Hearted Youtube comments on A Well-Rested Dog (@AWellRestedDog) channel.

I really like how you paired the music with the time periods, starting with ancient and moving through the baroque, classical, and romantic periods. That's a very nice touch
10000
This video reminded me greatly of my algebra 2 teacher in high school who was notoriously behind on the pace that the curriculum demanded, but for the sake of having students scratch their heads at the ideas with each other. The kinds of ideas behind math feel like such an incredible system that’s been arranged to work with itself in so many different ways, but often the class is framed in pure stress and only in how to do the executional requirements of math. Her class really illuminated the things about math that I enjoy, but it is very difficult to keep this enthusiasm up taking in more math classes with professors who just see it as I’m giving you the tools to pass the test. This video really brings to light how much there is to improve with schools teach subjects in a way that can be more informative and natural to understand.
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I'm a private Maths tutor. I've always wanted my students to understand WHERE and how the concepts we study together came to be, but, sadly, it's extremely inefficient, especially at a college level... They DO engage, though, so I usually give them extra hours for free even though it REALLY hurts my wallet, so I stopped doing that for the time being. Reading through the comments, and seeing how grateful people are for this video makes me genuinely happy! Beyond measure! Enough to make my eyes tear a little!! I have saved this video, and who knows? Perhaps a future student of mine will voluntarily ask me those questions, in which case, I have the perfect video to refer them to! My appreciation can not be expressed in words! Thank you so much for putting this together, and for showing me that students all over the world really do want to know the history behind Mathematics!!!! <33333
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1:52 Where it began? 2:39 Geometry 3:30 Zeno’s Paradox 4:03 Rectangle smaller than Circle. Or not? 7:43 800s Arabic Numerals 9:00 Coordinate Geometry 10:28 Sin(X) Cos (X) 12:06 Derivative, Integral 12:50 Galileo & Kepler 14:57 Newton 16:08 Leibnitz 17:05 d - differential, infinitesimal Fluxions 18:29 Diplomat Leibnitz brought ideas to more smart people 19:32 They contributed huge 20:05 Infinite Series 21:17 Limits 21:56 Function (X, F(X)) 23:20 Over and over again 23:43 Infinity Itself ♾ 24:17 Reflections • Built around a story 25:38 Jousting with Infinity 26:24 I want to understand important math 27:53 • Professor tries to explain what’s going on • Once he starts doing examples, I start paying attention Infinitesimals - philosophers wrestled with it Expect students to stumble 29:27 Calculus Reform Movement 1990s
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Great editing and presentation! I recommend any math-heavy majors to take a history of math course during undergrad— it’s essentially this video but you dive into the proofs and deeper biographies of each contributor.
583
Well, I feel utterly pathetic about how I spent my summers in high school now. Jokes aside, this is an awesome and clearly explained summary of the history of calculus - I learned a lot watching it. I would love to hear more about various ancient theories of math and physics, as I find the way they justify them to be fascinating.
45
I've always wanted a good video on the history of Calculus, since I always like knowing the history of Maths; this video was really great, thoughtful and original, thank you
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This is such a professional video! I loved how you gave every person and event you described a really tangible visualisation and I could follow your video perfectly. Animation, explanation and clarity (as well as title) are without a doubt amazing. But I want to emphasise something else I especially liked, which is the narrative. According to your channel info, you enjoy literature, which is quite noticeable given the excellent “dramaturgy“ of your submission. I very much like this approach because it’s making your video very memorable; along with the visuals and the outstanding interview at the end (which wraps it up very good), I‘m not even surprised that your video has blown up so much. Long story short: What an excellent video, I hope and suspect you‘ll win.
