Hearted Youtube comments on Mathologer (@Mathologer) channel.

  1. Calculus is incredibly easy and trivial if you already know calculus
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  2. It is easy. The harder part is learning all the prerequisite material you need to know to start to learn calculus. But if you know algebra, trig, and geometry really well, calculus is incredibly easy.
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  3. Looking back on calculus, most of the things I actually had issues with were not the core concepts, but in fact was my ability to perform algebra without making small mistakes, remembering and applying trigonometric identities, and getting used to new notation. To anyone going through Calculus I urge you not to stress too much about it, just do your best it comes in time!
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  4. Division by 7 always produces 142857. Spare key to the Universe, if you lost the master copy
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  5. One of the first exams I had in physics the teacher gave us velocity over time graphs and we had to “be the car” and move in distance over time. Now that I’m 63 and still remember this tells me it was one of the best learning tasks I ever had.
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  6. In high school, I was surprised by how by far the hardest parts of Calc I and II simply involved a lot of steps of algebra. Things like partial fraction decomposition are a major pain, but actually integrating the resulting rational functions was very straightforward--once you did the necessary algebra (completing the square, etc.). Then in Calc III, I found it was much the same. Vector algebra is obnoxious, but the calc part really isn't so bad. I will say though that it gets much worse. Nonlinear differential equations are way harder than anything you have to deal with in a high school algebra class. I'd sooner factor ten solvable quintics than stare at a system of nonlinear PDEs until my brain melts.
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  7. In school whenever I noticed patterns such as these divisibility tests, my teachers discouraged me from pursuing them because they themselves were not sure if they'd always hold and were concerned they'd lead me astray. Another example that I recall is my noticing that each power of two is equal to one more than the sum of the lesser powers of two. That's well-established and taken for granted in computer science, yet was unknown to my teachers and regarded with skepticism. I remember also my mom pleading with my teachers to stop counting my work wrong for my daring to use techniques I developed myself from having explored the mathematical foundations of the rote mechanisms they taught. I understand that the pressures on elementary school math teachers drive them to stick with safe techniques, but for them to feel threatened by a student privately moving beyond that is frankly an indictment of the whole system of education.
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  8. As an Indian it is so disappointing that so far I wasn't aware about this Indian gem...... But I am grateful to you for revealing it before us🙏🙏🙏
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  9. I wish my childhood teachers had shown half the love and passion for knowledge that you do. Thanks for your work!
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  10. Do you really think im going to watch the whole 50 minutes? Because you are totally right
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  11. Your proof is decent, Mathologer, but Nathan's proof is by descent.
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  12. If it isn't Euler it's Gauss. Remember folks, if a murderer comes into your house and asks who proved a theorem you never heard of the Best survival strategy is to say "Euler or Gauss"
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  13. (HO)³ : A Christmas joke for mathematicians (HO)₃ : A Christmas joke for chemists
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  14. This demonstrates something non-math people don't get: Infinity is full of trap doors, subtleties, and other frustrations. The early infinity theorists like Cantor nearly lost their mind over this kind thing.
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  15. Mathologer: What does a partition have to do with a pentagon (aside from beginning with "p"). Me: blinding flash of insight They both end in "n"!!!
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  16. this man sort of comes across as a bond villain but is friendly enough so that I think he would be the assistant to the bond villain and would end up somehow disarming the nukes of the villain as a sort of double agent. these are the things I thought about in college. and I wonder why my degree didn't work out.
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  17. Ramanujan is the classic kid that doesn't listen in class, forgets to take notes, does no homework but then FREAKIN' ACES the test because he found his own way of doing things... He will never cease to amaze me!
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  18. The most memorable part was when you giggle, and my wife in the other room says "You're watching that math guy again?" As always, thank you for expanding my knowledge base.
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  19. Every part of calculus is mirrored in sequence calculus EXCEPT the chain rule. This is what makes infinitesimal calculus extraordinarily more powerful.
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  20. I was taught the concept in elementary school, under the name “casting out nines”. Sadly, it was presented as a trick or technique, without real explanation, which I had to discover for myself. So much is lost when mathematics is taught as a bag of techniques without the underlying beautiful patterns!
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  21. Shirt = To infinity and beyond?
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  22. The concepts of calculus are easy, and so is making programs to do it. The hard part of calculus is how they teach it in school. They want you to solve it with all of the rules to memorize. But memorizing all those rules- and the exact situations in which to use them- is the difficult part. The ideas of differentiation and integration can frankly be understood by anyone who can understand the area of a circle and how to graph a line; in other words, a late elementary school student or older. But for me, calculus was the first math class where suddenly there was no ability to look at a problem and know immediately how to solve it; you had to try different things on the same problem until it worked. And that does make it more difficult than any previous math class. Granted, it really doesn't have to be that way. Teachers could teach it differently and you wouldn't have that problem.
