This Is the Calculus They Won't Teach You
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- čas přidán 1. 05. 2024
- "Infinity is mind numbingly weird. How is it even legal to use it in calculus?"
"After sitting through two years of AP Calculus, I still feel like I don’t know anything about it."
"What do you mean that historically, integrals came before derivatives? Seriously, what’s the deal with calculus?"
There is an inspiring story hidden behind the formulas and word problems of single-variable calculus-a story that should be told in every introductory calculus course, but usually isn’t. Regardless of if you’ve taken a few calculus courses before or are just beginning your study of calculus, this video aims to give a taste of the insights that can be gained from learning about the history and philosophy behind the key ideas of this field of math… brought to you by a dog and some rough animations!
This video was part of #SoME2, a math video making contest created by @3blue1brown in the summer of 2022.
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Chapters:
0:00 Chapter 1: Infinity
1:49 Chapter 2: The history of calculus (is actually really interesting I promise)
2:19 Chapter 2.1: Ancient Greek philosophers hated infinity but still did integration
7:43 Chapter 2.2: Algebra was actually kind of revolutionary
11:14 Chapter 2.3: I now pronounce you derivative and integral. You may kiss the bride!
19:53 Chapter 2.4: Yeah that’s cool and all but isn’t infinity like, evil or something
24:14 Chapter 3: Reflections: What if they teach calculus like this?
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LINK TO FURTHER READING AND SOURCES: docs.google.com/document/d/1K...
Thank you very much to Dr. David Bressoud for letting me interview him!
If you have any questions, thoughts, recommendations or you notice any mistakes, please do share!
=====================================================================
CORRECTIONS LIST (periodically being updated):
3 : 47 I start a description of Archimedes' circle proof here, but I want to note that the one I present is a modified version of it; it does contain a few "hand-wavy" mistakes near the end and may still be difficult to follow; that's on me. My goal with showing this proof wasn't to give a proper explanation of it, but to give a taste of what I thought is the spirit of rigorous reasoning. If you would like to see something that is closer to Archimedes' argument, there's a link in the further reading you can check out--or you could also just google "Archimedes circle proof".
8 : 45 I made a typo... Viete lived from 1540-1603, not 1540-1693
14 : 35 This is embarrassing. Kepler's 2nd law is true because angular momentum is constant, not because velocity is constant. Whoops!
A lot of comments have brought up Indian contributions to calculus that I left out, particularly the Kerala School and Madhava of Sangamagrama, where the first instances of derivation came about. A few reasons for why I missed this in my research could be because attributing the beginnings of calculus with Indian mathematicians seems like a relatively new historical narrative, and many sources in English likely have a bit of Eurocentric bias. Regardless, this goes to show how the narrative I shared does have its flaws, and similarly to the misleading impression of calculus I criticized modern introductory courses of spreading, this narrative is not the whole picture. If you have any sources you'd like me to add to the further reading, please let me know!
I may have suggested that Euler discovered the number e, but he did not--some attribute it to Napier, and many others before Euler used it. On that note, I probably misleadingly attributed a lot of other ideas I brought up to one or a few people, when they are much more nuanced; so take the briefly brought up associations in this video with a grain of salt. This video is intended to share a broad narrative instead of establish definitive history of calculus. Hopefully this can just act as an intro to the subject! - Zábava
#SoME2 is finally over. What a journey it was! Thank you all for the attention and constructive comments. I'm incredibly honored to have been chosen as a 'winner'... and I'm very excited to be getting that pi plush lol
That being said, if you're interested in learning more about the history of calculus, there's a link to the further reading (and a list of corrections) in the description.
Have a good one!
Let’s goo this was so good
Congratulations!
This video was amazing! I could already see it winning something in SoME2!
DOG SWEEP
Ok, time to reveal that you take a tiny bit of inspiration from Bill Wurtz :)
Reference: czcams.com/video/xuCn8ux2gbs/video.html
Congratulations! Well deserved!
I really like how you paired the music with the time periods, starting with ancient and moving through the baroque, classical, and romantic periods. That's a very nice touch
Thank you for noticing!
I agree! Loved the video
Oh I didn't, just enjoyed the greek part and the rest I wasn't paying attention, very curious.
I actually wasn't expecting the Renaissance music this way (without chords and all that we learn during school)
Omg! He did that? Now I am gonna have to watch this
Well, at the baroque part he put Mozart's 40th Symphony, which was composed in the late 18th century and is a great example of classicism, not baroque.
I strongly believe that every field should have historical context in its introductory phase, and this is a great example of it. Very well put together...
This is my biggest problem with a lot of math classes. They teach you all the rules and theory but the practical applications (which make the subject interesting to common folks) are often skipped and sometimes hidden in the back of the book.
@@Fuzzballexactly. all that students see are numbers and numbers and letters and letters. they’re never told anything except this is the formula now plug in this number. There is usually zero attempt to relate math to the real world, to relate real life happenings to mathematical concepts. I think this video beautifully displayed how a circle’s area = r • c/2. Instead, formulas are just written down for students to copy.
@@Fuzzballthat's what engineering is for :)
No we wouldn’t remember any of it, if you want it you’ll go find it if you want it bad enought
@@jumping_beanz6209 you wouldn’t be tested on the historical context, Only on the subject matter. However, given history to math adds a nice touch towards teaching the subject and makes the class more engaging.