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Still waiting for part 2 and 3. You've done an amazing job, keep going even if the viewcount does not reflect the quality of your work. I've waited 9 months and I will wait even 9 years, because this is one of the most life changing videos I've seen on YT. I show this to people who need it and it changes them, it's a tool for people like me who try to help others. It's very different when I say something to them or when I show that someone else (you) says the same thing. Existential crises are fundamental to our own development, yet people tend to prefer to live in blindness than to face new information. Thanks so much❤
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PLEASE MAKE MORE VIDEOS 🙏🏻 this was incredibly well done, your voice is pleasant to listen to, you were deeply thorough yet entertaining, and even with only grasping half of what was said I was able to watch all the way through and appreciate it. I am an adult maths learner - after fifteen years in history I’ve switched to coding and computer science. In this effort to better myself, I’ve returned to maths to better understand comp-sci and have gotten to college algebra with mental blood, sweat, and tears, but I want to keep moving forward and get to calculus! I may have only grasped bits of the content, but your video has helped me understand where I’m going and what to strive for, plus a deeper appreciation of the human historical struggle to understand and advance this knowledge. Thank you and I hope you make more math related videos (maybe algebra??? I can hope 😅). Loved the quotes, but did you know text in sans-serif fonts are easier for dyslexics and neurodivergent people to read? Not always as aesthetically pleasing, but I know a lot of dyslexics pursue maths and if you use a lot of quotes or written content in future, I just wanted to offer that bit of knowledge if it can help. Either way, well done! May your channel grow and be very successful! 🎉👏🏻✨⭐️👏🏻🎉
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Amazing video. A great way to connect the mathematics and logic of a famously hard suybject to the history and life of its' creators. This reminds me of when a friend of mine, pressed for time and credits to complete his degree, chose a notoriously easy class of "History of information engineering", knowing that just being present and submitting a small 4 pages essay he would get full marks. He instead fell in love with the subject, read both the syllabus books and got very excited at the experience of learning how physicists, mathematicians and engineers developed and struggled with the concepts that we covered in other courses, on how Einstein was absolutely a mathematical genius, but also a very sloppy one, how long these ideas we are expected to cram in our minds in weeks required decades to develop, and some of the most brilliant people at the time just didn't get it. Its speaks volumes about the difficulty of translating these immense subjects and ideas into 4 months courses, how far we've come where integrals and infinitesimal are basically normal knowledge for the average 18 y.o., and how limited our teaching methods still are. I think similar issues of focusing on "teaching things" while forgetting to give context, time and freedom to students to engage, digest and personally process the concepts arise in almost any field of education, from history to biology to chemistry to art to literature. Germ Theory required decades to not sound completely insane, a good part of modern and contemporary art was ousted for almost a century for being "wrong". But i'm glad someone is trying their best to share a different view, and to work to share these ideas with the weight they deserve
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The ammount of huge discoveris just casually named per minute astonishes me hahshs. I did not expect that about the Aryabhata in the 10:29. Like, how did he do it? What were the sin and cos functions known as back then? and how did he do it
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But what about people who don't fear death? Like certain people who commit suicide or people who live really dangerously willingly and with full awareness of the possibility of death at any moment. I don't think that the realisation of death is scary to everyone. I'd be content with dying 10 minutes from now and wouldn't find that much worse than living forever. Being immortal would only be better because there are no deadlines, so there would be more long terms goals i can persue and I could live more chill. However dying a week from now would be much worse than dying 10 minutes from now because within that week I couldn't get any joy from working on long term goals since I would know that I could never finish those
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This reminds me of bill wurtz (which is a very good thing)
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I definitely agree it'd make much more sense to teach calculus with this historical context; I think Lockhart mentioned this a bit in his essay "A Mathematician's Lament" but this spells it out in such an engaging way. Great video!
