Calculus is Impossible Without These 9 Things
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- Опубліковано 19 тра 2024
- Dive into the 🌀 heart of calculus, beyond Newton and Leibniz, and discover the 9️⃣ pivotal discoveries that shaped its evolution! 🚀 From ancient Greece with Archimedes’ ingenious methods to the revolutionary insights of Lebesgue in the 20th century, calculus is a tale of relentless pursuit of knowledge. 📚
🔍 Ever wondered how calculus transitioned from the visual task of finding areas and volumes 📏🔵 to the complex world of algebra and beyond? 📈 Join us as we unravel the fascinating journey from the Method of Exhaustion to the profound realms of Real and Complex Analysis, illuminating the minds and methods that paved the way. 🌟
Discover how:
- Ancient techniques laid the groundwork for modern mathematical thought 🏛️
- The Renaissance brought a new dimension with the Method of Indivisibles ✂️
- Coordinate Geometry bridged shapes with graphs 🌐
- The study of Tangents and Optimization 🔍 revealed the nature of curves
- The Fundamental Theorem of Calculus 📚 connected differentiation and integration
- Rigorous foundations in the 19th century 🏗️ refined calculus’ core
- Real Analysis 📉 and Complex Analysis 🌀 expanded calculus to new frontiers
- Lebesgue Integration 🧮 revolutionized our approach to integrating functions
💡 Witness the incredible evolution of calculus and see why it's more than just Newton and Leibniz. It’s a vibrant, evolving field that touches everything from geometry to quantum mechanics! 🌌
👉 Subscribe for more enlightening journeys through the history of mathematics and the ongoing adventure of discovery! #CalculusEvolution #MathHistory #InfiniteDiscoveries 🌍✨
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I’m a third year math student and must say; this video is very misleading. You could never find a woman who would willingly listen to your math talk in the wild😂
But I'm a woman majoring in pure math and watching this rn 😭😭
I did!
Wrong I know who would
Sexist and unfunny joke
I could never find a guy interested in a math major woman like me, they just want instagram or AI gf sooo 😂
I just discovered it, and I already love this channel! May I ask what program you use for edition?
Yes, it is super basically though: Keynotes. Haha it is shocking what you can do with this tool if you know how to use all its functionalities. Btw, you have some very interesting content too! I will watch some more today 😁
@@dibeos Thank you!
Bro this video is well made
The amount of research , presenting, and motion graphic ❤
You put some serious efforts in this one
Thanks for recognizing the effort !!!! 😄
Really great video I am really grateful as a book collector that you added the books to the development of calculus, will go and look for copies of these titles in the future thanks!
Wow that’s great, glad you liked it. And thanks for the feedback. Check out some of our other videos ;)
The video is quite short, which excuses that some things are missing, but I think mentioning this would have been no big problem...
* The method of exhaustion was invented by Eudoxos, about 100 years before Archimedes.
* Archimedes used, additionally to the method of exhaustion, also already a method quite similar to the indivisibles of Cavalieri.
* Tangents to curves were already discussed by the ancient Greeks. What was knew with Fermat was determining the _slope_ of the tangent.
* Interpreting the slope of the tangent as the instantaneous rate of change was first done by Newton, not by Fermat, as far as I know.
* The fundamental theorem of calculus was first discovered by James Gregory, not by Newton or Leibniz. Unfortunately, Gregory apparently did not really recognize its importance, and additionally, his works were not widely distributed.
* In the formulas at 8:15 and 8:30, it is not explained what the deltas mean. Perhaps the width of the rectangles? But why do you use different deltas - the rectangles all have the same width? Additionally, the formula at 8:30 is formulated quite strangely; the three dots probably imply that this goes on forever, i. e. you need to take another, additional, limit? Usually integrals are defined by limits in a different, more clear way.
* It's not clear to me what exactly is the differene between "real analysis" and the discovery directly before, defining differentiation and integration rigourously in terms of limits. I thought exactly that _is_ real analysis.
Oh really? Why do you say so? Could you tell us how he used it? I did not know that
@@dibeos E. g. look at the article "Archimedes' Method for Computing Areas and Volumes - Cylinders, Cones, and Spheres" by Gabriela R. Sanchis. The method described there is very similar to that of Cavalieri.
I'm pretty sure the deltas are different because function is riemann-integrable iff any partition (b1,b2,...,bn), such that widths of all bi go to 0 as n approaches infinity, gives the same sum as the result. In other words you can't just check one partition into say n equal size parts and that's also why calculating integrals using only definition is so difficult
@@ahasdasetodu6304 You are right about Riemann integrals; but at 8:15 and 8:30, what is discussed is Cauchy's definition of the integral, which was simpler than Riemann's definition.