As a first year engineer and past experiences with calculus i find what David Bressoud said so relatable "students only start paying attention when the professor actually starts doing the examples"
Like how so? The students didn’t care about how the problems work to find an answer or that they were simply just lazy? I want to be an engineer myself and calculus is making me shit myself. I’m a senior right now I highschool and I had to self teach myself PreCalculus over my junior year summer to be in the class now. I’m always paying attention from changing my wrong answers to the right answers, asking questions, and coming right after school with only 10 minutes to finalize my questions due to my vocational school for automotive being in NY. It’s because I want to be an automotive engineer. Thanks and I hope you respond to my reply.
@@notorioussmoke2836 idk
@@notorioussmoke2836i belive it's the first one.Your average folk(even if they like math) won't be as inclined to learning some random solution compared to giving them all the proofs as to why you're doing what you're doing
@@notorioussmoke2836idk if it'll help but, I suggest you look for indian math classes on yt, you can get everything from basic highschool trigonometry and calculus to level sufficient to start engineering school. Some videos are in hindi (you can still practice from there) you might find good English ones too. Its that we have alot of compulsory calculus in the last 11th and 12th of highschool so videos help to learn from basic to advanced
Me dividing 1 by 0 🗿
I thought I hated math but when you combine it with the historical context it’s almost a thing of beauty 🤷🏻♂️
Same
I still hate it
@@smuglook8087 bc ur a twitch viewer
With emphasis on "almost" :)
Almost???????????? It's gorgeous!
This was honestly an emotional experience for me. It put into perspective how far as a culture we have come, that we can now learn things as teenagers what it used to take entire lifetimes to touch. I cannot tell you how much I appreciate the obvious effort and love you put into making this video. Thank you
Thank you for the warm comment! :D
you have to be joking right....
@@henkhenkste6076 you have to be joking, right?
totally agreed. it makes me happy seeing someone (you) appreciate things like this!
Fr exactly
Great job. I am an engineer who graduated in 1972. The math that we were taught was mostly memory work. I learned more about calculus from my engineering professors than I ever did in math class. Math could definitely be taught differently and could be easier to understand if taught like this.
I think it's better to teach math in a classical way: series -> limits -> derivatives -> integrals
Historical calculus is neat, I suppose, but it kinda jumbles fundamental understanding.
@@scisci7702I agree. I learnt calculus with integration first and that was really hard to grasp. Didn't help that the book we were supposedly using as reference was in the classical order.
Doesn't hurt to hear the history and talk about concepts from a top level. I think an overview lesson would be nice, but then I think the classical structure is still better. I was considered a great student my whole life and I got the grades in calculi and all, but I still feel like I learned more later in life from CZcamsrs than reading the books and having lessons. That hurts 😂
That is because applied mathematics is beautiful
@scisci7702 this is the way I was taught calculus. How are you expected to understand integrals without derivatives, and derivatives without limits?
Just found out this was your only upload and now I’m devastated.
They posted another video! Enjoy
I’m an engineer who exactly fits the stereotype your guest mentions. I struggled to get through calculus in school and only barely made it. Adding the humanity of how calculus was developed over generations, as this video does, is exactly what was missing from my courses. I wish this concept (or CZcams for that matter) existed 25 years ago.
im an engineering student right now who thoroughly enjoys these concepts in math and calculus, but still struggle to memorize it all and the notation and equations. 😅 it really is just a lot of information, that obviously according to the video took hundreds and hundreds of years to develop
@@AtomicVertigo_Comics how are you finding engineering?? I'm in my last year of high school and ive applied for engineering at uni so I was wondering what it is really like...how hard is it?
@@puddleduck1405 Well I might have an answer for you. Basically, if you want to survive in engineering, just work on the basics (algebra, trigonometry). Also, expect it to be stressful, tough and have lots of homeworks.
@@johnvincentjimar4157 no geometry?
@@aca4262 Well, that depends on which university and engineering discipline you take.
I'm a private Maths tutor. I've always wanted my students to understand WHERE and how the concepts we study together came to be, but, sadly, it's extremely inefficient, especially at a college level... They DO engage, though, so I usually give them extra hours for free even though it REALLY hurts my wallet, so I stopped doing that for the time being. Reading through the comments, and seeing how grateful people are for this video makes me genuinely happy! Beyond measure! Enough to make my eyes tear a little!! I have saved this video, and who knows? Perhaps a future student of mine will voluntarily ask me those questions, in which case, I have the perfect video to refer them to! My appreciation can not be expressed in words! Thank you so much for putting this together, and for showing me that students all over the world really do want to know the history behind Mathematics!!!!
They sound alike they’re really lucky to have you as a teacher
What we should be asking ourselves is what's the point to this world of wonder we've created if it leaves us with so little time that even explaining how it works to the next generation is too time consuming. Maybe it's time we rethink some of the fundamentals to our society before it all falls down. Maybe it's already too late.
Thank you for teaching this way!! I had a statistics teacher who took the same approach and it was the one time in my life when math wasn't completely mind-numbing.
@@colbyboucher6391 I wish I'd had YOUR statistics teacher...
