Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. I for one really appreciate this short interlude type video. The smaller, more easily digestible content without needing to establish a large number of foundational knowledge is refreshing!
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  2. Pascals triangle seems to be everywhere
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  3. Music, "Chris Haugen - Fresh Fallen Snow" (I hear it on a lot of videos, love it)
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  4. Madhava is an Indian (Keralite) mathematician. Actually I am watching this video miles away from his native place (Irinjalakkoda, sangamagrama as you said). Nice work sir👏
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  5. 11:01 this moment is meme-potential. had me laugh out loud at his expressions
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  6. 65yo, haven't used calculus in over 40 years, still remember the heart of calculus and find it easy to follow this wonderful presentation. I see calculus as "depowering" or "powering" operations. Exponents become addition and back again. I imagine this ranking of increasingly more powerful operations, and calculus as the rules for going up and down in effect. Very similar to the way explained here by graphs and the table of elementary operations. Go up for slope, go down for area. From the first it seemed so intuitive back when I was young. Then again, so did dancing molecules which led to my career in medicine and biochemistry as an expert in single carbon metabolism ( the dance of the B vitamins). Mathologer is a wonderful channel because he loves this. There's an inherent beauty that simplicity brings; but you must first love knowing for the sake if knowing, not some other goal. Sorry, an old man reminiscing of when he still had a functional mind here. Soon again, I will think.
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  7. Merry Christmaths!!
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  8. Why there is 27 missing on your "I can't even" t-shirt?
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  9. It is impossible that they did Tailor's series (well, we have to use the same term for clarity) with verses. I think they did do some form of symbolic math, but it was the tradition to use only verses in the final copy. One reason for that may be that they thought it would be harder for future mathematicians not familiar with their symbolism to understand the symbolic math compared to reading verses.
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  10. This channel is mostly above my head but the quality of education here never ceases to amaze me <3
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  11. This was one of the most ah-ha-dense videos you've made. Long time fan; this was one of your best. I came away thinking about an entire mathematical space I hadn't thought about much before.
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  12. I remember noticing that the 2nd difference of the square numbers is constant and the same for the 3rd difference of the cubes when I was about 12 in school, so this is weirdly nostalgic. I've never learned about any of these details though! Very cool
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  13. This makes me want to crack open my old calculus books.
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  14. I couldn't wait for the video proof of the Christmas thoerem and found something AMAZING on mathoverflow that I wanted to give you a heads up about in case you had not seen it before. I think the famous one sentence proof can be Mathologerized using the incredible geometrical interpretation of the involution in the answer by Moritz Firsching to the MathOverflow question titled "Zagier's one-sentence proof of a theorem of Fermat". I have read many books/papers on polynomial automorphisms and never saw anything like that before in my life. After going through a bunch of proofs I think the one-sentence version is the best hope to do at the level of your videos using that geometry trick to explain where the involution comes from. There is also a wonderful numberphile video on this topic with an outline of the proof.
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  15. given that us Jews weren't allowed to own land or animals etc etc, we had to go into banking and trading and the like, so of course we know a lot about it :)
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  16. we need mythologer vs 3B1B teaching competition. they pick 5 random subscribers from the 2 channels and teach them something. then those teams have a competition to see who is a better teacher.
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  17. I love the feeling of having just about finished watching another great math video, and then I remember this is Matholologer and I've only just finished chapter 2 of 5! You spoil us with knowledge!
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  18. There are no ways to rearrange these terms to get exactly Pi, because this algorithm can never actually be run. Unlike other infinite series that sum to pi, this one can only generate up to the number of significant digits you already know. To produce Pi exactly, you have to already know the value of Pi exactly.
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  19. there's a small error in the red 'pentominoes' at 28:10 : one of the shapes (the 'W' shape) has 6 instead of 5 squares
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  20. my answer for the nxn points in a square is: sum of (i*i*(n-i)) from i=1 to n-1 so for 5x5: 1*4+4*3+9*2+16*1 wolframalpha says that can be simplified to (1/12)*(n-1)*(n^2)*(n+1)
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  21. A great math video to start the new year!
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  22. You know that it is going to be a great video when it is Mathologer, you have just started the first second of the video, and you've already seen three comments pointing out how exceptional the video is. I am confident that I am going to agree with your assessment.
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  23. Although technically, Euler's polyhedron formula also works perfectly for non-convex (concave) polyhedra, as long as they don't have any holes.
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  24. Most memorable: the optimized leaning tower! Although it was very messy, I think there's a lot of beauty in the fact that the most optimal arrangement of bricks is such a mess. It reminds me of how an extremely simple physical system (like a double pendulum) can result in chaos!
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  25. Ramanujan and Euler is everywhere ... And I love it ... ❤️
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  26. This is my boyfriend's favorite video. He watches it at least once a week.
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  27. Encore une vidéo prouvant le génie de Ramanujan. Démonstration hallucinante !!!! Bravo, comme d'habitude. Les vidéos mathématiques les plus géniales du net.
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  28. Math was very challenging until grade 10, honestly, in my case, I understood math very quickly afterward. Calculus was the easiest subject during university. Now after 10 years I still remember these rules. Math is all about understanding concepts and visualization of problems in your head, most students I came across learn math by doing examples and memorizing types of problems, at first glance, it seems the correct approach, but in reality, when the problem is slightly changed they struggle to solve it.
