Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. This video is my best shot at animating and explaining my favourite proof that pi is irrational. It is due to the Swiss mathematician Johann Lambert who published it over 250 years ago. The original write-up by Lambert is 58 pages long and definitely not for the faint of heart (http://www.kuttaka.org/~JHL/L1768b.pdf). On the other hand, among all the proofs of the irrationality of pi, Lambert's proof is probably the most "natural" one, the one that's easiest to motivate and explain, and one that's ideally suited for the sort of animations that I do. Anyway it's been an absolute killer to put this video together and overall this is probably the most ambitious topic I've tackled so far. I really hope that a lot of you will get something out of it. If you do please let me know :) Also, as usual, please consider contributing subtitles in your native language (English and Russian are under control, but everything else goes). Today's main t-shirt I got from from Zazzle: https://www.zazzle.com.au/25_dec_31_oct_t_shirt-235809979886007646 (there are lots of places that sell "HO cubed" t-shirts) Merry Christmas, burkard
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  2. When you mentioned Calculus Made Easy I thought, "Hey, I have that book!" and ran to the bookshelf to retrieve it. As it turns out, no I don't. I have a book called Calculus the Easy Way by Douglas Downing of Yale University, © 1982. It's a fun little book wherein the protagonist is involved in a shipwreck and washes ashore in the land of Carmorra where he, in essence, helps its denizens invent calculus in order to answer burning questions involving the speeds of trains, the areas of fields, the simple harmonic motion of a spring-powered chicken scaring machine, etc.
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  3. Geoff Smith, who wrote the problems for this film (and some of the Olympiad questions) was my lecturer in first year. When the film came out they were extras for our problem sheets.
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  4. Despite serious competition, Mathologer remains the greatest math channel imo ^^ Thanks for another awesome video!
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  5. Nice explanation of calculus. However, I would have preferred the masterclass on Galois theory you promised three years ago 🙂
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  6. Good Stuff Burkard! :)
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  7. Every month when Mathologer comes out of his hiding, you know it's going to be a great video
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  8. One day I hope to answer your “did you see it?” with an equally enthusiastic “Yes!” 💕🐝
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  9. You have a gift for showing us what math is really about. It's pure amazement, wonder, curiosity and entertainment. Thank you for capturing the essence of math!
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  10. I have literally used a slide rule for a quiz in engineering school around 2014. The battery in my calculator died and I didn't have a backup. But the rules of the class said I could use any device for calculation with the professor's permission. So I dug the slide rule out of my bag, held it aloft and said "Excuse me, professor! May I use this for the quiz?" He - having grown up in the age when digital calculators were still uncommon, at best - laughed out loud and said "If you know how to use it, sure!" He was certainly proud that I aced the quiz with that slide rule.
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  11. I feel like Ramanujan was an alien that was sent to Earth to accelerate our knowledge in mathematics, and once he taught everything he could to the human race, he left Earth to teach another underdeveloped civilization.
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  12. "Are we there yet?" "No just 1+1/2+1/3+1/4+... more minutes."
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  13. I actually guessed Gauss! Take that Mathologer! Me: 1 Mathologer: 387ish
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  14. Thanks for making a video about my theorem!
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  15. Archimides was doing calculus without algebra. No wonder he's your favourite. That's pretty much the spirit of this channel if you think about it.
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  16. Surprised you didn't call good and bad numbers nice and naughty numbers respectively.
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  17. Calculus is only hard until the point where it clicks in your head and then you feel: "How could I not understand it?" Tangent 🤣: Archimedes was really close. I think he makes for an incredibly plausible "what if?" scenario. What if he discovered calculus? How much would it change the world?
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  18. Ramanujan was and is great.
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  19. This is perhaps the best math video I've seen. Clever, well-explained, and elegant. Keep up the great work. Stay safe amid the Covid.
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  20. 69 x 10k subs, nice :^D
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  21. When I started learning Calculus in High School, I began to realise that everything I had learned in maths before then from simple arithmetic, geometry, algebra and trigonometry was leading up to it. Does this mean that one reason we learn how to add and subtract is so that we can eventually do Calculus?
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  22. /w magic
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  23. (28 March) Really bizarre, this video was basically invisible for almost two weeks with hardly any recommendations going out to fans. Only now YouTube has decided to actually show it to people. Who knows, maybe it was a mistake to mention cat videos in previous videos and the YouTube AI is now under the impression that the target audience for these videos has changed :) The longest Mathologer video ever, just shy of an hour (eventually it's going to happen :) One video I've been meaning to make for a long, long time. A Mathologerization of the Law of Quadratic Reciprocity. This is another one of my MASTERCLASS videos. The slide show consists of 550 slides and the whole thing took forever to make. Just to give you an idea of the work involved in producing a video like this, preparing the subtitles for this video took me almost 4 hours. Why do anything as crazy as this? Well, just like many other mathematicians I consider the law of quadratic reciprocity as one of the most beautiful and surprising facts about prime numbers. While other mathematicians were inspired to come up with ingenious proofs of this theorem, over 200 different proofs so far and counting, I thought I contribute to it's illustrious history by actually trying me very best of getting one of those crazily complicated proofs within reach of non-mathematicians, to make the unaccessible accessible. Now let's see how many people are actually prepared to watch a (close to) one hour long math(s) video :). Have a look at the description for relevant links and more background info. The first teaching semester at the university where I teach just started last week and all my teaching and lots of other stuff will happen this semester. This means I won't have much time for any more crazily time-consuming projects like this. Galois theory will definitely has to wait until the second half of this year :( Still, quite a bit of beautiful doable stuff coming up. So stay tuned.