People like you are the ones who deserve to get those millions and billions not celebs or players
It doesn't matter what the subject is, finance, calculus, databases, cell biology, integrated circuit boards, inorganic chemistry, accounting, psychology, etc. I discovered the best way to learn is to go back from where it started historically. It's not necessary to study the individuals who contributed to the subject-matter but what they contributed and how that led to the next contribution. It's the only way I care to learn and I don't understand why it's not being taught this way. I went through College calculus never understanding how I could ever use the equations I was solving.
maybe they feel all other student who really want to study will stufy like us some who dont are given thid beacuse if we learn by struggling we involve more learn more and connect more
" I don't understand why it's not being taught this way" Look up the 'Curse of Expertise' - the experts who deeply understand something will see it very differently to students learning it for the first time. And so there's a natural tendency for experts to teach badly, unless they deliberately learn to avoid it.
I struggled throughout high school with math, because all of these rules they were teaching seemed so arbitrary and so never knew what to focus on. (Or frankly why I should even care)
Now that I know that its structure was formed by so many different people with at times contradictory understandings of the subject, it all makes perfect sense.
I hope this far more comprehensive style of teaching mathematics becomes a more common thing, because there are probably more students missing out on this fascinating discipline as I did.
Thanks for this video explaining how all of this fits together.
They would teach the methods but never the history or method of discovery in high school. No wonder I hated math, it had no humanity in it.
@@davidcollins2648 this might be also why I excelled at English but did terribly in math. Literature is humanity, so I am invested in it's meaning and complexities as a human being. But math I'd always taught as numbers, rules, and untouchable ideas. No wonder I was atrocious at it.
Giving the milestones in math human journeys and perspectives totally changed it all. The values and significance of math are now reflected everywhere. How isn't this methodology taught in every school?
@@80s_graffitisame thing. tested top 3% in my state and top 5% in the nation by ACT scores, with a 35/36 in english but a 25/36 in math, despite math being my best subject all the way until geometry lmao
This is exactly what I hate about how Maths is taught in school. In most Math classes, it's so hard to understand why all these concepts and definitions and formulas were "contrived" from and why they were made in the first place. When professors "teach" matrices, a student merely leaves with the knowledge: it is a collection of numbers, it can be diagnolized, it could be multiplied with a vector, it somehow solves system of linear equations, etc. Students are never taught the history, that the matrix is simply a notation chosen to represent linear transformations or just anything about the history of why the matrix construct was made. These aspects need to be taught more often, because typically some Maths get defined and exist in the way they are simply because it was convenient and valuable for past mathematicians
Im in high school and was always bad at math until i recently started to connect math with real life examples and videos like these really help
The amount of effort you put into this masterpiece is unimaginable from the animations to going through years and years of math history. Seeing a single video on this channel saddened me a little I wont lie, because this is extremely well made and after taking calculus 1 through 3 made me appreciate what I have learnt more, you gave it value. Very few times do I get out of a 30 minute YT video feeling as good as this video made me feel, this deserves to be put as summer prep for every calculus course out there. Simply splendid.
I am honored, thank you!
@@AWellRestedDog He isn’t lying bro this is truly a masterpiece
Delighted. Thank you!
Goed laten wij het hierbij het dan ook bij simpel houden ,maar zoals gewoonlijk gaat het puur om macht en geld niets anders de rest is gewoon erin gecalculeerd als bijzaak, even leuk meegenomen of is het genomen ? Jij wilt niet liegen joh, laat mij even bijkomen, de leugen die zichzelf voorliegt mag wel eens in de krant komen dik op de voorpagina HOE DE LEUGEN REGEERT
@@ThunderAppeal if you cant appreciate the effort that goes into researching, scriptwritting, animating and editing a 30 minute video on an interesting topic ehile also making it entertaining, then that truly is on you my friend. You are clearly the minority in this situation and not for a good reason. You are entitled to your wrong opinion.
This is what I've been saying to myself all this time. We need to incorporate the history of the math we're learning otherwise it just feels like I'm learning it to pass a class. Thank you for this video. SoME is truly a godsend.
oh man for sure and i thought i was the only one
Yes, math paired with historical stories is a great way to introduce context and is quite frankly very exciting
What is SoME?
@@janusmarais7580 its a hastag trend> summer of math exposition
absolutely agree.
You are very gifted at explaining calculus. I was a math teacher and I definitely would have used your video if it existed back then! A lot of history and also notoriously hard concepts to teach are now well presented on CZcams. That’s the idea behind classroom flipping. Calculus always seemed best taught by exploration such as doing labs and puzzles, or in an applied context like physics. Perhaps it’s like the proverbial elephant and we’re all among the blind men saying rope, fan, tree, snake, wall, etc.. This suggests that math is discovered and maybe that’s the real key take away (because I’m pretty sure it’s not L’Hôpitals rule).
gosh, this is absolutely amazing. No words, you are an artist, a philosopher and a mathematician, and also a youtuber.
This video reminded me greatly of my algebra 2 teacher in high school who was notoriously behind on the pace that the curriculum demanded, but for the sake of having students scratch their heads at the ideas with each other. The kinds of ideas behind math feel like such an incredible system that’s been arranged to work with itself in so many different ways, but often the class is framed in pure stress and only in how to do the executional requirements of math. Her class really illuminated the things about math that I enjoy, but it is very difficult to keep this enthusiasm up taking in more math classes with professors who just see it as I’m giving you the tools to pass the test. This video really brings to light how much there is to improve with schools teach subjects in a way that can be more informative and natural to understand.