Was it not James Gregorie to first Publish* his findings on calculus, not necessarily discover?
I'd argue that measure theory should probably be included as well. Lebesgue measure is neat and all, but it's still limited in scope.
Yes, but in a matter of impact, Lebesgue integral is very interesting because it shows us how to generalize Riemann integral, which is a shocking fact when you just learn it.
@@dibeos I'm not denigrating the inclusion of Lebesgue integration (it is what kicked off measure theory, after all), just that it's kind of 1 step from a vast generalization (measure theory is arguably the ultimate form of integration, at least that sees frequent use). You mention functional analysis, which is kind of stunted without abstract measure theory (eg. Lusin's theorem, Riesz-Markov-Kakutani's theorem, and the Radon-Markov theorem).
@@ffc1a28c7 yeah, I guess you are right… Measure theory however deserves a whole video on its own. I’m thinking how to balance out a deep explanation of it with a simple one that “anyone” can understand.
Everything you say is correct, but this video probably is probably meant for a broader audience.
@@ccbgaming6994 exactly, I intend to make videos that go deeper on some topics as well, but I do believe that starting with the intuition and big picture is always the best learning strategy, in any case
great video! i enjoyed watching! thank you!
Thanks, what did you like about it?
@@dibeos the historic perspective of the evolution of calculus! I never heard before about some of the most recent contributions to the discipline that helped to shape modern calculus
This important clarification as to what exactly Newton and Leibnitz are owed credit for with respect to the universe of mathematics is similar to what exactly Charles Darwin is owed credit for with respect to the science of biology. Just like how Newton and Leibnitz didn't actually invent calculus (as asserted here in this video), they instead formulated and codified the guiding principle of this branch of mathematics; Darwin didn't invent the theory of evolution (prominent biologists contemporary to, and preceding, his contribution to the life sciences were already in the midst of discussing and debating over evolution), he instead discovered the mechanism by which evolution operates: natural selection -- the explanation which rendered Lamarchian evolution obsolete
Yeah, I agree. Actually I do not like to use the word “invented” in science in most cases (despite the fact that I can use some times by force of habit). We can say that Newton and Leibniz discovered Calculus instead, and not on their own at all. As Newton pointed out, there were some giants’ shoulders involved there
@@dibeos Math and Calculus were invented. Not discovered. A discovery is done as in the example of of discovering a new island. The island was not invented but discovered.
@@user-ky5dy5hl4d that’s a very interesting topic to discuss. For some people math is obviously discovered. For others it is obviously invented. I am not quite sure to be honest. Every time I think about it my opinion oscillates between them. I couldn’t decide. For now, I’d say that it sounds wise to say that it is both. But what makes you so sure that it’s an invention?
@@dibeos What makes me so sure? The invention of square root of -1.
@@user-ky5dy5hl4d yeah, this is a pretty strong argument. And this is one of the cases that “convinced me” (not that much actually) that in the end math is a mix of inventions and discoveries.
Bravi, bel video!! Posso chiedervi che software avete usato per editare i video?
Thanks!!! Just keynotes :)
the level of editing is incredible , and just 1,5 k subscribers
I hope he (algorithm) hears you, bro!
2:41 you are "proving" that the cylinder volume is pir^2H, knowing that the cylinder volume is pir^2h (where h is the infinitesimal height)
…i (really just me) would suggest you use * for multiplication in text like that?
…if you feel lil fancy, then π over pi?
Hmm, with the cylinder, you're skipping how we got that area of a circle. Did we use infinitesimals as well?
ya, it's a bad example. (why not just use the one?).
Liked the unique video format. Including your gf in. ( supposing it s your gf and not sister lmao ) And also included some parts veritasium excluded. Like inscribing and *circumscribing* a circle. He missed the second part. ( I believe ). All in all. Great video. Definitely stands out from the rest.
Edit. After watching more of it. Love that you give countless examples. Since most people don t watch videos with a pen and paper.
Thanks, wow! That’s some really special feedback right there! Btw, Sofia is my wife ;)
super high quality, I learned a thing or two
Thanks! Please, let me know what was insightful to you. I like to ask that because it’s always hard to know if what is obvious for me is also obvious for other people
Thank you
Clicked randomly ,stuck on the content intentionally.Good work sir btw i was till the 5th point or so😅
Great! And did you like the most (up to the 5th point)?
@@dibeos 1st one cuz it was the origin and start of an era🙂
nice content keep going
multivariable and tensor calculus and differential equations? functionals or stochastic or fractional or discrete calculus? :
Yep, you are right. And I sincerely struggled to not talk in depth about some of them, however we tried to keep the video as concise as possible. But it is a great hint for us for future video 😉
@@dibeos :O
You should do more videos, you teach ideas very well and I think you could create a school!