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  24. If you consider the right boundary of the Problem, where you interpreted the Rules to mean that you only turn over one card, then there should turn up an interesting result if the cards are layed out in a circle. That would mean that when turning over the rightmost card, you would also turn over the leftmost card. That way, the sequence would not need to terminate, i think. Because you could shift the Face Up cards infinitely to the left and looping around when they "hit the edge" of the deck.
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  25.  @plaierdifortnaiti9955  On the same level as an integral from 0 to 0
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  26. As a 50 year old man, I may have done better in maths if I had teachers like you! Thank you for your simplification of complex maths. :-)
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  27. Let's gooooooooooooooooooooooooo! :D
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  28. Most memorable part: me losing my life after failing the “no nines sum converges”
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  29. A "short" video for a change, "only" 30 minutes long :)
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  30. Hey. Compared to the amount of minutes in 2000 years, this video is remarkably short.
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  31. Minecraft villager be like: 5:30
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  32. WOW IT TOOK ME MY ENTIRE DEGREE TO MAKE SENSE OF THIS THEOREM AND HERE MATHOLOGER COMES SHUFFLING CARDS TO PROVE IT CLEARLY
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  33. Looks like I unknowingly introduced this to myself and my wife and daughters with a little game we used to play while travelling. We would add up the numbers on license plates and see who came up with the "digital root" the quickest, even though we didn't know that was the term to use. We saw very quickly that any combination of numbers that add up to 9 could be eliminated so 572 would be 5 without going through the process of adding. Later, as 3 or 4 number plates lost its challenge, we included letters. The letters "I" and "R" could automatically be eliminated since they corresponded to the number 9 and 18 respectively. This expanded the challenge because you had to figure out the numbers corresponding to the letters. As you played the game this became more intuitive when you could eliminate combinations of letters that added up to 9 for elimination. Example GSP562 would be 1. One of my daughters got so good at it that within seconds she could get the digital root of signs with just letters such as names of towns or short sentences.
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  34. Sometimes you wonder how mathematicians come up with things... Other times, you wonder how mathematicians don't come up with things...
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  35. Once you add both the triangles and squares, it looks like a 4D projection.
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  36. There's actually a sort-of-explanation for why e^π is roughly π+20. If you take the sum of (8πk^2-2)e^(-πk^2), it ends up being exactly 1 (using some Jacobi theta function identities). The first term is by far the largest, so that gives (8π-2)e^(-π)≈1, or e^π≈8π-2. Then using the estimate π≈22/7, we get e^π≈π+(7π-2)≈π+20.
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  37. Really appreciate how much effort is put into these videos. Very well structured and illustrated. YouTube really doesn't deserve this level of effort.
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  38. Ah yes, my favorite mathematicians, iron man and towel man!
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  39. This is just the discrete Fourier transform working in the background. Amazing video !
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  40. Two 3b1b AND a Mathologer upload? I am almost in heaven...
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  41. This is mathematical proof that cutting corners gives bad results ! ;-)
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  42. I get the feeling that Euler was a pretty smart guy.
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  43. My solution to the coin paradox: imagine the two coins are like gears with the centers fixed in space. Both turn once every time the other one does. Then imagine the camera rotates with one of them, so it looks fixed. This feels more intuitive since nothing "rolls away" or gets wound around.
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  44. I love how much of induction in this video even tho the word "induction" is not mentioned
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  45. The other paradox: how every Mathologer video manages to fit in so many interesting facts and beautiful demonstrations!
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  46. Any divergent series: exists Ramanujan: Allow me to make it convergent.
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  47. People will stay at home Time to make 1hour long video
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  48. Mathologer recently hit 500K subscribers and I would like to thank you all for your interest and your support over the years. Since I started the channel four years ago, it has pretty much been a one-man labour of love. However, maybe now is a good time to take Mathologer to the next level and hire someone to assist with editing the videos, preparing subtitles, etc. In preparation for this, I recently monetised the videos by switching on the least annoying ads on YouTube. I also just launched a Patreon page a couple of minutes ago: https://www.patreon.com/mathologer If you enjoy these videos and you can afford it, please consider taking out one of the Patreon memberships or making a one-time donation via PayPal: paypal.me/mathologer :) My plan is to also use this Patreon page as a platform to share more Mathologer materials with you, get into live chats, etc. Let’s see what’s possible and what makes sense here. Merry Christmas :)
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  49. At first I was sceptical as there is no "real magic". But then I saw an infinitely stretchable rubber band and now I'm convinced magic is real ;D
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  50. Always appreciate when a Rubik’s cube example “accidentally” gets you some group theory ;)
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