#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!
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
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)
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.
@@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.
@@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
@@notorioussmoke2836many students in these classes may only apply a single minute of one lesson, once, and i’m considering the breadth of majors who end up having to take these classes. it’s hard to get someone to pay attention to something they are well aware they will not use in their careers. showing how it does apply to some problems, and how calculus leads to correct answers/solutions to these problems is more engaging. As much as i obsess over patterns, application is everything, otherwise it’s just patterns.
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
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 UA-cam 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.
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!!!!
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.
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 UA-camrs than reading the books and having lessons. That hurts 😂
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 😂
@@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
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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 UA-cam. 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).
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.
@@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.
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.
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.
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
@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"
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 ua-cam.com/video/bQ53xy9gRLw/v-deo.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.
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!
@@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.
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.
@@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
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...
I'm a nerd and I already finished school but I never got any education on calculus. My business course does not have this subject as our maths only revolve around business stuff (accounting, depreciation, taxation, interest rates, etc.). It was all very mathematically simple. So I hopped on to UA-cam and tried to get a head start on learning more math. And I gotta say, THIS IS THE MOST IMPACTFUL video I've ever watched re: Calculus. I actually feel more interested to move forward now. I tried jumping into equations and solutions but I always thought, "why are people doing this? What's the point?" And this video gave me the answers. Thank youuuuuu
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.
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 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!
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.
@@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).
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!!!
I used to hate math and be terrible at it. I have improved but I still am not good. But recently I have started to enjoy math more. Seeing how everything math is just logic really makes it more fun to learn. It's like solving a puzzle. Very much unlike how general education teaches math, e.g. making us memorize formulas or simply stating concepts as rules instead of logical discoveries/conclusions.
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!!
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.
math became beautiful to me after reading kepler, I realized music and number and geometry all express eachother idk if this is common knowledge but it blew my mind
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!
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.
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.
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!
"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 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.
@@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.
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.
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.
8:35 you just missed this part: Al-Khwarizmi's popularizing treatise on algebra (The Compendious Book on Calculation by Completion and Balancing, c. 813-833 CE[13]: 171 ) presented the first systematic solution of linear and quadratic equations. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications.[12]: 14 Because he was the first to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation),[14] he has been described as the father[6][15][16] or founder[17][18] of algebra. The term algebra itself comes from the title of his book (the word al-jabr meaning "completion" or "rejoining").[19] His name gave rise to the terms algorism and algorithm,[20][21] as well as Spanish, Italian and Portuguese terms algoritmo, and Spanish guarismo[22] and Portuguese algarismo meaning "digit". In the 12th century, Latin translations of his textbook on arithmetic (Algorithmo de Numero Indorum) which codified the various Indian numerals, introduced the decimal positional number system to the Western world.[23] The Compendious Book on Calculation by Completion and Balancing, translated into Latin by Robert of Chester in 1145, was used until the sixteenth century as the principal mathematical text-book of European universities.[24][25][26][27] (Wikipedia)
I did leave out quite a lot of his contributions unfortunately, which I regret. When I have time, I'll try to remember to add a link to the further reading!
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.
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..🔥👏🏻👏🏻👏🏻
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.
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.
My impression when first learning calculus was that the ideas presented that were unique to it were much simpler, less baroque, more smooth if you will, compared to trigonometry or algebra which I had been studying exclusively up until then. I was first presented with math as an abstract that was jagged, but calculous presented math that was soft. To me that makes its ideas simpler.
I've always wanted a good video on the history of Calculus, since I always like knowing the history of Maths; this video was really great, thoughtful and original, thank you
Thank you! I was surprised that I couldn't find any (mostly) comprehensive videos on the history of calculus before I made this. Part of my motivation to make this video was to fill that missing piece!
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.
Helping my son recently with his high school pre-calculus, I simmered with rage at pure mathematics that I hadn't felt since college. This is math to find how many angels can dance on the head of a pin without actually measuring the feet of the angels, their dancing skill or the breadth of the pin. I do feel that blending the history of Calculus' origins would help; Stephenson's Baroque Cycle was a delight.
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.
The first calculus course I took most of the class ended up failing and dropping (myself included). This came as a shock because I had run through pre-calculus effortlessly without paying much thought. Unfortunately that class was very poorly taught (the professor even had their own notational system). Over the break after failing that course I picked up a “Calculus for Dummies” book and the following semester I wrote a 10 page biography on Newton for an English class and I unpacked the history of Calculus. I got much more out of those exercises than I did the previous Calculus course because I had to put concept and context before procedure. When I took Calculus again (at a different school) it was effortless.
That's an inspiring anecdote, thank you for sharing! I haven't had the misfortune of getting a teacher like that, but I have little respect for people who intentionally make a subject much more difficult than it needs to be. I'm glad that learning the history of calculus also helped you understand the subject better!
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.