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Very interesting video. But let me point out, all the calculus that you mentioned in the video is definitely taught in calculus classes. It's the history part that's generally glossed over—and that's lucky for students. I agree with some of the things that Prof. David Bressoud said, but not all. Let me highlight the most important thing that he said: "Students are pressed for time." As an engineer who's been through engineering college, I agree wholeheartedly with that. Anything that's taught in class takes time away from a whole bunch of other things that could've been taught in its place. Now I don't speak for all engineers. But let me tell you, my motivation for learning any subject in college was not its history. Knowing how that subject will help me in my major—and subsequently, in my professional life—was motivation enough. Can I build a better car if I know that—historically—integration came before differentiation? If I were to see a question on my calculus exam on the differences between Newton's and Leibniz's approach to differential calculus, I'd scream. Consequently, if it's not going to be in the exam, it need not be taught in class either. Remember the time thing. Prof. Bressoud is also correct that as an engineer, I'm not particularly interested in rigorously proving mathematical results. Math is a tool—one of several that I use. It's nice to know that it's built on solid axiomatic foundations and rigorous logic. But not necessary to keep proving it over and over. In the same way, you don't need to understand thermodynamics or electromagnetism to drive a car. Clearly, it's different for math majors—they do need to prove results rigorously. Many of the math courses we engineers study are taught in math departments by math professors. So I understand why they follow the axiom-proposition-proof approach. It's not ideal, but I can live with it. Incidentally, some of the specialized math courses I took were taught by engineering professors. You could tell from the subject names: "Advanced Engineering Mathematics," "Probability and Statistics for Engineers" and such. Guess what—these subjects did start with the motivating problem statement first, then showed how to use mathematical tools to solve them. Emphasis on problem solving. Rigorous proof was deemphasized, though often given as a homework assignment. Let me conclude by repeating that you don't need the history of those subjects to keep you motivated. If anything, it adds to the cognitive overload and/or confuses you.
5
Loved this video! I might have been one of the few who didn’t have an existential crisis in the beginning unfortunately since I went to the beach today with my dog and something so simple still left me feeling utterly content as the clock was ticking by, so even with the prospect of dying, by the last second I closed my eyes and smiled. (That’s not alarming right? A part of me wish I had that exhilaration for living that you aimed to evoke within us but I think I actually just had that this morning since that’s what forced me to get out of the house on a Saturday and appreciate life anyways) Okay but there are some parts of the Adam and Eve story that can be argued contrary to what you said. The serpent told Eve that she would “surely not die” if she ate the apple, for “God doth know that in the day ye eat thereof, then your eyes shall be opened, and ye shall be as God, knowing good and evil.” I don’t think Eve ate that apple accepting the prospect of death, rather, she didn’t want to be inferior to god and his knowledge, and thus by gaining his knowledge she might as well be immortal since she is as god herself, the highest part of their hierarchy (the ultimate goal right?) Also, I don’t think Adam and Eve gained the capability of love after eating the apple, if anything they were more open and connected with each other before, when they were not tainted by the fear of practicing evil and the wrongdoing of immodesty. Let me know if you want to hear more, I’d love to discuss this stuff. I found your channel through the math video and I absolutely love the stuff you put out, keep up the great work!
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i don't fear death anymore, but i assume that instinctually I'll preserve my life if i have the choice bc i haven't killed myself despite spending most of my life wanting to have an Off button... (I've been homeless, institutionalized, overmedicated at a young age, abused, and I'm formally trained in Zen meditation, lost my speaking voice to multiple surgeries and had to relearn how to speak.) However, I'm afraid of how I'll be treated while I'm senile, bc I'm very autistic and even with my lifelong medical history and diagnosis, people don't know how to treat old ppl unless you give them more money than I'm capable of generating in my lifetime, let alone senile autistic ppl. I'm not afraid of decay, so much as how people react to it.
4
first calculus lecture i paid attention to
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IMO With all due respect, I think that the intention behind Abraham’s story was not about death, rather it was about his faithfulness to God… Abraham still followed God’s orders even if that meant sacrificing his son that he’d been longing for a very long time. He wasn’t trying to spark up life because he was aware of death, it was just his faithfulness to God since God was the one who gave him his son, Isaac. Interesting perspective though! keep going man :)
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WONDERFUL video!! 😮 subscribed! suggestions: . text appears and disappears too quickly. . you show the dates where calculus begins for maybe a fraction of a second, and they're very small. keep them there! . the volume of revolution formula shows up also for a fraction of a second. . there are many examples like this. . you use a lot of pronouns and when you make text disappear so quickly, this makes it hard to follow your video . you refer to the people who spread arabic numerals to europe as "these guys" or similar. just say their names. . you show the arabs avoid quartics and negatives and powers of n by just quickly zooming in. say "fourth powers and negatives and arbitrary powers". . again, there are many examples. in general, most visuals should have a descriptive audio component. why do we need revolutions about an axis? "look at this arabic architecture full of domes and minarets! they all use this principle."