Thank you for sharing your experience. I'm glad to hear about teachers like that!
The education system runs on syllabus, exams, assignments, practicals, vivas, theseis, project which all are useless.
They should tell story of how equations came to exist (without using time frame, complicated language, complicated names for obvious reasons it don't become boring) .
You are saying right. I often wonder why teachers or professors don't want to explain the history. They just want to complete the syllabus, they don't want to overwork for trying to explain where I came from, who made it, why you should learn this, where is it applied.
"often the class is framed in pure stress and only in how to do the executional requirements of math" exactly
Once you develop a really deep understanding of the basics of a class, you should be able to fly through the material if you have to.
1:52 Where it began?
2:39 Geometry
3:30 Zeno’s Paradox
4:03 Rectangle smaller than Circle. Or not?
7:43 800s Arabic Numerals
9:00 Coordinate Geometry
10:28 Sin(X) Cos (X)
12:06 Derivative, Integral
12:50 Galileo & Kepler
14:57 Newton
16:08 Leibnitz
17:05 d - differential, infinitesimal
Fluxions
18:29 Diplomat Leibnitz brought ideas to more smart people
19:32 They contributed huge
20:05 Infinite Series
21:17 Limits
21:56 Function (X, F(X))
23:20 Over and over again
23:43 Infinity Itself ♾
24:17 Reflections
• Built around a story
25:38 Jousting with Infinity
26:24 I want to understand important math
27:53
• Professor tries to explain what’s going on
• Once he starts doing examples, I start paying attention
Infinitesimals - philosophers wrestled with it
Expect students to stumble
29:27 Calculus Reform Movement 1990s
You forgot 7:59 he just rickrolled us and almost no one noticed lmfao
Tnq
For the first time in history, an integral equation is stated by Jyestadeva.
The sankalita(integral/summation) of a pada(variable) is half its varga(square). ∫xdx=x²/2 +C
From the basic to the very advanced, Yuktibhasa is the founding text of calculus Jyestadeva (1500-1575) or one of his predecessors had also arrived on the concept of double integration. Multiple integration appeared and developed in Europe in 18th and 19th centuries.
I greatly appreciate your efforts in making this video, and I hope you continue making more, this is both interesting and informative whilst being entertaining
I loved this video, and also the first week of every class as an engineering student.
Where I lost hold of the subject matter was where the neccessity of memorization took precedence over the story being told.
One positive lesson learned was for me to treat calculus in particular as a language. What I needed to do better in my undergraduate-level calc classes was to become fluent in that language by recognizing puzzle pieces of that language. I needed to memorize trigonometric substitutions. I could visualize the concepts, yet that rote work was my challenge.
A historically motivated teaching method would be fantastic; I do think that going down a level to the problem-solving motivation would be even better, especially for us engineers
@Jake you make like An Inductive Summary of Physics, for a similiar process. Professor Ellias is still developing his course which you can see czcams.com/video/bQ53xy9gRLw/video.html
Frankly the issue is there isn't enough time. Most students take Calc 1 in high school and a 40-60 minute class just doesn't cut it (especially when teachers are responsible for preparing their students for the AP exam a few months BEFORE the course is even completed)
@@branpod “especially when teachers are responsible for preparing…”
That’s why society is dysfunctional. We have an educational system designed to tell people WHAT to think rather than show them HOW to think. Plato understood how to educate children, and he’s been dead for over 2,000 years.
@@branpod Totally agree. Took Calc BC (1 and 2) in HS and totally bombed the AP exam. Retaking Calc 1 in college where lectures are longer and I can learn on my own has made Calc feel like a walk in the park
@@josephcoon5809 the question is whether that works at scale or not. In a system where everyone is forced to learn, can you generate enough curiosity/intrigue to push the course forward? And how do you do it given the time constraint?
As someone who enjoys learning, I obviously prefer the Plato method. But how to implement it given the constraints we have (every child must be educated, must ensure certain standards among education level) is the million dollar question.
I feel sad that these western mathmeticians published their theories and discoveries and that are still available, but Indian textbooks where burnt off in attacks on oldest Universities of the world, what knowledge could be there !
I was also surprised at first to primarily find mentions of western philosophers / mathematicians in books and articles about the "entire history" of calculus. There is so much that the Abbasid Caliphate, Chinese and Indian civilizations (just to name a few) contributed over thousands of years, but I'm guessing that a combination of there being a lack of readable / intact sources and historian bias has contributed to the shaping of this kind of western-focused narrative.
Chill dude. Nalanda wasn't that big of a deal in Mathematics, it was mostly philosophy and most of the books in Nalanda were there in China during its destruction! The Indian books are not there only because people stopped studying them, and focused more on astrology! All the books that have survived were not like 1000s of years ahead of Europe, they were at times only 100-200 years ahead! The Gurukul system focused on the transmission of knowledge from teacher to student and not amongst teachers. The caste system prevented almost everyone from gaining an education, unlike in Europe where even poor people could get an education through philanthropy. This is the reason why Indian Mathematics died, not because Nalanda was destroyed!