I love this. The history and stories of maths and mathematicians is criminally ignored. It’s the story of how we learned to think and problem solve, a incredibly detailed recording of what cultures valued and how tiny steps in progress is made by individuals who almost always have a balance of collaboration and competition with the minds before and of their time. People remember stories, not mathematical formulas. It’s easy to forget that they are the same thing.
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 UA-cam I want to stay on. Thank you so much for this amazing mini lecture :)
So when I first watched this I did not understand it at all. After 5 math history videos for Veritasium coming back to understand all of this feels so rewarding. Thank you for the amazing video.
Excellent video. I failed Calculus 1, retook it and passed with a C, I failed Calculus 2. Meanwhile I aced Foundations of Math and Number Theory, I do think understanding the motivations and allowing the student to play with the concepts facilitates understanding and knowledge. Pure math isn't easier than calculus, but it does feel more intimate becaude you build your understanding from axioms, that's why I think it felt easier for me.
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.
Dr Bressoud is so correct. My interest in calculus came when I noticed how it is applied to modern science. It not only made me excited but I became intrigued. So I then wanted to understand the history and therefore when my professor speaks in class, I listen and soak it up like a dry paper towel.
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.
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!
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
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.
@@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.
Thank you so much for your insights about how calculus is being taught in classrooms . For years a question that has always stuck to my mind was how many of the great discoverers in the past had so much mastery in the concepts of each topics and how they were even able to visualise things like Archemidies infinitly cutting a circle to form a parabola . I always used to wonder where the modern education fell short , Through this video it made me think how Gotfried Wilhelm Leibniz who was initially a lawyer was able to learn mathematics directly from Christian Huygens himself , it makes me wonder it it would’ve been the same if he was educated from an educational institution of his time . In my opinion what the modern educational system lacks is the attitude of discovery . In my years in high school I was never taught any of these concepts behind calculus, how calculus was being taught to us was just to simply byheart the forumulas and apply them in questions , we were never given the concepts behind these formulas or weren’t even presented with a chance to question them . Watching this video and knowing more about calculus it is stupidly funny how integrals were simply just defined as functions to find the area under the curve . I do quite heartly welcome the idea of including the history such topics being taught in school and colleges .
oh my god. could you make this a series or something? the lack of this kind of education is why i failed math from middle school on and now go into a blind panic whenever i have to count anything. i need to know WHY the rules are what they are, how they came to be, how we know they're correct.... thank you thank you thank you.
Always happy to see people advocating for the genetic approach to mathematics. Yes, in the years following the initial discoveries we've created some nice and tidy proofs and rigorous categories, but those are very unnatural places to start from a pedagogical perspective; they may be easy enough to understand on their face, but it's often very difficult to see how someone got to that point in the first place and why it is significant. Mathematics education needs more focus on history and less on rigor, at least until you get to grad school then you can more heavily emphasize rigor, which is ultimately just about convincing people of your mathematics and, thus, pertains more to the trade of the mathematician than to the field of mathematics itself.
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 its 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.
PLEASE MAKE MORE VIDEOS 🙏🏻 this was incredibly well done, your voice is pleasant to listen to, you were deeply thorough yet entertaining, and even with only grasping half of what was said I was able to watch all the way through and appreciate it. I am an adult maths learner - after fifteen years in history I’ve switched to coding and computer science. In this effort to better myself, I’ve returned to maths to better understand comp-sci and have gotten to college algebra with mental blood, sweat, and tears, but I want to keep moving forward and get to calculus! I may have only grasped bits of the content, but your video has helped me understand where I’m going and what to strive for, plus a deeper appreciation of the human historical struggle to understand and advance this knowledge. Thank you and I hope you make more math related videos (maybe algebra??? I can hope 😅). Loved the quotes, but did you know text in sans-serif fonts are easier for dyslexics and neurodivergent people to read? Not always as aesthetically pleasing, but I know a lot of dyslexics pursue maths and if you use a lot of quotes or written content in future, I just wanted to offer that bit of knowledge if it can help. Either way, well done! May your channel grow and be very successful! 🎉👏🏻✨⭐️👏🏻🎉
I'm honored to have so many adults appreciating my video, and it's a pleasant surprise that this was able to merge your specialty with the new subject you're trying to learn more about! Best of luck with your journey. And thank you for the font recommendation--I completely forgot about that!
Well, I feel utterly pathetic about how I spent my summers in high school now. Jokes aside, this is an awesome and clearly explained summary of the history of calculus - I learned a lot watching it. I would love to hear more about various ancient theories of math and physics, as I find the way they justify them to be fascinating.
Between optimization problems and newtonian physics as well, it was fairly obvious how useful and revolutionary calculus was. You'd have to not be paying attention to not see how useful optimization was in production. Or maybe I am easily impressed at making optimally efficient cans. But if you think that's boring that is kind of on you. Although I did get lucky taking physics and calculus the same year and seeing the connections. Then again I like learning for learning's sake, I was definitely the student that it was enough to show that it was logical and consistent. I was entranced by the innate beauty of it, and truly fell in love with math at that point. Of course I like history too and would be fine with sparing a week or so, but I'd like to keep it largely the same. However, I took it in highschool and we had more time to go over stuff.