3
I hate how limits are used for calculus, so I wish you would have gone deeper into the infinitesimals vs no infinitesimals debate more. I know it unfortunately has the ability to cause a comment section to devolve into violent anarchy, but I think it is worth exploring since it would discuss pretty interesting math and I liked the way you went over the history up until now.
3
Excellent video. Very well scripted. Is it only me who still doesn´t understand how peoplethroughout the centuries and all over the world could have equated being remembered with being immortal? I mean, why would you care about being remembered if you´re not gonna be there to hear people tell our story? I understand the desire to leave something useful and/or beautiful for the following generations. That would be basic altruísm. But being remembered? Have people just been decieving themselves into believing that peoples memories have anything to do with them? I just don´t get it...
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Yeah, thank you so much for replying! I’d love to continue this discussion (and I really love disagreeing) but I think it’ll be better over email. Btw I started checking out your footnotes and I just wanna say that calling them Pawnotes moving forward is the only way to go
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At 14:35, I don't think I'm understanding what you're saying. The velocity around an ellipse is not constant for a planet. Aren't the planets moving at their slowest speed when at their farthest, and fastest when at their closest?
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I was an Engineering Physics major, and my favorite professor always took time at the end of lectures or concepts to stop and recount the history and who was the one that discovered or first formulated the concept we just learned. It was fun having him for Analytical Mechanics, or Electromagnetics I and II, and finally more modern classes like QM or QC because the history portions of the lessons became more and more modern. Dudes with powdered wigs turned into Victorian Era Englishmen, and then turn of the century guys solving the atom and solid state materials and finally we're talking about stuff people discovered in the 1990s and 2000s. Contextualizing the physics concepts I was learning really grounded what I was doing to me, and it helped me move my brain from 'just learning a bunch of equations to apply' to thinking about the problem that needed to be solved and knowing which tools to use and why they worked. Finally being able to 'visualize' some of the 3+ dimensional math that Jr, Sr, and Grad level courses require (like divergence, curl, and tensors), is something I think a lot of physics majors can relate to. Starting from the history of the problem being solved, like "well we know a current causes a magnetic field to 'twist' around it, how do we quantify that?" is far more useful than jumping straight to "well you take the curl here and you get the magnetic field!"
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This video doesnt work for me because I have more insight into the theory of this topic then you, and while Id be difficult to directly point them out because of the complexity of the topic making any remarks undermines the topic itself as the dragging statements become flawed I will give the video a chance but from the intro what i will say is that thats the most how should i put this generic or dragged out existential idea and its quiet isolated and dug in a hole and keep digging deeper ifygm
2
This actually made me read David's books, first pages in, it is awesome!
2
i was questioning litrally everything that was being said in this video. but then half way through i remembered this video is from a secular point of view which means it removes god from the whole picture, though there were mentions of god in literal sense , god was still out of picture here, and now the video and the ideas in it are making sense to me. now that i've watched the whole video and realised i clicked on this video because it was about existential crisis (which i later forgot during the video because i was so busy being triggered until i wasnt). and it concluded in us pursuing faith and wisdom during crisis (which if i relate to the story of prophet ibrahim are basically tests given by god to trust our faith in him) it made sense A LOT OF IT INFACT. thats not the thought process i was taught and it was really hard for me to continue watching without being triggered or thinking how it related back to my ideologies, and all i can say is i agree with the conclusion but from a different perspective.
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Beautiful video, cute dog!
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I asked this a while ago and am hoping you or someone sees this and steers me in the right direction, because Im really having a hard time understanding why we use infinity. The part around 4:57 seems pretty convincing for infinity. Except I have one problem: why do we assume that we can keep cutting the pieces smaller and smaller? Doesnt this already assume infinity? Or what if the crossover point (where the curvy difference is less than the circle - the rectangle) is when the curvy area is = 10^(-googleplex) units, which doesnt exist in reality? Doesnt that mean it doesnt happen in reality?