@@swagatochatterjee7104 bro you are very innocent, huh 😂, Indians who invented zero number system, navigation even the first plastic surgery was done in India in time ancient than ancient, you need to gain some knowledge first... Go and read some history and facts 😂
@@swagatochatterjee7104 lmao you dont know shit do you?
@@AayushPatel-gc3fw Alright yk I've really been questioning the whole 'india invented 0' because I'm an Indian and it makes no sense such a simple concept was 'made' by us. Aryabhatta may have made some serious mathematical innovations but no fucking way 0 was made by us
40 years since I was in AP math classes and this ignited the excitement I had about math back then. Math rocks.
It’s a very interesting journey which obviously went through a lot of math trauma was rediscovered but appreciate your efforts!
This would probably have to be the best made video I've seen from someone with under 10k subscribers.
This is the quality you'd get from professional full-time channels with teams.
Very well done.
Thank you! :D
@@AWellRestedDog i just wish the audio was a little cleaner but other than that this video was great. I didn't even know you had less than 10k subs i just assumed this video was made by a professional content creator if that makes sense.
My first calculus course was entirely theoretical, (honors calc, U of Michigan, 1971), which was great for me. We actually evaluated only three integrals the whole semester. My brain is great at seeing relationships, but lousy at memorizing formulas. The approach I had in that first class helped me solve three-dimensional sphericak integrals when I could not remember formulas, and made it possible to teach 3-d integration to someone I was tutoring after not touching calculus for years.
One of my later undergrad classes did have a lot of historical context - like this, showing how collisions of ideas pushed the path of mathematics. I doubt I would have appreciated the class as much had I not already had a firm foundation in the subject.
The problem is that people think that there are "right" and "wrong" ways to teach math. One size does not fit all - I am more comfortable with a strictly theoretical approach, while others may be better with a, for lack of a better word, developmental approach.
One other observation: the ability to handle abstraction is dependent on both experience and brain development. I've known a number of people who "didn't get math at all" in high school, who, when they were in their late twenties or even thirties, has to take an algebra course required for graduation, found (with excellent instruction, I would add) found that things "made sense". Some even went on to become math majors - something they would have never expected. Math not taught at a student-appropriate level is a disaster.
ok
Me right now. I "didn't get" maths at all as a kid, and now in my twenties after studying computer science, AI, and physics, I'm rediscovering all the mathematical wonder I missed out on back in childhood. Now that I'm looking at things from an applied/practical perspective, even the theoretical aspects of pure maths are starting to make complete sense.
great comment
color me envious
@@DanielRodrigues-bx6lrim in the same boat! AI has increased my motivation conquer “mundane” subjects with renewed vigor!
Amazing video my man. Thanks for making it!
Thanks for shedding light on the beauty of calculus, looking forwards to more videos in the future.😍
Great editing and presentation! I recommend any math-heavy majors to take a history of math course during undergrad- it’s essentially this video but you dive into the proofs and deeper biographies of each contributor.
Great editing? There were several spots where he flashed things on the screen so briefly, if you blinked you might not even notice them.
@@jursamajshouldn't have blinked then
@@jursamaj that's the CZcams joke edit meta man, where have you been?
Absolutely
@@quintinpace2627 I've been on YT for decades, never heard of that.
I took Calc 1 twice (credit didn't transfer) and it wasn't until I was like 2 years into my EE major that I really understood what these weird terms (derivative, integral, limit) meant in a conceptual sense. I really love calculus now
Go on...
@Steven Ortega Well for one, repeated exposure. The more you're seeing it, the more likely you are to have it explained in a way that clicks. I think something else that helps is realizing that things like integrals and derivatives are physical and not things mathematicians made up. Think it more as "discovered" as opposed to "defined". It may help to consider something physical like finding the area of a baseball field by fitting a function to the outside wall. I'd encourage anyone to at least mentally work out things like the bounds, function, and a potential answer as a way to see things in a more physical sense.
Similar experience. I took macroeconomics a year after calc 1 and 2 and I remember at one point messaging my prof saying "Wait... are we just finding derivatives and integrals?" and he was like "Yep, but we don't use the terms in the class because most students wouldn't have taken calculus"
You know, taught this way, people who normally don’t care at all about Maths in general might actually understand it and appreciate it but the way it’s taught makes it almost seem like something you learn throughout your education arbitrarily. I hope as many people as possible get to see this video and maybe it changes something in how people view the subject!!
What an amazing video. I really hope you make more. They would be just an absolute delight to watch
I can't believe that the video is 30 minutes long, it went by so quickly! It gave me a sense of awe and wonder for mathematical struggle and achievment, so thank you! I love thinking about what some of these great mathematicians/physicists would be able to accomplish with our modern tools...
same here it feels like a snap
I greatly appreciate this approach to calculus. So often we hear what someone did (invented) but not what they had to think (and how they had to think) in order to do it. This approach, especially annotated with the timeline, provides a lot of insight. This deserves many more subscribers than it has.
I've been looking for this video for 8 years since my Calc 1 class. Thank you!
