Summer of Math Exposition

Nice video on recursion and generator functions

Great video and speaking voice. I enjoyed the topic as well as the pacing and flow of the information presented. I learned new things, and I liked the level at which it was explained. Keep up the great work!

Loved all the math facts in there (in fact I’ve made videos about a lot of these over the years!). However, I felt the video overall was hard to follow because it switch topics many times. I also feel it didn’t in enough depth to fully explain parts to an audience who hadn’t seen it before (for example, I hadn’t seen the Lucas numbers primality thing before and felt like I wanted more on that one!) Basically, doing a more streamlined in depth video on any one of those topics could be a great math video, but all of them together is not as strong.

I liked the style of “here’s just a collection of interesting related math that’s fun”, I hope that’s what you were going for. Your care for the subject came through and is encouraging for wonder in the subject. Maybe tighten up a few spots, but that’s probably hard to do with the unedited format.

Number of “ums” is unfortunate, but goes with the style.

Mathematically, I think you could touch more on why the ratio thing works to give you the r equation for both phi and psi. Phi is kind of believable, but why does psi come out too?

This video had lots of interesting content. It discussed many aspects of the Fibonacci numbers and sequences related to it. I was personally not aware of the primality test based on Lucas numbers. The video would have had a bigger impact if you improved the narration. Perhaps you could have divided the video into smaller sections and done a few takes of each to get a smoother narration.

There are a lot of interesting features of the Fibonacci sequence in here, and you explain each of them well.

The progression doesn’t feel like it flows naturally. You’re jumping from one cool fact to the next, without a natural progression of why one leads into the next or a signpost for where the video’s going. Having a clear story you want to tell would tighten the video a lot.

Also, you say “um” a lot, to the point where it’s distracting. I know how hard it is to cut out the filler words, but it would help.

The content of the explanation is very good, but the shape of the explanation wasn’t as good. For example, the narration didn’t sound like you enjoyed the topic or found it interesting, and at times the explanation felt disconnected

My advice would be to have a script, practice it, and change it with two goals in mind: making the explanation more engaging, and making it easier to follow

Fun stuff to play with. Would work better as a livestream than it does as a video but still fun.

Fibonacci is overdone, maybe a more surprising subject would engage people more. Also, the presentation could be improved.

Motivation: 4 / 9 – It’s a nice entry point to the topic of Fibonacci numbers – quite popular, but still not the one people usually use. But, for me, this video was hella chaotic, and I couldn’t really see where you were going with it. Didn’t know what to expect in the end, if there was something to be worth watching the whole thing for

Clarity: 6 / 9 – the best point of the video are your explanations, which are decent and clear. The problem is that this casual, “talk” style of this video pulled me out of being interested and focused a lot. I’m not saying that that it could not be done like that, I just think you can work on that – trying not to “hmm”, or pause. Maybe some more editing would fix the issue (?)

Novelty: 1 / 9 – Topic of Fibonacci numbers has been covered A LOT already and from a new video about such popular topic I expect showing some fresh point of view or new results. I didn’t receive those in your vid.

Memorability: 3 / 9 – I just don’t think that this style of presentation works for me, sorry.

Overall: 3.5 / 9 – Generally there’s a lot of room to grow here and this video shows that you have the ideas and knowledge to create great videos. Keep growing and good luck!

• Really interesting video and went in the unconventional direction of looking at different series coming from different seeds. Could do with better visuals, but other than that is pretty engaging with plenty of real-world applications.

I would say the audio could be improved with audacity or something like that. Please cut out the umming and other blank space! For the Binet formula you didn’t justify the assumption that it could be written in the form A phi^n + B psi^n, which is quite an assumption tbf. For the Lucas formula you just wrote “phi_n + phi_n” twice hehe. For the generating function you didn’t explain why we should care about it, and also you can’t just factor x^k out of the whole sum since k is only defined within the sum. Further, for the ratio proof you said “we’ll come back to it”, then you didn’t come back to it!! The proof only works if you assume that the terms converge to a common ratio in the first place, which is quite an assumption.

Other than that very interesting video !! Very cool!

All of these fact have been covered many times on YouTube but the nice arrangement of them and the layout/flow of how the facts ended up relating to each other was well done. I will note that editing can be your best friend. Removing extra ums and awkard pauses while you’re collecting thoughts or figuring out where to go next would have greatly helped with the flow. That or addtional practice could add that extra polish to really make this video stand out. It didn’t try to re-invent the wheel but did put it in a nicer package - ok maybe not the best metaphor. Importantly though, when the content being presented is relatively “simple” that presentation has to be perfect because there is nowhere to hide.

This is a somewhat unfocused but enthusiastic look around the neighborhood of the Fibonacci sequence. It has a distinct artistic and expository style that works well for such an exploration. If I have one stylistic recommendation, it’s that this choice to “graze” and survey the area rather than taking an orderly look at specific topics is definitely already turning people away— so forget about those people! They’re not who you’re here for! Lean even further into this. If you don’t already know the mathtuber Combo Class, take a peek. You’re probably not aiming for his level of theatrics, but I think you might find some inspiration.

Back to the video, the weakest part by far is the introduction section re: your running habits. Adding 3 [min] to 5 [min/km] to get 8 [min/mi] is fully gross, and 5+8 isn’t much better. Even if you intended it purely as ragebait for engagement purposes, I think it toes the line of irresponsibility, because it’s such a well-documented problem with math classroom instruction that in word problems students are rewarded for smashing numbers together without thinking about “what they mean”, i.e. disregarding units.

(Now I’ll be honest, I never realized that the mi/km conversion constant is so close to phi— that’s really cute. And this is a case where the units are strange but the result does have real meaning. But if this is the intended payoff for “if you consider this to be just a coincidence, hear this out,” then… yes that’s honestly such a good example of a fact about numbers that is just a coincidence, that it’s probably now my go-to example.)

I have no other serious criticisms, but here are a few minor complaints:

• You mention Taylor series but don’t actually use them in the video, just power series.
• I’ve only ever seen “Miller–Robin” written Miller–Rabin. (I know Hebrew vowels don’t always transliterate well, so take it for what it’s worth.)

A complaint I wish to lodge more forcefully is that I definitely think you should have spent a minute or two justifying why those combinatorial models actually count Fibonacci numbers! I think your audience would be okay glossing over it like you did, so I don’t count it as a flaw of the video. But the lesson of “if the model satisfies the recurrence and initial conditions then it’s the same” is both far-reaching and reasonably intuitive. You do a lot in this video so I wouldn’t recommend any big additions, but this seems like it would have been a small time increase for relatively large payoff.

These particular mathematical topics are in a very crowded expository space— many people have done work here, and to be blunt I’m not quite sure what gap this video is filling, which people aren’t being served by the huge array of other offerings. I decided not to weigh that against you because it turns out the answer is “me”, I guess— your use of Lucas numbers to motivate Binet’s formula raises to me an interesting space/time tradeoff question. I don’t think that was your intention, but one of the advantages to a style like yours is that it allows you to drop hints like this left and right (c.f. “almost all” seeds, the binomial triangle, etc.), and this one was just the one that happened to work for me.