Summer of Math Exposition

I’ve been doing some projective geometry this week (having a look at the Fano Plane and finite-field projective spaces etc), so this video is on-the-ball for me :) Your video is bold and I like the effort put into building up the motivation for the conjecture, rather than just explaining what the definitions of all the terms are. Good job!

The style is a nice breath of fresh air from the usual 3Blue1Brown-like videos, and I felt the intro and pacing was good. The main overall motivation for the topic felt mostly like that it was notoriously hard to explain and that it’s a Millennium prize problem, which did intrigue me, and is probably the best motivation for this topic for a Youtube video, but it’s not as strong as the motivation I’ve seen in other videos. I do like that the video started with the problem statement to give a clear goal of what to work to.

In my personal opinion, I don’t think that this video’s topic is particularly memorable, as it’s just a problem statement. We don’t solve it as it’s a conjecture, so we’re just left with understanding a statement that may or may not be true.

Still, however, this video was a nice watch.

Great video that manages to introduce a lot of difficult concepts with easy-to-follow explanations with visual animations that help a lot. The rythm is good and the voice/facecam help give the feeling of being guided through it all seamlessly.

Novelty and memorability are the points that could be improved

Nice review of a advandce tropic.

Great video. I am now ready to solve the hodge conjecture. Once I claim the prize I’ll give 10% to the channel

Very ambitious topic. Unfortunately the abstract nature of it wins over and the topic becomes hard to follow. Could do with more narrative flourishes to keep interest. For example leading the viewer to think that a circular loop can be algebraic and then introducing a contradiction like a plot twist. Otherwise the presentation is good, just feels like reading a textbook. Not really taking full advantage of the video format.

I’ve been a subscriber to your channel for a while. This is one of your best videos. Generally speaking, I think your more math-y videos of late are well above your earlier videos. One little gripe: you take off and then continuously play with your bracelet minute 17 onwards. I kept on thinking this would payoff at the end of the video in terms of topology, but it didn’t ^^.

Sometimes the visuals are a little too dark and not very visible.

Some small things could be improved: - While I really enjoy the mix of talking-head sections and animations/illustrations, the cuts are a bit too frequent. In particular, there are a few instances where you are on screen for like half a second which is a bit weird. - The way mathematical expressions and text are rendered (in LATeX or not) could be more consistent. - Some minor pedagocical stumbling blocks. Like, when you introduce complex numbers, you say that they have real and imaginary parts, but you do not say or show what that is. The calculus part felt rushed. But overal, a wonderful video. And by a large margin a much better explanation than most I have seen in alg geo I have seen in alg geo.

Good introduction: avoids stating problem directly, gives historical background. Actual problem stated very simply. Good production value of set & audio properties. Singularity exception discussed and executed well. Liked explanation of Stoke’s Thm and topological holes. Encoding Rotation was an easy explanation of a difficult concept.

Even though I didn’t catch everything—at least not on the first viewing—I find it very educational. Definitely something to recommend to students.

One minor criticism concerns the overly uniform pace; some difficult moments would benefit from a more cautious approach.

Love the video. I really appreciate the historical background.

What a beautiful video. Hodge conjecture built this well in 30 mins, I am baffled. Historical significance, narrator showing themselves and speaking, animations where necessary, and most importantly, everything connecting so beautifully in the video as it gradually moves ahead. 30 minutes felt like nothing here. This video checks out all the points, novelty (for explaining such a complex conjecture so beautifully), memorability (even I can explain this to someone else now in the future), clarity (goals were clear, and repeated at intervals so we are not forgetting it), and motivation (clear at the beginning and in betwen the video timely).

Really excellent production level video regarding all aspects. I loved the video and would recommend everyone in my circle to watch this atleast once.

Professionally made video. It starts well and storytelling part helps at the beginning. But, as the topic progresses, video becomes more like a presentation in a mathematical conference, becoming hard to follow if you do not have the jargon used in the mentioned topics. So the claim of explaining the conjecture with storytelling is only valid at the beginning, maybe up to the half of the video. I could not follow the second half well, so I may not be evaluating that part fairly. My suggestion is to have more animation that directly speaking to the camera, and lowering the pace for important parts with more examples/animations or whatever.