This is actually the coolest video I've ever seen. I'm currently in applied calculus 2, where the content is extremely accelerated and the exams are 80% of our grade. I have always been interested in the deeper proofs of the concepts however, and I usually try to answer homework questions by forcing myself to solve the problem by deriving the equation or process from the taught equations in the book, instead of a calculator. This video answered many of the questions that I was frequently unable to overcome this far, and honestly brought a tear to my eye knowing other people out there think like this. Thank you so much for making this!
1:07 Damn, I thought I was the only kid who ever lay in bed haunted by the concept of infinity.
Me too, until that book so confidently and nonchalantly declared how universal apeirophobia is lol
@@AWellRestedDog Infinitude needs to come with a warning label because it can really mess with your mind if you let it. When I was a kid I came up with my own somewhat inferior version of what I would later learn was Zeno's Paradox: for one object to touch another, it would have to pass the closest possible distance between two objects; but since, whatever distance that was, you could always move halfway closer to it, I concluded that perhaps things never actually touch, and it's just an illusion that we think they do.
I watched this over a year ago, but now coming back to it (almost) post real analysis is really enlightening. Like I actually know what you are talking about the epsilon and delta values and how that plays into what calculus actually is on a conceptual and foundational level. Its super weird and hard to summarize, so you did a great job explaining it imo.
Thank you very much for making this Video!
This video managed to answer several questions that I had about calculus, questions that I'd spent a frankly ridiculous amount of time and energy trying to work out. So thank you. I'm honestly shocked that this channel doesn't have more subscribers, especially considering how easy it is to see the amount of thought and effort that you put into this.
I am a huge lover of the history of calculus and 100% would love to see this as a continued series. Great work and great humor as well!
Man, we need you. Pls, carry on producing content
I love the content, and this has excited me tremendously to continue my studies in calculus. Thank you
Great video! This is definitely something that was mostly missing from my classes, so it's very valuable to have a clear, accessible summary like this.
Edit: Congratulations!!!
Thank you, I'm glad you saw it like this!
Wow, an amazing new math channel! I've seen documentaries on the history of calculus, but I think your take on this was even better.
Thank you, I am honored!
because his emphasis on pairs and duality does make the lore much more spicy
Such a well-made video. It's truly sad that given that we only have 3 months to cover integrals, derivatives, series and limits, there is not enough time to teach it in-depth. Math with history is such a beautiful thing. Makes me feel like I want to keep learning forever.
1st video 1st hit. Congratulations man! This video was awesome. Most students are taught math without exploring the beautiful “mathematical thinking” that gave birth to these concepts.
I have about a month of Calculus 1 to complete and I’ve been falling behind lately and felt unmotivated. With your video, you’ve brought back the excitement to study those ideas thoroughly. Great job!
How did it go?
Thank you for asking. I caught up pretty quickly and did well on my finals. Now as I am in Calc 2 and we do multivariable calculus things've got even better though significantly harder.
@@kacperdrabicki best of luck!!
@@kacperdrabicki How are you doing now? And what's your major, if you don't mind sharing? I am a CS undergrad, 2 years from graduation.
@@jayvaibhawverma I am a physics major in Poland. I passed my first year of studies, began my second but eventually I had to take a gap year due to personal matters. I will be back in October this year and will have two years left (BSc is 3 years long).
This might be one of my favorite videos on youtube. The context of the math is so imprtant, and it was only once I got to engineering physics, that my professor started talking about why so many numbers are based on peoples names. This idea that these little concepts we were using for literal piece of their creator's mind pushed through time and into my mind was insane. Knowing more about them, their state of mind, what they did in their lives, and how that got them to the point where they grasped such a monumental idea is just a whole other train of thought that really allowed me to encompass math with this nice bow like a present.
Fitting quote:
"If I have seen further than others, it is by standing upon the shoulders of giants."
- Newton.
Good job on this video, man. I really mean it, I learned a lot.
I hope you won the math/education contest. If not, you should have. This is a work of art that needs to be preserved.
I'm a medical student with a casual interest in Mathematics and I'm amazed at the clarity you explain concepts. The animations were great and the story was riveting. Looking forward to your next videos!
Thank you, I'm honored!
I am a Political Scientist with a casual interest in Mathematics, and I agree with your sentiments entirely.
@@AWellRestedDog please make videos on history of mathematicians
@@robmaelstorm23 Im a chicken with no Education, and i agree
This is among the best well-made videos I have ever seen. Please make more, sir! I look forward to learning more from you!
Aryabhata just finding Taylor series of sin in the 500s
This was incredibly interesting, thank you!
I went into this without ever having studied calculus, and I now feel like I could go into it and actually start learning it and understanding it. Thanks for the great video.
This video is so smooth to watch, 30 mins long, yet it felt like 5 minutes. I cannot push more the idea that historical interpretation is one of the fundamental "theorems" to learn in a math class, and even science class. This disscusion of course extends to giving time for wondering on remarkable subjects of math. And I'd push to say that students, such as myself are very amazed by pathological results in math and science, but they need time to mush theese interesting concepts, especially when they imply infinity, either potential or as a value.
This channel is so underrated please make more videos you did an amazing job! 🎉❤
I love your effort to distribute calculus for all, you have a new subscriber here !!
29:15 I love the idea of mixing the calculus with its history. By teaching the history in calculus, students will become more interested in studying calculus. Then some/more of the students might research more about the history of calculus.