Actually the ideas of series was well established in Kerela School Mathematics in the 13th century way before Euler started working on them, they should have also known about differentiation and integration but they didn't formalise it.
@@gasun1274 no dude. chill. Don't bring in your nationalistic talking points. I won't sympathise with you! There was never any continuous tradition of mathematics in India before Europeans came. So chill! No aeroplanes were present in India in the Vedic age. The discoveries we made in isolation, were almost during the same time Europeans made and were great ones. One shouldn't need western validation for the same! And trust me any decent Western Historian of Science knows about all the Indian achievements. Focus on the achievement and not who did it! This is the Indian philosophy!
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!
I am an engineer and totally agree with prof Bressoud's observation that no single engineer says that calculus is usefull on a daily work. Totally true (at least in my country). But as far as I can recall, calculus is always taught as a developmental tool to reach some particular target or to solve a specific problem, not a general purpose tool (like excel). That is, to me, the true value of calculus: being a tool that enables you to develop another tools or solve problems; much like a programming language enables you (with reasonable time to learn, practice and code) to write a software masterpiece
as someone who hasn't taken a single lesson in calculus yet, I'm glad I came across this video. It paved the way to me actually being interested in calculus and excited to study it, which to me is great since all my life math has been a weakness of mine, even though I've appreciated the beauty behind it before. This video helped me further appreciate said beauty, and further set in stone my motivation to actually start trying to befriend the monster that is mathematics.
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 :)
I'll never forget watching this video and realizing my understanding of Calculus is also now an atom of Calculus. This is exactly what I needed. Infinity as a never-ending process is the most profound and intuitive explanation of infinity that I've ever heard. I now understand infinity as part of every equation - an allowable virtual boundary constrained symmetrically within the equal sign itself. I began teaching myself Calculus during the pandemic, and I stumbled with way more than infinity. I really believe my understanding of Calculus has gone from linear to exponential. Can classic physics be modeled in integration and can quantum physics be modeled in differentiation? With that being said, isn't electromagnetism explained with Calculus as a whole? Say what you will about UA-cam and big tech, give them credit for providing the platform that allows me to turn huge corners like this one! And let's not point fingers at academia. It's at the mercy of economy. I really hope we can stop looking for villains. We will always find them. If it's not person A, it will be person B. Like a never-ending cycle. Thank you!
I hope you continue finding success in teaching yourself. I do not share your optimism regarding academia. They aren't at the mercy of economics. They are at the mercy of their own intellectual arrogance and pride, and most care more about their standing among peers than they do about actually teaching students. I attended a private religious university, and even there, the arrogance and weakness of the professors and administrators was boundless. I actually feel hatred for them, because of the energy and time i wasted trying to impress them, and because of how they have degraded and perverted the pursuit of knowledge, which i regard as sacred. I don't know where to go to get the education i really want.
While earning a BSEE, I also struggled through those three packed semesters of Calculus, linear algebra, differential equations, complex variable theory, and advanced ideas from Euler. I never used any of it during my engineering career. But the engineering curricula also taught me to solve problems effectively and efficiently, and how to refine those solutions. Some skills were taught, but most were learned intuitively during those five years of high pressure learning. I'm glad that I did it, but I wouldn't want to do it again.
I did use calculus in engineering for aerospace. But, I did not really start to understand a little bit of the basis until grad school and taking partial differential equations and dynamics there. I never did get to understand tensors and maticies and worked with computer models of heat transfer in business for many years. Numerical methods were always my favorite math classes. I could follow your video and everything you said easily (Very well done), but I cannot do the calculus techniques anymore. I will send this to one son who can do calculus in his head and got a degree in art history…now he is getting an MBA. Round and round it goes...
Decades ago, in my teens I happened across these 3 beauties: *Men of Mathematics by E.T. Bell *Calculus Made Easy by Silvanus P Thompson *An Introduction to the History of Mathematics by Howard Eves. Needless to say, I absolutely devoured them back to back & cover to cover, totally fascinated by the biographies & personalities with their challenges, struggles & triumphs. That set me on a path of personal 'mathematical enlightenment,' education & discovery, which I still enjoy to this day. Whenever people ask me "Why Math?," I love to tell them, "Because it is artistic, beautiful & complex"....abc, all at once. To quote the great genius Carl Friedrich Gauss: "Mathematics is the queen of the sciences..." An apt tribute indeed!! 🤔
On the subject of infinity: Strictly speaking, none of rigorous mathematics deals with actually infinite constructs. You fundamentally can't. You can, at most, allow infinitely many possibilities with a finite description of which possibilities are allowed. It's just a matter of how honest you are about what you're really saying. Coming at things from a more constructive perspective often illuminates a little better what supposedly infinite constructs are really about. And playing at the edge of them leads to interesting conclusions which are often misunderstood to say more than they really do, like how observations about the logical contradictions inherent in supposing you can "pair up" possibilities from 2 finitely-describable spaces leads to the declaration that there are "multiple levels of infinity"... which is a much bigger statement, and doesn't really make any sense. The error was in identifying the philosophical notion of infinity with those equivalence classes of "pairable" spaces in the first place. The same goes for non-standard analysis with its "actual infinitesimals". They're no more "actually infinitesimal" than any other "infinite" construct in mathematics. What makes them different from limits is that they're *actually numbers*, not that they're "actually infinitesimal". "What if we could make limits fully behave like numbers, instead of only mostly? And maybe some other stuff like dirac deltas while we're at it?" I'm all in favor of that, and I think it can definitely lead to more intuitive ways of teaching and understanding calculus.