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  29. Hey Mathologer, My solution to the Strand Problem has a much more intuitive way to find the x^2+x = 2y^2 identity. It helps a lot to instead write in this way: x(x+1)/2 = y^2 x is the largest number house, and 1 is the 1st house. The sum of all house numbers is the average of the highest house x and 1, so (x+1)/2, multiplied by the number of houses there are, which is x. Ergo, sum of all houses is x(x+1)/2. If the sum of all houses is equal to a perfect square, y^2, then the occupant lives in the house y. After you reach this point in the puzzle, you can solve with wolfram to find all solutions. (1,1) (6,8) (35,49) (204,288) (1189,1681) Wolfram gives an equivalent formula to the one you reach at end of video. Would have done it myself but too lazy 🙂
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  30. The beauty of the interconnectedness of mathematics
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  31. Top paypal: markus persson, aka notch :)
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  32. Back in my early teens I was fascinated by this stuff. I'd spend hours re-discovering all these relations (nobody taught me that in school, but I stumbled on it myself by some chance). Thanks for the fun reminder 😃
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  33. There is a slight problem in the coding challenge: It can be implemented only on a device which has infinite storage and can do infinite precision arithmetic in finite time.
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  34. I was introduced to the Steinbach ratios 8 years ago. When I am working with the heptagon ratios, I prefer using the three side lengths of a heptagon with the smallest side negated: a=2sin(τ/7), b=2sin(2τ/7), c=2sin(4τ/7) Using these values, any polynomial f(x,y,z) such that f(a,b,c)=0 also has f(b,c,a)=0 and f(c,a,b)=0 It also has the property that ab+ca+bc=a+b+c+abc=a²+b²+c²-7=0 Also, to expand on your formulas at 43:00, A(m,n)=C(m,n+1), B(m,n)=C(m+1,n), and C(m,n)=(1*(r/1)^m*(s/1)^n+r²*(-s/r)^m*(1/r)^n+s²*(1/s)^m*(-r/s)^n)/(1+r²+s²)
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  35. 13:43 "Fun, no? ... Well I don't care. I think it's fun."
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  36. Hey Mathologer! What are the three chords at the beginning of your videos? Are they somehow important, or do you just like them?
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  37. I made it to the very end.
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  38. The optimal solution is very dependent on the exact happiness function used. It is not clear that getting equal parts of the contested estate rather than, say, proportional to the initial claim is a better happiness function.
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  39.  @Mathologer  High school maths (Algebra and Geometry) teacher here. The reason that we don't do classical geometry anymore is because school is compulsory. Back when classical geometry was taught at this level, school was an elective or privileged activity. The people who were taking classes did so because they wanted to and/or understood the value of it. Most people do not value math. Take a look at your subscriber count compared to mindless entertainment like Markiplier or something. I have good reason to believe that most of my students are not only uninterested in math (in fact, they hate it -- even the cool stuff), but are incapable of comprehending it. So how did the school curriculum respond? By boiling all of the math down so that the students with the lowest math performance could still pass the classes -- that is to say, teaching kids how to push buttons in a calculator, but not why the formulas work or what they mean. It's a waste of everyone's time, but that's what you get when teachers become glorified babysitters for families with working parents.
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  40. Mathologer making complicated math available for amateurs since 2016
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  41. If you use surreal numbers you can make the paradox "disappear". This summation is an infinite set of games which has a total game value of ON (infinite moves for Left Player) + OFF (infinite moves for Right Player) better known as DUD (Deathless Universal Draw). The winning move is not to play, because there is no winning move. Surreals make infinity easy and clean!
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  42. "This is the first Strand type puzzle"
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  43. Most memorable: fractal visualization of no-9's series being finite
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  44. A few years ago, a friend of mine participated in a popularization event for high school students (Maths en Jeans, Paris) and we offered an iPad to any student that would come up with a working solution for the 5th row. We had kids waiting in line to try, and they did not mind (nor go away) after we showed up that it was impossible. It’s one of my fondest memories as a teacher.
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  45. ALSO just to add, because (1 + 2 + ... + n)² is just 1³ + 2³ + ... + n³, we can replace each squared triangular sum with that so we can get rid of the pesky squares and get a purely cubic pattern :D
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  46. 2 minutes in and you've already blown my mind Mathologer! Thanks! Love your videos
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  47. Yeah! And as someone from the 16th Century who knows a fair number of medieval scribal monks, seeing the printing press being used is always a bit gut-wrenching knowing what they going through right now because of the printing press. This channel isn't going to commission an artist to draw something for a couple of seconds of transitions between chapters. It's not taking away anyone's job. It's the perfect use case for generative AI - to liven up and add moderate-quality art to something that would otherwise not have any.
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  48. What do I do with a quarter garment?
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  49. 19:00 Zagier's "One Sentence Proof". In case you want to investigate a bit I'll leave here a rough explanation of what an involution is. Imagine a process that pairs elements so if you have element A it returns element A' and vice versa: for element A' you get A. One example of this would be when you get a direction, say North (in Projective Geometry we called it a point at infinity). If we had a parabola tangent to the Y axis, drawing lines parallel to the North would give us either 2 crossing points, 1 unique double-crossing point (the tangent to the parabola through the Y axis) or 0 points. These crossing points form an involution since each relate to another and vice versa through some crossing and all involutions behave in a way that you always get a double point that is related to itself, which we can call a fixed point. This fixed point is what assures that we have an odd number of answers, that we can then interchange y and z in the involution and then get 4y^2 = (2y)^2 which summed to x^2 yields p. In the proof, the involution is crafted very delicately so it proves Fermat's Christmas Theorem, but I've not spent the time to look into how it exactly works. I hope this helps understand that part of the video.
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  50. 36:29 there is always more to dig on every subject in math, this is a never ending quest.
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