Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. I have almost no grasp of basic algebra. I watch these videos in complete aww of the innate problem solving potential of human beings. I feel like learning math is akin to finally being able to leave Plato’s allegory cave, in that math seems like a key to understanding the entire world around us.
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  2. I am not a studied mathematician by anyone's measure. Yet, I carry away so much from your videos! Thank you so much for your well-constructed presentations. This one was wonderfully startling!
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  3. Calculus is so beautiful and elegant theory....and also it is really easy if learned from the correct teacher or book
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  4. It was me, I discovered this proof back in grade school when making arts & crafts. I wrote a note in my journal of discovering the proof, but I had to also go back and watch Power Rangers.
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  5. As many people have already pointed out in the comments, a compromise between the Talmudic method and the proportional method would involve some kind of hourglass shaped containers. This would smooth out the payout curves, but I can't think of any other practical benefit. Just something fun to think about.
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  6. Legendre looks angry!
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  7. "I'd like to finish off the video" he says roughly half way through the video...
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  8. I use the subtitles on YouTube to compensate for my hearing loss and I kindly suggest that you watch this video with the subtitles to see the issue of having crucial information/animation in the lower parts of the video. I hope that this is seen as the constructive feedback that it's intended as.
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  9. Hydroxide, hydroxide, hydroxide!
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  10. I love the second "simpler" proof. It is intuitive and I can even explain it to members of the family who are not true maths lovers.
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  11. The most memorable part was me dying because I didn't know the no 9's series was convergent
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  12. We were taught Heron's formula in Bulgaria. And half the perimeter is denoted as p, not S. That's the area.
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  13. I fear most schools prefer not to promote "visual proofs" since it could have pupils do them when the visual is "close enough" yet still false. Meanwhile, the algebraic ones have "rigid" rules, that can be more easily explained and corrected.
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  14. A Strand Is A Part Of A Rope Or Bond, While Stranded Means Being Washed Up On The Shore, And Being Stranded Is When You Can't Go Home.
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  15. Now that I have watched this video it's been up for 50 minutes and 94 likes so at least two people liked it in the same minute. This is not interesting up to here, but this number will initially increase for a bit and then decrease later. And the peak is dependent on the number of notification bells and subscribers. So with this simple thing we can find out about the number of notification bells set on any channel. (Disclaimer, I don't know if you can actually see this number anywhere on YouTube or not)
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  16. Mouse flavoured cat food. How have they not thought of this?
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  17. Absolutely amazing. I did not want the video to end!
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  18. Best part of this was realizing how I can use the logic to solve 3 of my yet unsolved ProjectEuler problems! Awesome video!
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  19. I kept hearing "a 4k+1 prime" and wondered how or if the primality mattered. It's amazing how late, and how crucially, it finally comes into play.
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  20. I love this video. When you mentioned the problem, I first thought that it sounded familiar, then realised that I've heard of it before, including the fact that it is not possible to move 5 steps past the line. However, I have never seen a proof of it before, and I thoroughly enjoyed the proof.
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  21. Thanks a lot, Mathaloger! I have studied some works of Madhava but didn't know about these beautiful correction terms. Our textbooks in India still reflect a post-colonial mindset, resulting in a significant lack of awareness and ignorance. Unfortunately, many important contributions from Indian scholars are overlooked or not adequately highlighted. For instance, Baudhayana, who authored the world's first geometry textbook, including the Pythagorean theorem long before Pythagoras, is rarely mentioned. Similarly, Pingala's profound insights into permutations and combinations within the context of literature are often disregarded, despite their beauty and significance. Aryabhata's foundational work in trigonometry, which forms the basis of our modern understanding, also receives insufficient attention. Furthermore, there's no mention of Madhava, or any mathematician from the Nila school, in our great textbooks. They only perpetuate a subtle sense of inferiority complex by failing to acknowledge these remarkable achievements. It is high time for a change in our educational curriculum. One aspect I particularly admire is India's significant contributions to philosophy and spirituality. These traditions are not only highly logical but also explore the limitations of logic itself, as evident in the concept of non-dualism. Additionally, architectural marvels like the Kailash temple exemplify India's profound knowledge in the field of architecture. Regrettably, we have lost a great deal of knowledge due to constant invasions, including the destruction of the precious Nalanda University, the world's first residential university. There is so much more to be said about India's marvelous contributions to the world. It is my hope that our generation recognizes and appreciates the immense legacy left by our ancestors. Thank you so much again. Keep up the amazing work that you do!!