Thanks Dave, we are 249 hours of watch time away from monetization, which means that as soon as we start to be paid from ad sense we will reinvest 100% of the money into the channel by hiring an editor, so that we have more time to improve the content, publish videos more often and open our online platform where people can learn virtually anything of Math & Physics. The idea is to provide such good quality content that people will be able to “graduate” in Math or Physics just by following the online classes. That’s the plan. It is a long way to get there haha but we will make it. Stay tuned 😎
damn ! at first, i thought this channel had at least a lakh of subscribers. Btw....please don't have a conversion when discussing topics which often needs channeling of focus
Bro this a great video, but the marker sound effects are giving me goosebumps, like that feeling you get when you hear nails across a chalk board! Please tone it down!
Thanks for the valuable advice! We will fix that. Could you show me exactly where in the video? This way I’m sure about what/how to fix it
@@dibeosFor example, the sound effects starting at 0:43 are the ones I’m talking about. But I think, in general, your sound effects need better mixing throughout the video. I showed this video to two friends and they both commented that the sound effects were louder than the dialog at some points. I hope this helps! Great content 😊
@@dylanjm_ man, thank you so much for these tips, really. When you make the video you don’t notice these things (cause we are so used to it, since it takes around a week to produce). We will definitely tone down the sound effects and improve their mixing throughout the video ✅
Can we have the womansplanning version please!
Yes!
We need more
Yes, we do! And yes, we will have!
Fantastic video.
Thanks! We appreciate :)
Great video
Thanks :)
Descartes seems as underrated as Dirac.
Ok, maybe Descartes is “underrated”, but Dirac? I mean, he got a Nobel Prize and is considered one of the top contributors to Quantum Mechanics. I don’t think you can get more recognized than that in physics…
this video is going to be hit
Glad you think so ;)
Good summary, but too complex for single short video
It is true, we tried to condense it as much as possible but to be really fair to each subject we would have to go deeper into them. Дякую Артем!
@@dibeos you mixed Russian and Ukrainian languages =)
Дякую - it is Ukrainian word, it does not exist in Russian language
Артём - it is Russian variant of my name, and symbol ё does not exist in Ukrainian language. In Ukrainian my name will be Артем.
@@forux you are right, sorry. But give me a break, I am a foreigner 😅 thanks for the correction, though! (Fixed it!)
@@dibeos i just explain it, no complains =)
@@forux дякую ;)
Math, including calculus were invented not discovered.
All math is based on nature, it's a decodification of what already existed in a way that the human mind could understand.
@@lowrhyan567 I would disagree with your opinion. Where do you see infinity in nature? Where do you see square root of negative one? Where do you observe time?
It’s not enjoyable to watch two people pretend to have a natural conversation.
Thanks for the critics. I hope that we fixed that for the video we will publish today. Let us know, please ;)
Calculus was invented by Madava,
Oh really? Why is that?
in 14th century Madhava , “Kerala school of math” gave the infinite series for trigonometric functions and for pi, now called as Madhava Leibniz series for pi (Madhava Wikipedia) , Bhaskara 2 gave early form of rolle’s theorem, derivative =0 at extremes ( history of calculus Wikipedia)
Lol invented is a huge word madava did enter the field first of many giving so many theorems but did not invent a formal way of using his theorems to find other theorems, so we can't say he invented it.
There are many more mathematicians in India the fact that people know only madhava or Brahmagupta is straight sad😢
He gave birth to it and Newton Libntez were unknown to it later it evolved as calculus. Actually Madava did an define integral there.
Source : Dawn of Science by springer and Crest of the peacock @@orangesite7625
Madava arrived at taylor series of Sine cosine, arctan by using definite integral
Source : Dawn of Science by springer and creast of Peacock
I get the feeling the female mathematician is not happy with the ongoing mansplaining she is forced to endure.
Hi! Sofia here :) I’m not an actress so don’t mind the face. But I scripted the video and decided who gets to say what, so, whenever there’s planning it’s as much mine as it is Luca’s. Hope to have clarified things ;)
Oh my god
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Saddam Hussein!
What do you mean?
The red graph in the thumbnail looks like the Saddam Hussein meme@@dibeos
@@dibeos The hypothetical depiction of Saddam Hussein, depicted sitting and red, in a cave, became a meme.
It also became a meme to observe the depection in unrelated pictures.
@@caspermadlener4191 yeah, honestly I just found out about this meme looking it up hahah
I appreciate this video, if you make a future video I would also include some things about volume as the integration of cross sections🧮❤
Yes I do want to make a video talking about them, but it would rather a video on calculus in 3D or higher. Thanks for letting us know that we are not the only ones interested in it 😅