Maybe One day, By researching its history, There is a chance that If they find the smallest flaws in Calculus, they can rewrite and re-shake the whole calculus, and then we might be finally able to solve the Millennium Problem that can be only solved by the new/rewritten calculus.
This is my idealistic idea but it may not be the realistic idea.
@@nihilisticboi3520 While there certainly aren't flaws in the formulation of calculus, I think there is a lot of room to develop new perspectives on it that may be incredibly helpful for solving difficult problems.
What a great video! Learning the true context of any subject is so much more important in tackling with the rigor that comes up later. I remember feeling completely lost during my real analysis classes because I just couldn't wrap around these ideas of epsilon-delta definitions. I remember thinking how in the world did someone even begin to think about these ideas. Turns out, it didn't happen overnight. There were hundreds of mathematicians and philosophers involved in this dialogue over a course of thousands of years. So of course, I would feel lost if I skipped the meat of the all that development and directly started with the modern formulation.
man... thank you for this video!
Wow, in college I learned series, limits, differential, then integral. It was so natural, and my instructors all made me love it! Naturally had to go on to diff eq, linear algebra, and pde's! Lucky to have had such great instruction making the rigor and painful homework worth it 🥰
This is my favorite math video EVER!!! All these things we take for granted in uni (ex. the Cartesian plane) makes sooo much more sense and interesting once you understand where they came from. This is the side of CZcams I want to stay on. Thank you so much for this amazing mini lecture :)
I've never learned calculus in a formal setting and I'm just starting to delve into the subject. This was so clear that I was able to understand everything, except some of the specifics of the notation, with very little background knowledge!
Please please please make more videos! I would love to learn more from you.
I always struggled with math in school because I wanted to know why concepts led into each other and what questions were asked that led us to these solutions. And I was always given the stink eye and dismissed by my teachers. I couldn't learn math from memorizing formulas, but this historically informed approach really worked for me.
Once again please please please make more videos! And thank you so much for this experience 🥰
Thank you, I'm really glad you were able to follow this without having formally learned calculus. I wanted to make this as friendly to people who didn't know calculus as possible, so I'm happy to hear that that worked for you!
And I am planning to make more videos (though not exclusively about math. If things go to plan, the next one may look at the literature and anthropology of loneliness), but it will take a really long time!
@@AWellRestedDog over 4 months still not enough?😢
After doing the precise definition of a limit in high school, through calculus and multivariable calculus I never really understood wtf it was about, finally after years of looking at it, with the historical perspective I got what it meant and why it's actually important.
Thank you so much for that explanation.
Great video and David Bessoud’s words really clicked for me. In my first year of calculus I was baffled by how the hell anyone could have came up with it. Algebra is quite intuitive and then going into calculus it feels like you have to take a leap of faith in the sense that you must just learn the stuff without really grasping it as your pressed for time. I remeber thinking that they should teach a history of math class before learning calculus just to understand how people came to these great ideas. Really reassuring to hear that many others have thought this too.
As someone who didn't connect with Calculus at all and subsequently failed; I found the history behind what it took to build up the knowledge fascinating, thank you for taking the time to present this.
Mactan
I don’t wanna know none of that nothin!
This is just incredible!
The telling was fast and that got me really focused and interested, I really enjoyed and even laughed. I love this kind of lectures, that makes you want to think everything through.
Love it!
One of the best math videos I have ever seen. It honestly made me tear up when you mentioned the "pair-ness" involved calculus and it's rich history. This is the testament of how far we have come as a species and how far we can still go. You, sir, have created a masterpiece. Thank you for this.
This video is soooo good. I can’t even imagine how much research and work went into this. And I love your simple animation and presentation style! I’m currently in Pre-Calculus, on my path to become a civil engineer. This video really calmed me down about continuing on to Calculus, so thank you for that.
Please make more videos if you’re able to! I’d love to see you tackle other topics!
Absolutely stellar video! The production was quality enough to teach clearly and be entertaining. And as a student fresh out of AP Calculus (AB), this was brilliant. Know the history of calculus really did help develop the ideas behind it all. Thank you so much. :D
This is one of the best some2 videos I've watched. It totally doesn't feel like 30 minutes long, and the history of mathematics in general is just really really fascinating, and helps frame math is such an interesting and different way, and makes it way easier to understand these ideas.
Thank you, I'm honored that you think that!
I'm doing my first year in computer science and as a guy who isn't satisfied with just memorizing equations and getting high scores in exams but actually wants to understand the uniqueness, usefulness and subtleties of these mathematical/scientific concepts....this is one of the best YT videos I've ever watched. Thank you, you've just earned a subscriber.
humanity of math is a great way to describe the video.
I've always failed math lessons because they only show the numbers, not the background of it.
I had no idea you had a second channel until 3Blue1Brown's video. This is amazing. Great job, man.
This has been very enlightening, both in terms of clarity on subject matter and reflection on effectiveness of pedagogy. Thank You!
This is an incredible video, so well made, I really enjoyed it and learned a lot. Thanks
Anyone learning calculus would benefit massively from this video. And not just calculus- these are extremely important events in the history of mathematics we're talking about. Well done to the person who made this video. Not all heroes wear capes..🔥👏🏻👏🏻👏🏻
I don't wear a cape....