This kind of leads to the bothering fact that many things in advanced theoretical mathematics are just that: highly theoretical. Sometimes the entire idea or question is based on a set of borderline arbitrarily chosen rules that were just established or agreed upon in order to make the entire concept work.
I think part of the hard problem with infinites and infinitesimals is the switching back and forth between the object that is the infinity or infinitesimal and the endless procedure that is the infinity or infinitesimal. I think fractional dimensions are in order to make limits fully behave like numbers. At the limit, the procedure 'folds' into a fractional dimension where the limit is cast as an object actualizing its value.
_> The error was in identifying the philosophical notion of infinity with those equivalence classes of "pairable" spaces in the first place._ Why is that an error? If both spaces are innumerable but one is inescapably larger than the other, why isn't it fair to denote them as differently sized infinities? That serms to perfectly sum up the situation. In a way i take more issue with the opposite mentality: of always associating mathematical concepts with reality. Maths on its own doesn't describe reality. It describes relationships between entirely abstract concepts. Even in physics we always use idealized approximations to the physical world. Take for example how we derive the escape velocity of a gravity well, where we integrate from the current distance to infinite distance from the center of mass. That equation implicitly assumes the universe to be infinitely large, eternally static, and that the reference mass is the only source of gravity in existance. That scenario does not and can not exist in reality, but it's still useful to study since a lot of real scenarios are "close enough" to this ideal. Infinity may only be an abstract concept seperate from reality, but so are numbers in general. They don't need to describe physical situations. They only need to describe relationships to other numbers. If infinity can be defined and manipulated the same as any other number, what makes it different from other numbers? That we lack an intuition for it? If there's one thing mathematics and science should have taught us, it's that human intuition is both limited and unreliable in subjects of fact and logic.
@@volbla We seem to be mostly on the same page here, I'm just applying the same caution you mentioned about the boundary between math and physics to also put a boundary between math and philosophy. As long as we're clear that we're only talking about a mathematical construct, it's perfectly fine to call those infinite numbers and to say one is bigger than the other (Though in constructive mathematics, for example, you may find that cardinalities can't be proven to be totally ordered, and other wierdness. It's worth some caution even then). It's also worth remembering that there are a lot of different ideas about how to extend the concept of a number or a quantity into the transfinite, and they don't agree about a lot of things. What people often do with the cardinality thing is claim that mathematics has discovered something about the nature of infinity (the philosophical concept), but to understand what really has and hasn't been proven, you need to unpack the stack of definitions you used and be conservative about how you map them to anything real.
I can't believe this is your first video!!! Amazingly written and well researched!! Also the name of the channel is really cool! Looking forward for more videos!
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 really want to appreciate the work you put behind this. I'm a first year CE college student and I still have a vague idea about Calculus and Analytic Geometry. I always ask my senior highschool teachers about this, but their answers doesn't really satisfy me and only perplexed me more. Since the pandemic hit, I can only rely on videos on YT to truly understand calculus. Thank you so much, sir!
![The most beautiful equation in math, explained visually [Euler’s Formula]](/img/n.gif)
#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: ua-cam.com/video/xuCn8ux2gbs/v-deo.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
@@notorioussmoke2836many students in these classes may only apply a single minute of one lesson, once, and i’m considering the breadth of majors who end up having to take these classes. it’s hard to get someone to pay attention to something they are well aware they will not use in their careers. showing how it does apply to some problems, and how calculus leads to correct answers/solutions to these problems is more engaging. As much as i obsess over patterns, application is everything, otherwise it’s just patterns.
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
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!
Just found out this was your only upload and now I’m devastated.
They posted another video! Enjoy
same, this was so random
@@enjer3618 new video!
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 UA-cam 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
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 UA-camrs 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?
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
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.
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.
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.
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.
Aryabhata just finding Taylor series of sin in the 500s
aryabhatta died in 550 AD and taylor series were introduced around 1700's.......
He never did
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!
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 UA-cam. 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).
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.
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 UA-cam joke edit meta man, where have you been?
Absolutely
@@quintinpace2627 I've been on YT for decades, never heard of that.
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.
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"
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 ua-cam.com/video/bQ53xy9gRLw/v-deo.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.
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...