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  23. It seems that you are able to provide a geometric interpretation for any mathematical concept that exist. Simply amazing.
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  24. Fermat: "Hey, here's this cool thing about numbers." Mathematicians: "Amazing! Can you prove it?" Fermat: "I already did." Mathematicians: "Wow! Can we see it?" Fermat: "Hmmm... nah."
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  25. This proof was discovered by Roger Heath-Brown in 1971, and was later condensed into the one sentence version by Don Zagier. It's one of two proofs of this theorem found in the wonderful book "Proofs from THE BOOK" 6th ed by Martin Aigner and Günter M. Ziegler in chapter 4.
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  26. I tend to forget that Burkard is actually German (?), so when he read out the title from Moessner's thesis I was like: "Damn, his German is amazing." and felt silly a few moments later...
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  27. I remember seeing this video 3 years ago when I really was getting into maths and science. I could never make sense of how this could possibly work. What's nice about this video is that now I'm studying chemical physics and have the maths to fully understand this. Kind of nostalgic looking back on problems that I once was unable to grasp.
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  28. As easy as the derivate of e^x
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  29. All YouTube:trees Mathologer: let's sum quadrillion of powers
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  30. I'm convinced Tesla thought this was a neat mathematics trick, and someone picked it up as "mystical" because Tesla is smart.
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  31. I don’t think I can express how grateful I am to live in a time when I can be taught by one of the best math teachers in the world from my bedroom. Thank you so much Mathologer, we don’t take you for granted.
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  32. When he said “what a crazy, crazy year right?” I’ve been conditioned to expect him to say “Wrong!” 😂
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  33. When you showed the manuscripts(written in my mother tongue Malayalam, spoken over by only less than 40 million people in a small state known as Kerala in India) towards the end of the video, it gave me chills literally. I am glad that the efforts of these ancient Indian mathematicians are being appreciated by the mathematics fraternity all over the world.
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  34. "If you're ever captured by an evil toymaker, you'll be ready" And they say math has no real-world applications.
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  35. You're the Bob Ross of mathematics.
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  36. A new upload, great stuff <3
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  37. Do this? Pascal's triangle Do that? Pascal's triangle What time is it? Pascal's triangle
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  38. When I want to double a cube, I just pull out my complex ruler and e^i(pi) compass and get to work. Easy.
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  39. That moment when you realize the number line is just the 1d case of Moessner's Miracle...
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  40. This is mad! I am a PhD student who is actively studying number walls! Specifically, I have written a program to generate the number wall from a sequence and I have some nice formulas for the number of sequences that have a given window in their number wall. They have some beautiful relationships to diophantine approximation over function fields and linear complexity! It's so excititing to see them be popularised more.
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  41. The opposite of this is a vuvuzela, which is a horn with finite surface but infinite volume
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  42. I love this process. We learnt this before moving on to “conventional” calculus at my school and I took it for granted that everyone had too.
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  43. I'm Brazilian and I've studied the high school in a technical school. I recall learning about Heron's formula as a secondary topic, but no proof nor any thorough explanation, as the one presented, was given. Thanks for the lecture!
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  44. As a programmer, I sometimes wake up with "dream functions" lol
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  45. I have no idea who dislikes videos like this. The amount of effort put into it is just tremendous.
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  46. Ramanujan was such a great mathematician that on 22nd Dec.,as his birthday is celebrated as national mathematics day in India.
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  47. 7:17 Actually, I would argue that neither you nor the young man in the clip missed out on that oversight, because there was no oversight to miss. The coach never stipulated that all of the cards had to end up being face-up, only that the sequence of moves had to terminate. In other words, the task was simply to show that there is no possible infinitely long sequence of moves, or to put it in yet another way, once you apply a move to any arrangement of cards, it is impossible to apply any combination of moves to the resulting arrangement such that the result is the original arrangement. Therefore, the answer to the question of what to do if only the right most card is face down is to do nothing. Such an arrangement simply represents a terminating condition. Also, about the shorter video, I actually enjoy this format very much and would enjoy more shorter videos.
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  48. Madhava was truly one of the greatest mathematicians of all time
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  49. <3
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  50. Imagine discovering this in the 1980s, then learning that actually some geezers had gotten there not only before the invention of computers, but before the printing press...
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