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I should be studying for my cal2 final, but WOW THIS IS SUCH A WELL MADE VIDEO OH MY GOD DUDE!!!!! You've come so far from making Minecraft videos on your phone, and all of your content is genuinely so well made. Dude like actually, congratulations on winning a section of the contest, you truly truly deserve it! Can't wait to see what's next from you ^^ (also sry I'm late)
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Having children is not the same as being immoral. You die. Your child is not you, nor any of their children, and etc etc. I don’t see how you accept that as true. It can make you feel better that something of what you do on earth has a effect that lasts”forever,” in that it was not all for nothing(not that it is, I’m just arguing this point). It isn’t the same as you personally staying alive and experiencing things.
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Idk about this one my friend. It relies on many assumptions one being that the abrahamic stories even made sense. He made Adam with no wife and no understanding of good and evil. He then says dont eat of the apple that tells you what im even saying. I just dont see it as a usable story on the human condition. However you can see it as the dichotomy between child and parent. The parent with knowledge, power, and authority is a god to a child who knows nothing of the world. Who has to be told their own name. Would it be right to demand that child understand something you know they physically cant comprehend. Achilles i believe is a grwat example of mans condition. His body is strong, his glory known throughout the land, unmatched on the battlefield. But literally none it matters on any scale that is the world. What he does, doesnt matter to anyone other than him and the ones he effects and that is life.
1
This is gotta be the most meaningless video i have watched on YouTube. Your interpretations make me feel so sad on how basic human understanding is to want something to represent something we think is important or true. Better spend my time watching a TikTok meme video than your pile of nothingness interpretations. Death gives value to living, and if you're living then you will die eventually, then living has value. If you recognize the value of living then you would live, if not you would die. It's that simple. Bro there was a moment that you said you kinda liked when you were dying. Live your life and draw motivation from other things than death and meaningless and badly interpreted immortality.
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I'm a pure math graduate and in university I ALWAYS spent a few days reading the history of each topic. I highly recommend anyone trying to understand math do the same. So overall great video and I'm glad you make this point. I also like that you bring up integrals being first historically. I actually also think that they should come first logically. There are two points that I don't agree with in this video however: 1) Your characterisation of limits is as some sort of invitation to "if you wanted to, ask that question over and over until you are satisfied" is IMO not a good way to think about it. Mathematics is not temporal. Things either exist or they don't, things are either unique or they are not. The fact that you could in theory follow a "process" over time of successively choosing smaller values is completely irrelevant to the mathematics and in my opinion only confuses the matter. The mathematics provides you convincing proof that should be satisfying if you understand it without you having to ask any questions. There is a delta for every epsilon. That's all you need to know to prove formally by contradiction that the integral gives you the area (using the measure theory definition of area). While historically this solves problems around how people were thinking about infinity, logically it is no more illuminating of the nature of infinity than any statement involving "every" number. Eg, the statement "for every number n, there is a number which is n+1" requires no more or less understanding of infinity to be comprehended than a limit does. I could make the statement that, if I wanted to, I could keep choosing bigger and bigger n and you'd keep giving me n+1 until I'm satisfied. But that would be silly. The statement already says it's true for every n; picking a bunch of n's to test, or even just mentioning that you could hypothetically pick a bunch of n's to test if you wanted to, does not contribute anything that wasn't already clear from the statement. 2) Unless I missed it, you should really have mentioned Eudoxus of Cnidus. It's my view that he should be given the most credit for the development of calculus. His work is often incorrectly credited to Archimedes (the Elements was, to a large extent, an aggregation of previous work by many people). He certainly understood limits better than Newton did. Though I will say I am glad that you at least did not blindly give credit only to Newton and Leibniz the way everyone else does.
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Comming in terms with death is something that everyone just accepts and as you said that sharing your wisdom allows you to become immortal (which I agree with) but should we really think that death is necessary? Can we not try everything in our power to peruse immortality? (not through religious beliefs but through science)
1