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
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'm a nerd and I already finished school but I never got any education on calculus. My business course does not have this subject as our maths only revolve around business stuff (accounting, depreciation, taxation, interest rates, etc.). It was all very mathematically simple. So I hopped on to UA-cam and tried to get a head start on learning more math. And I gotta say, THIS IS THE MOST IMPACTFUL video I've ever watched re: Calculus. I actually feel more interested to move forward now. I tried jumping into equations and solutions but I always thought, "why are people doing this? What's the point?" And this video gave me the answers. Thank youuuuuu
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.
I'm 56 years old and took Calculus I & II twice, and this is the first time I've actually *gotten* what it is about. THANK YOU.
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 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).
40 years since I was in AP math classes and this ignited the excitement I had about math back then. Math rocks.
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
I used to hate math and be terrible at it. I have improved but I still am not good. But recently I have started to enjoy math more. Seeing how everything math is just logic really makes it more fun to learn. It's like solving a puzzle. Very much unlike how general education teaches math, e.g. making us memorize formulas or simply stating concepts as rules instead of logical discoveries/conclusions.
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!!
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.
math became beautiful to me after reading kepler, I realized music and number and geometry all express eachother idk if this is common knowledge but it blew my mind
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
@@WhiteStripesStripiestFan Im a chicken with no Education, and i agree
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.
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.
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?😢
@@AWellRestedDog not fair, there are only 2 videos on your 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.
gosh, this is absolutely amazing. No words, you are an artist, a philosopher and a mathematician, and also a youtuber.
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!
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.
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.
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!
8:35 you just missed this part: Al-Khwarizmi's popularizing treatise on algebra (The Compendious Book on Calculation by Completion and Balancing, c. 813-833 CE[13]: 171 ) presented the first systematic solution of linear and quadratic equations. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications.[12]: 14 Because he was the first to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation),[14] he has been described as the father[6][15][16] or founder[17][18] of algebra. The term algebra itself comes from the title of his book (the word al-jabr meaning "completion" or "rejoining").[19] His name gave rise to the terms algorism and algorithm,[20][21] as well as Spanish, Italian and Portuguese terms algoritmo, and Spanish guarismo[22] and Portuguese algarismo meaning "digit".
In the 12th century, Latin translations of his textbook on arithmetic (Algorithmo de Numero Indorum) which codified the various Indian numerals, introduced the decimal positional number system to the Western world.[23] The Compendious Book on Calculation by Completion and Balancing, translated into Latin by Robert of Chester in 1145, was used until the sixteenth century as the principal mathematical text-book of European universities.[24][25][26][27] (Wikipedia)
I did leave out quite a lot of his contributions unfortunately, which I regret. When I have time, I'll try to remember to add a link to the further reading!
Proofs for quadratic formula were already given by Indian Mathematicians like Brahmagupta , Aryabhatta and Sridhara and some others.
@@धर्म_रक्षक can you cite their works and books? Would like to know more
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.
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....
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.
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.
My impression when first learning calculus was that the ideas presented that were unique to it were much simpler, less baroque, more smooth if you will, compared to trigonometry or algebra which I had been studying exclusively up until then. I was first presented with math as an abstract that was jagged, but calculous presented math that was soft. To me that makes its ideas simpler.
I've always wanted a good video on the history of Calculus, since I always like knowing the history of Maths; this video was really great, thoughtful and original, thank you
Thank you! I was surprised that I couldn't find any (mostly) comprehensive videos on the history of calculus before I made this. Part of my motivation to make this video was to fill that missing piece!
Achtung Engländer!!
@@flappypancake85 Was?
It’s a very interesting journey which obviously went through a lot of math trauma was rediscovered but appreciate your efforts!
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!
Helping my son recently with his high school pre-calculus, I simmered with rage at pure mathematics that I hadn't felt since college. This is math to find how many angels can dance on the head of a pin without actually measuring the feet of the angels, their dancing skill or the breadth of the pin. I do feel that blending the history of Calculus' origins would help; Stephenson's Baroque Cycle was a delight.
“Simmered with rage” ?
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.
The first calculus course I took most of the class ended up failing and dropping (myself included). This came as a shock because I had run through pre-calculus effortlessly without paying much thought. Unfortunately that class was very poorly taught (the professor even had their own notational system).
Over the break after failing that course I picked up a “Calculus for Dummies” book and the following semester I wrote a 10 page biography on Newton for an English class and I unpacked the history of Calculus. I got much more out of those exercises than I did the previous Calculus course because I had to put concept and context before procedure. When I took Calculus again (at a different school) it was effortless.
That's an inspiring anecdote, thank you for sharing! I haven't had the misfortune of getting a teacher like that, but I have little respect for people who intentionally make a subject much more difficult than it needs to be. I'm glad that learning the history of calculus also helped you understand the subject better!
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.
