formally and instead told me about this which I didn’t need? Why is the formula so complicated to prove? These are all questions whose answer came clear once I started looking at the proofs on wikiproof… they are messy and long indeed. Still, I liked that the video made me curious about a thing I probably had already seen but forgot about.

Finally, I was expecting something more: maybe more series if there are any? Or the factorization of cosine? Or even maybe an enunciation of the weierstrass factorization theorem: even if few people will actually understand it, it will feel as if it’s a “better fitting” result than the theorem shown that, although interesting, is not entirely the point

Introduction contained good motivation for the main idea. Desmos visualization was helpful to describe the infinite series convergence. Could use color better in the main portion of the video in order to differentiate different terms, ideas, etc. Likening math work to an art form was a good connection that students should take to heart. Mathematics used were fairly simple to follow. Appropriate for intended audience.

The animation could use some work. Also, not my favorite concept.

This was good. Clear explanation, you told why you want the infinite product terms to converge to 1. I wish you had indicated a reason why we might want to factor the sine function. Your pace was good and you showed step by step so we could flow the factorization, rewriting of terms etc. I especially appreciated your example of different forms of factoring namely x^2 -7x + 10 = (x-5)(x-2)= -5(-x/5 + 1)(-2)(-x/2+1) = 10(1 - x/5)(1 - x/2). Very nice use of the Desmos graphs too. Thank you.

Lovely gentle introduction to complex analysis! Well motivated and great use of desmos to show the key ideas without overwhelming the viewer. Really nice stuff! As an add on/teaser to more math, at the very end you could mention that this kind of factorization is also used in the Riemann zeta function to connect the prime numbers to analytic functions too.

I really enjoyed the video! It’s always really interesting to see how specific sums and products, which - at first glance - have nothing to do with pi, tend to end up at pi somehow anyway.

I also appreciated the historical insight into Euler’s thought process, it was quite interesting.

The formulas and graphs were clear and concise, and the audio quality was good enough.

Fantastic video, extremely well done!

Motivation: 3/9. Touches on infinite series/product representations of functions, but the applications are not mentioned here.

Clarity: 9/9. Every step is explained and the approach to factoring sine is presented as something a viewer could come up with themselves. I would have liked to see a proof of the elegant theorem.

Novelty: 7/9. Infinite products and the identities derived by setting them equal to series almost never even show up in the videos I’ve seen before.

Memorability: 6/9. The infinite factorizations are interesting and leave an open question of what else they can be used to derive.