Overall, a good entry, well done!

Very brave and very impressive. Excellent (veritasium style) exposition. Clearly the gole is too ambitious, so you “failed” no one without significant back-ground will understand the hodge conjecture. However this is  a very successful failure. Almost anyone can learn something from your vidio. I am a professional mathematician and I enjoyed it. I am sure that undergrads will enjoy it too. Some comments:

1. when you say something false (and you have to) worn the viewer explicitly. this includes the “definition” of homology, and some other things that I do not remember now
2. the  Q-coffitions are not needed in your resolution, you did not spesify the coefficient field of the homology ring, so it could have been Q
3. make vidios that extanding weach of the many topics you overviwed and sugest them to the viwer. alternativlly you vcan use existing ones. GOOD LUCK!!!

I like the video, thank you.

The setup / background / talking head shots are great.

An ambitious subject matter!

Math undergrad (rusty though) here, so lots of new / rusty concepts to me.

Moving to topology and then calculus was quite speedy and I would have benefited from a bit of prep. Alternatively could there have been more visualisations to help understanding in these sections, as they were more talking head heavy.

Great introduction to the Hodge Conjecture! I haven’t seen its proper statement before, so it’s nice to get an idea of what it’s about.

I will note is that at 15:07, for example, and a few other points in the video, the torus is essentially invisible, so it’s hard to tell what the animation is showing.

I also got a bit confused with what you meant by rigidity and being “cut out by equations”, so maybe you could’ve spent a bit more time on that?

Anyway, thank you for this!

The video could have been helped a lot by more animations and less literal hand-waving. It could have also been helped by a list of the concepts that would be presented throughout the video in a summary at the beginning, and then taking a pause to go back to that list occasionally to understand how far down the conceptual road we have gone before continuing on. Most importantly, the thumbnail should be more straightforward. The thumbnail includes an equation and object that are not addressed at all in the video. In a really good SOME video, the complicated equation needing explanation is usually broken down piece by piece, with each piece opening a door to the various verbal explanations which this video does contain, but with a more thorough visual than just a flash of “dz” or repetition of the same spherical loop animation. I was left with a lot of questions by the end like “What is a harmonic form vs a differential form?” “What does it mean for a form to be “concrete” in a way that allows operations?” “What does it look like for a rotation to change or not change a form?” “Is there any visualization of P,P?” Maybe this would land better for a math grad student which I am not. I do very much appreciate the historical context, the music, and the willingness to be in front of the camera so much. So with more animations and more careful breakdown of the concepts I would have appreciated the video more.

I really enjoyed this video. It’s so cool that there is now a good explanation of the Hodge conjecture on the internet.

I do think I started to get a little lost toward the end. It felt like things sped up a bit, and I think the visuals earlier in the video helped to make things easier to follow. It might just be that there is no way to make good visuals for the rest of the video, and I definitely feel like I gained a lot of understanding overall.

you had me until like 3/4 in, and then I couldn’t really follow. I think if there were more visuals things would be more clear.

I do feel like I learned a lot and understand the conjecture more, just not fully

Hi Voyager ! This explanation is a very good one! … The speaker has a very clear and beautiful voice explaining such complicated topic… Certainly is a good try but in my opinion the subject deserve more time to digest the explanations of the different parts of the math branches involved, if the intended audience is not familiar with such elaborated concepts expressed… Maybe with more graphics and some good chosen samples it could be more accesible to the general public as it was the declared intention said at the beginning of the video. Even though, my limited comprehension of the math areas that converge to the Hodge conjeture now is better than before !

Thanks!

Nice try to tell what abstract math mean using analogy. Much work has gone into this. When mathematicians reason with math they don’t think in the rigorous math formalisms but rather in analogies like the river and the stone.

Suggestions for improvements:

Concentrate more on the math and less on the person. I think your piece would improve if you took away the person completely or just a few sentences in the beginning. A person should add not distract. But that is my own opinion so take it for what it is. Others might think otherwise.