I love how expressive the dog's "arms" are, even if they are just circles
I love this. The history and stories of maths and mathematicians is criminally ignored. It’s the story of how we learned to think and problem solve, a incredibly detailed recording of what cultures valued and how tiny steps in progress is made by individuals who almost always have a balance of collaboration and competition with the minds before and of their time.
People remember stories, not mathematical formulas. It’s easy to forget that they are the same thing.
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 UA-cam I want to stay on. Thank you so much for this amazing mini lecture :)
So when I first watched this I did not understand it at all. After 5 math history videos for Veritasium coming back to understand all of this feels so rewarding. Thank you for the amazing video.
Excellent video. I failed Calculus 1, retook it and passed with a C, I failed Calculus 2. Meanwhile I aced Foundations of Math and Number Theory, I do think understanding the motivations and allowing the student to play with the concepts facilitates understanding and knowledge. Pure math isn't easier than calculus, but it does feel more intimate becaude you build your understanding from axioms, that's why I think it felt easier for me.
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.
Dr Bressoud is so correct. My interest in calculus came when I noticed how it is applied to modern science. It not only made me excited but I became intrigued. So I then wanted to understand the history and therefore when my professor speaks in class, I listen and soak it up like a dry paper towel.
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?
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!
I hope you won the math/education contest. If not, you should have. This is a work of art that needs to be preserved.
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!!
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.
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 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.
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.
Thank you so much for your insights about how calculus is being taught in classrooms . For years a question that has always stuck to my mind was how many of the great discoverers in the past had so much mastery in the concepts of each topics and how they were even able to visualise things like Archemidies infinitly cutting a circle to form a parabola . I always used to wonder where the modern education fell short , Through this video it made me think how Gotfried Wilhelm Leibniz who was initially a lawyer was able to learn mathematics directly from Christian Huygens himself , it makes me wonder it it would’ve been the same if he was educated from an educational institution of his time . In my opinion what the modern educational system lacks is the attitude of discovery . In my years in high school I was never taught any of these concepts behind calculus, how calculus was being taught to us was just to simply byheart the forumulas and apply them in questions , we were never given the concepts behind these formulas or weren’t even presented with a chance to question them . Watching this video and knowing more about calculus it is stupidly funny how integrals were simply just defined as functions to find the area under the curve . I do quite heartly welcome the idea of including the history such topics being taught in school and colleges .
oh my god. could you make this a series or something? the lack of this kind of education is why i failed math from middle school on and now go into a blind panic whenever i have to count anything.
i need to know WHY the rules are what they are, how they came to be, how we know they're correct.... thank you thank you thank you.
Always happy to see people advocating for the genetic approach to mathematics. Yes, in the years following the initial discoveries we've created some nice and tidy proofs and rigorous categories, but those are very unnatural places to start from a pedagogical perspective; they may be easy enough to understand on their face, but it's often very difficult to see how someone got to that point in the first place and why it is significant. Mathematics education needs more focus on history and less on rigor, at least until you get to grad school then you can more heavily emphasize rigor, which is ultimately just about convincing people of your mathematics and, thus, pertains more to the trade of the mathematician than to the field of mathematics itself.
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 its 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.
PLEASE MAKE MORE VIDEOS 🙏🏻 this was incredibly well done, your voice is pleasant to listen to, you were deeply thorough yet entertaining, and even with only grasping half of what was said I was able to watch all the way through and appreciate it. I am an adult maths learner - after fifteen years in history I’ve switched to coding and computer science. In this effort to better myself, I’ve returned to maths to better understand comp-sci and have gotten to college algebra with mental blood, sweat, and tears, but I want to keep moving forward and get to calculus! I may have only grasped bits of the content, but your video has helped me understand where I’m going and what to strive for, plus a deeper appreciation of the human historical struggle to understand and advance this knowledge. Thank you and I hope you make more math related videos (maybe algebra??? I can hope 😅). Loved the quotes, but did you know text in sans-serif fonts are easier for dyslexics and neurodivergent people to read? Not always as aesthetically pleasing, but I know a lot of dyslexics pursue maths and if you use a lot of quotes or written content in future, I just wanted to offer that bit of knowledge if it can help. Either way, well done! May your channel grow and be very successful! 🎉👏🏻✨⭐️👏🏻🎉
I'm honored to have so many adults appreciating my video, and it's a pleasant surprise that this was able to merge your specialty with the new subject you're trying to learn more about! Best of luck with your journey.
And thank you for the font recommendation--I completely forgot about that!
yes Please. Looking forward to the next synopsis.
Dyslexic fellow a as, agree I, yes.
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Well, I feel utterly pathetic about how I spent my summers in high school now.
Jokes aside, this is an awesome and clearly explained summary of the history of calculus - I learned a lot watching it.
I would love to hear more about various ancient theories of math and physics, as I find the way they justify them to be fascinating.
Lmao, thank you for watching. I'm really glad so many people have interest in this subject!
Discussing the history of math is more interesting than doing it but at the end of the day, schools still have to teach you how to do it.