This was very well done and even though I knew a bit about the history, I still learned quite a bit! You put this seemingly mysterious math into a new context that makes it much less of a mystery. I look forward to more of your videos :)
This is why I took "numbers" and Einstein classes in college along with calculus. Much of the concepts in this video were covered there. Gave me such a broader picture and understanding of math as a whole.
Sorry Max. Can I access this class online? Or is there a book that covers this I can buy?
@@adeyemiadeyemi6668 Unfortunately I don't remember the titles of the books I read, but if you're interested I would read up on the famous Greek mathematicians' work, not only their results but the logic they used to arrive there. Maybe start off with Euclid and gain an understanding of how geometry became a concept, and move up the historical timeline from there into algebra, calculus etc. I'm sure there's plenty of videos and books on the internet regarding these topics which are easily accessible. Galileo's "Two New Sciences" is great at demonstrating the thinking which led to the transition from geometry into algebra, and other topics. Einstein's "Relativity: The Special and General Theory" will give you a completely new insight on math regarding physics. The first 8 or so chapters of the book alone provides so much insight that you will be able to understand the basic concept of time dilation and length contraction (and calculate it), as long as you really take the time to make sure you're understanding what he's saying - which I think reading up on the other materials I suggested will greatly help.
been watching 3 Body problem, and I love how this history integrates into the theorys involved in the show/book.
this is an amazing and very informative vid, i loved the way you presented all the information and i definitely learned something.
im currently finishing a bachelor in economics and would love to go back to highscool so i could have you as a teacher, great video and channel!!
"The humanity behind math," if this were the starting point for any math course, many people, including myself, would see it very differently. Thank you for creating this video; it provides much-needed context for understanding the magnificent subject that math is.
This was a great video, it also shows how important history is to alot of topics and even a basic understanding of the history behind certain subject helps conceptualise and flesh out the basic concepts of a subject
What an awesome video. I really enjoyed the history you brought in this video. Thank you!
Thank you for this video. I am an engineer now. But I actually never liked math because I never understood the motivation behind it when I was in school. I just kept taking math classes because I had nothing else to do and engineering was what was open by the end. But I would have enjoyed my college classes a lot more if I understood the history and motivation behind calculus back then. For me it's not just enough to know the what mathematicians and physicists did it's kind of boring. Understandings their motivations and why they needed to figure this stuff out is important thing me and gives context to me as an engineer. I think context is important looking back on this and I think kids miss this learning math and physics. Videos like this make me appreciate stem much more now then I ever did in college. I really enjoyed this video.
this video is amazing! you should continue making videos like this, it's incredible and is now making me want to read calculus books in the library when school starts
:D I'm glad to have inspired you! You can check out the further reading in the description if you want my book recommendations.
Wow this is an incredibly appreciable explanation. I see why this won the SoME. Looking forward to what a well rested pup brings
As a current Aerospace Engineering student having just took calc 1, 2, 3, and diffeq in the last year I was familiar with all these topics, but learning about them in a linear context of time is such a great way of presenting them. Great video. Thank you!
Hey dude your really cool, i aspire to become like you one day :D
Hey bro can you tell me what aerospace engineering can do should I choose aeronautical or aerospace I want to go in fighter engineering fields
@@usaidahmed9566 from my college search most degrees are simply called “aerospace engineering” which can definitely be a step into fighter work as it encompasses structures, aerodynamics, controls, etc. but if u wanna go right into working with that sort of stuff I would say the Air Force is probably the fastest way to get there.
"having took"? Reveals preoccupation with left brain functions at the expense of the right. Hope you get to squeeze a little Shakespeare in there...
It shed a new light over the world of mathematics for me. I really love the approach this video has taken to humanize the efforts put into finding such huge feats in the history. I remember when I first took my calculus class, infinity and laws around it was a preconceived notion as if it existed for the sake of existence making you insensitive of the idea what it actually repesents. Im glad I came across this video :)
Wow this was a great radio. I've known some of the story but the way you tell it is really great. I look forward to future videos from you.
So great! Thanks for making a wonderful video!
When I studied maths at university I was blessed with great profs because many of the concepts I did not struggle with. It's somewhat surprising to me that you see these great minds like Euler, Leibniz etc who are so revered in the field struggle to get a grasp of something that is integral to introductory maths courses in 21st century.
Thanks man, Being a maths tutor, I know how much efforts you have taken to shoot this type of video, feels very lucky to find this video
Search Kerala madava caluclas
This is such a professional video! I loved how you gave every person and event you described a really tangible visualisation and I could follow your video perfectly.
Animation, explanation and clarity (as well as title) are without a doubt amazing. But I want to emphasise something else I especially liked, which is the narrative.
According to your channel info, you enjoy literature, which is quite noticeable given the excellent “dramaturgy“ of your submission. I very much like this approach because it’s making your video very memorable; along with the visuals and the outstanding interview at the end (which wraps it up very good), I‘m not even surprised that your video has blown up so much.
Long story short: What an excellent video, I hope and suspect you‘ll win.
:D Thank you so much for the constructive praise--I'm delighted that you liked my narrative and presentation!
@@AWellRestedDog What tools did you use to make the video?
Absolutely needed this video. Thanks
Brilliant, comprehensive summary of maths and adequate appropriate explanations. Thank you👏