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  22. If we really want to go back to the beginning of calculus, there's strong evidence that Archimedes had something very very close to it (including rigorous definitions of limits), if not bona fide integral calculus itself. Which is some 1600 years before Madhava. Of course, I would only be half survived if some even older Indian, Chinese, Babylonian, etc... mathematician had invented something equivalent to calculus even before that. Scholars typically remember the start of still-living lineages, rather than the original discoveries that faded for centuries before being rediscovered.
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  23. And the neat thing is that you can generalize the discrete approach to several dimensions, and talk about heat equation on grids... But why stop there? Isn't a grid like a special case of a graph? Like the plane, that is a very particular case of a manifold? With some reasonable hypothesis, many theorems have a parallel discrete contrepart!
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  24. Heard of this before, it’s just mod 9 arithmetic with a coat of mysticism thrown over it.
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  25. nice :)
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  26. The animation in this video is just insane - about the best I've ever seen on Youtube in fact. I can't imagine all the time it must have required to get all that to flow so smoothly. Well done. I especially liked the part about the bugs, shows you how to solve such a problem in visual steps - a great problem solving technique. And the animation was just beautiful.
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  27. I'm not a fan of the transition slides with the slightly twitching eyes, they're unsettling to look at and in general the use of AI makes me uncomfortable.
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  28. The last time Mathologer posted a video the night before my exam, I got selected even though I didn't prepare much. I'm hoping that the trend continues. :D Seriously though, the timing couldn't have been any luckier.
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  29. If I could only have had 30 seconds in Ramanujan's brain
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  30. Second proof is more simple and easy to spot, first proof is a little more complicated but elegant, in my opinion
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  31. My daughter (ninth grade) just sent me this video with the message, “this is so interesting!” Thank you for the proud dad moment, Mathologer!
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  32. Also, the point of leaving the last card only down, if you consider either that one card only is flip, or that no move is possible it is terminated.
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  33. Of course, it's not taught, but as long as one thinks, not teaching this won't stop a few, very thoughtful students from discovering this method.
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  34. 13:00 Taking a = 1 and b = c = ... = 2, we see that the output sequence for {n^2} must be {n! * (n-1)!}. Neat!
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  35. I am a Ph.D physicist and working as a data scientist but never knew this simple intro to e. Thanks .
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  36. I would love it, if you would continue with this concept! 🙌
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  37. Re: the end questions, undergrad computer science, and would be fantastic to see more of the "insane stuff" :)
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  38. Can you sometime do a geometric proof like these that shows why: 1^3 = 1 2^3 = 3 + 5 = 8 3^3 = 7 + 9 + 11 = 27 4^3 = 13 + 15 + 17 + 19 = 64 Etc
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  39. Those are some pretty non-christmassy glasses if you ask me, you're a beast.
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  40. Your teaching style is just so good! I think it's a combination of the interesting topics, your smooth as heck animations, giggles, and the quick glances you give at the end of each chapter to summarize (it's especially nice for note-taking!). Not even to mention the fact that you don't give direct answers to questions you bring up, but instead direct the viewer to introductory terms and topics to look up and gain knowledge themselves. I wish I could attend one of your lectures, but until then this will have to do!
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  41. Awesome video (im a 33m into the past time traveler)
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  42. "Hey programmers" I see my work is requested.
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  43. 5:38 All primes that can be written as a sum of two squares are primes
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  44. Thanks for the video! When I first heard about this proof, I asked Alexander Spivak who invented the visual version. And he said that there was no other source, it was his own idea. Because we don't know anybody who came up with this before 2007, it's almost certainly that he was the first. Unbelievable, but the Zagier's proof (and the previous proof by Heath-Brown) had appeared without any connection to geometry.
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  45. This log wheel also provides a nice illustration of Benford's Law, the "observation that in many real-life sets of numerical data, the leading digit is likely to be small" (wikipedia). If you pick a random point around the perimeter of the wheel, it is very likely that the number it represents starts with the digit 1, less likely that it starts with 2, etc. all the way up to 9 which is very unlikely. This is independent of the magnitude (decimal shift).
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  46. The most memorable is the fact of the partial sums being non integer.
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  47. For the width 4 triangles, there are 10 "essentially" different triangles, if your symmetries are permuting colors and reflections across the vertical axis. I used Burnside's lemma twice.
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  48. and a cool T-Shirt :)
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  49. Videos like this make me marvel at the internet. Growing up I could never have access to content like this but now I can watch a brilliant mathematical mind explain fascinating concepts to me. this channel is an example that should give everyone faith in the future of humanity.
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  50. For a "change," I see what you did there.
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