Between optimization problems and newtonian physics as well, it was fairly obvious how useful and revolutionary calculus was. You'd have to not be paying attention to not see how useful optimization was in production. Or maybe I am easily impressed at making optimally efficient cans. But if you think that's boring that is kind of on you. Although I did get lucky taking physics and calculus the same year and seeing the connections.
Then again I like learning for learning's sake, I was definitely the student that it was enough to show that it was logical and consistent. I was entranced by the innate beauty of it, and truly fell in love with math at that point.
Of course I like history too and would be fine with sparing a week or so, but I'd like to keep it largely the same. However, I took it in highschool and we had more time to go over stuff.
Actually the ideas of series was well established in Kerela School Mathematics in the 13th century way before Euler started working on them, they should have also known about differentiation and integration but they didn't formalise it.
Indeed, I realized from other comments that I forgot to mention the Kerela School. But I did add links in the further reading (in the description)!
a lot of amazing mathematical innovations made by indians were left out in western literature.
@@gasun1274 no dude. chill. Don't bring in your nationalistic talking points. I won't sympathise with you! There was never any continuous tradition of mathematics in India before Europeans came. So chill! No aeroplanes were present in India in the Vedic age. The discoveries we made in isolation, were almost during the same time Europeans made and were great ones. One shouldn't need western validation for the same! And trust me any decent Western Historian of Science knows about all the Indian achievements. Focus on the achievement and not who did it! This is the Indian philosophy!
@@swagatochatterjee7104well said
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!
I am an engineer and totally agree with prof Bressoud's observation that no single engineer says that calculus is usefull on a daily work. Totally true (at least in my country). But as far as I can recall, calculus is always taught as a developmental tool to reach some particular target or to solve a specific problem, not a general purpose tool (like excel). That is, to me, the true value of calculus: being a tool that enables you to develop another tools or solve problems; much like a programming language enables you (with reasonable time to learn, practice and code) to write a software masterpiece
as someone who hasn't taken a single lesson in calculus yet, I'm glad I came across this video. It paved the way to me actually being interested in calculus and excited to study it, which to me is great since all my life math has been a weakness of mine, even though I've appreciated the beauty behind it before. This video helped me further appreciate said beauty, and further set in stone my motivation to actually start trying to befriend the monster that is mathematics.
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 :)
man dropped one banger of a video essay and dipped
This is among the best well-made videos I have ever seen. Please make more, sir! I look forward to learning more from you!
I'll never forget watching this video and realizing my understanding of Calculus is also now an atom of Calculus. This is exactly what I needed. Infinity as a never-ending process is the most profound and intuitive explanation of infinity that I've ever heard. I now understand infinity as part of every equation - an allowable virtual boundary constrained symmetrically within the equal sign itself. I began teaching myself Calculus during the pandemic, and I stumbled with way more than infinity. I really believe my understanding of Calculus has gone from linear to exponential. Can classic physics be modeled in integration and can quantum physics be modeled in differentiation? With that being said, isn't electromagnetism explained with Calculus as a whole? Say what you will about UA-cam and big tech, give them credit for providing the platform that allows me to turn huge corners like this one! And let's not point fingers at academia. It's at the mercy of economy. I really hope we can stop looking for villains. We will always find them. If it's not person A, it will be person B. Like a never-ending cycle. Thank you!
I hope you continue finding success in teaching yourself.
I do not share your optimism regarding academia. They aren't at the mercy of economics. They are at the mercy of their own intellectual arrogance and pride, and most care more about their standing among peers than they do about actually teaching students.
I attended a private religious university, and even there, the arrogance and weakness of the professors and administrators was boundless.
I actually feel hatred for them, because of the energy and time i wasted trying to impress them, and because of how they have degraded and perverted the pursuit of knowledge, which i regard as sacred. I don't know where to go to get the education i really want.
I would be very interested in speaking with you about what you've learned and the method you have used to develop your understandings.
While earning a BSEE, I also struggled through those three packed semesters of Calculus, linear algebra, differential equations, complex variable theory, and advanced ideas from Euler. I never used any of it during my engineering career. But the engineering curricula also taught me to solve problems effectively and efficiently, and how to refine those solutions. Some skills were taught, but most were learned intuitively during those five years of high pressure learning. I'm glad that I did it, but I wouldn't want to do it again.
I did use calculus in engineering for aerospace. But, I did not really start to understand a little bit of the basis until grad school and taking partial differential equations and dynamics there. I never did get to understand tensors and maticies and worked with computer models of heat transfer in business for many years. Numerical methods were always my favorite math classes. I could follow your video and everything you said easily (Very well done), but I cannot do the calculus techniques anymore. I will send this to one son who can do calculus in his head and got a degree in art history…now he is getting an MBA. Round and round it goes...
This has been very enlightening, both in terms of clarity on subject matter and reflection on effectiveness of pedagogy. Thank You!
Decades ago, in my teens I happened across these 3 beauties:
*Men of Mathematics by E.T. Bell
*Calculus Made Easy by Silvanus P Thompson
*An Introduction to the History of Mathematics by Howard Eves.
Needless to say, I absolutely devoured them back to back & cover to cover, totally fascinated by the biographies & personalities with their challenges, struggles & triumphs.
That set me on a path of personal 'mathematical enlightenment,' education & discovery, which I still enjoy to this day.
Whenever people ask me "Why Math?," I love to tell them, "Because it is artistic, beautiful & complex"....abc, all at once.
To quote the great genius Carl Friedrich Gauss: "Mathematics is the queen of the sciences..."
An apt tribute indeed!! 🤔
On the subject of infinity:
Strictly speaking, none of rigorous mathematics deals with actually infinite constructs. You fundamentally can't. You can, at most, allow infinitely many possibilities with a finite description of which possibilities are allowed. It's just a matter of how honest you are about what you're really saying. Coming at things from a more constructive perspective often illuminates a little better what supposedly infinite constructs are really about. And playing at the edge of them leads to interesting conclusions which are often misunderstood to say more than they really do, like how observations about the logical contradictions inherent in supposing you can "pair up" possibilities from 2 finitely-describable spaces leads to the declaration that there are "multiple levels of infinity"... which is a much bigger statement, and doesn't really make any sense. The error was in identifying the philosophical notion of infinity with those equivalence classes of "pairable" spaces in the first place.
The same goes for non-standard analysis with its "actual infinitesimals". They're no more "actually infinitesimal" than any other "infinite" construct in mathematics. What makes them different from limits is that they're *actually numbers*, not that they're "actually infinitesimal". "What if we could make limits fully behave like numbers, instead of only mostly? And maybe some other stuff like dirac deltas while we're at it?" I'm all in favor of that, and I think it can definitely lead to more intuitive ways of teaching and understanding calculus.
This kind of leads to the bothering fact that many things in advanced theoretical mathematics are just that: highly theoretical. Sometimes the entire idea or question is based on a set of borderline arbitrarily chosen rules that were just established or agreed upon in order to make the entire concept work.
@@IIIRobIII True, though it may still be an interesting fact that ANY rules can make the concept work.
I think part of the hard problem with infinites and infinitesimals is the switching back and forth between the object that is the infinity or infinitesimal and the endless procedure that is the infinity or infinitesimal. I think fractional dimensions are in order to make limits fully behave like numbers. At the limit, the procedure 'folds' into a fractional dimension where the limit is cast as an object actualizing its value.
_> The error was in identifying the philosophical notion of infinity with those equivalence classes of "pairable" spaces in the first place._
Why is that an error? If both spaces are innumerable but one is inescapably larger than the other, why isn't it fair to denote them as differently sized infinities? That serms to perfectly sum up the situation.
In a way i take more issue with the opposite mentality: of always associating mathematical concepts with reality. Maths on its own doesn't describe reality. It describes relationships between entirely abstract concepts. Even in physics we always use idealized approximations to the physical world. Take for example how we derive the escape velocity of a gravity well, where we integrate from the current distance to infinite distance from the center of mass. That equation implicitly assumes the universe to be infinitely large, eternally static, and that the reference mass is the only source of gravity in existance. That scenario does not and can not exist in reality, but it's still useful to study since a lot of real scenarios are "close enough" to this ideal.
Infinity may only be an abstract concept seperate from reality, but so are numbers in general. They don't need to describe physical situations. They only need to describe relationships to other numbers. If infinity can be defined and manipulated the same as any other number, what makes it different from other numbers? That we lack an intuition for it? If there's one thing mathematics and science should have taught us, it's that human intuition is both limited and unreliable in subjects of fact and logic.
@@volbla We seem to be mostly on the same page here, I'm just applying the same caution you mentioned about the boundary between math and physics to also put a boundary between math and philosophy. As long as we're clear that we're only talking about a mathematical construct, it's perfectly fine to call those infinite numbers and to say one is bigger than the other (Though in constructive mathematics, for example, you may find that cardinalities can't be proven to be totally ordered, and other wierdness. It's worth some caution even then). It's also worth remembering that there are a lot of different ideas about how to extend the concept of a number or a quantity into the transfinite, and they don't agree about a lot of things. What people often do with the cardinality thing is claim that mathematics has discovered something about the nature of infinity (the philosophical concept), but to understand what really has and hasn't been proven, you need to unpack the stack of definitions you used and be conservative about how you map them to anything real.
I can't believe this is your first video!!!
Amazingly written and well researched!!
Also the name of the channel is really cool!
Looking forward for more videos!
Wait, really?! Amazing
I agree 😄
he did not research well. maths was first began in india
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 really want to appreciate the work you put behind this. I'm a first year CE college student and I still have a vague idea about Calculus and Analytic Geometry. I always ask my senior highschool teachers about this, but their answers doesn't really satisfy me and only perplexed me more. Since the pandemic hit, I can only rely on videos on YT to truly understand calculus.
Thank you so much, sir!
What is CE?