Thank you for this beautiful and important video. I used to think of myself as "not a maths person", and more of a creative person- assuming these things were opposites. I struggled through school maths, having been told I was not good at math by placement tests that I believed had accurately judged me. In university though I stumbled into an abstract algebra class and I remember having to prove that 0+0=0, and falling in love. Maths, it turns out, isn't an about memorising algorithms, it's about getting to the heart of why things are true. There's no recipe for that, and there's no comparison to the feeling of discovering a mathematical truth. It's such a pity most students never get to have that experience.
@@citrus4419 from the existence of an additive identity in a field (there exist 0 such that x+0=x for all x, in a field) which is unique(0=0+0'=0' after assuming two zeroes 0 and 0') and combining these two ideas by taking x=0
@Nadr Jomha the literally part got me😂😂 but on a serious note it is intuitive to us but to incorporate it into maths we need to derive them from some general axiom(field axioms) which deals with various systems apart from the reals(like complex numbers, numbers modulo some prime etc)
@Nadr Jomha glad to have been of help. Also I don't make a living working with numbers yet I am just a student but I wish to one day...thanks for the motivation!
@@wizardo9226 Asian high schools tend to focus on the relatively less "elegant" side of math. More focus is put on engineering math instead of pure mathematics. A lot of memorization is involved too. This is partly due to the fact that most Asian countries are still undergoing large scale industrialization and can't afford to do basic science research (physics, chem, pure math etc). So they put a higher emphasis on applied math and speed compared to American or British education which put emphasis on a lot of theory, "elegance" and understanding.
I had creative and rule based math teachers. And during my high school career, I explored the whole spectrum of grades in math, from being best in class to abysmal. I was retested in my final exams, because my result was two grades better than my teachers expectations. (A- in fact) When I was best in class I was fortunate enough to have the most inspirational and genius teacher I can imagine. I feel so much for you!
@@unoriginalusernameno999 lmao, why did you treat him seriously, the dude mentions rice as if it isn't the more civilized of foods, he should be counting his blessings that europe wasn't exterminated when others had the chance
As a young artist, I had the impression that Math was the opposite of art. Now that I've gotten a bit older, I wish that people didn't see a separation between the two. I've been taking small steps of teaching myself what I missed out on.
I can relate to this. Here in the Far East with the culture of respect and obedience, education is more along memorization. Schedules are really tight and teachers need to cram into the student's brains. Meanwhile, students don't really care as long as they can get the correct answer and pass their exams. They memorized the formulas and theories and just practise, practise, practise. Back in high school I felt like an outlier as I liked to ask questions like this video. If I get stuck on a certain question, or get something wrong all the time, I'd try to draw it out, sketch it out, and try to understand it deeper. I often get reprimanded by it, saying don't be weird, or, you're wasting your time. But for some reason this inquisitive nature hasn't really left me. I brought it along with me when I teach other things like maths, history and engineering. The students are still affected by the culture and they most often don't care, as usual. A few do have the initiative to ask questions. I just want the youngsters to learn something about the world that could be useful to them, and in a fun way.
I'm at around the same place as you, and I can't express my approval well enough through text. Wouldn't you absolutely abhor it when people keep telling you to "not waste your time" when it's really everyone else that's wasting theirs? What's the point of manipulating variables when you don't know what you're really doing? It's nothing but suppression of outward expression, curiosity, and the foundations of every great mathematician's most important traits-ignorant sabotage is what it really is.
You have no reason to feel called out. You're one of only two people, in my three decades of life, who's managed to get me interested in these things. Back in school it was cold dead memorization. I remember none of that, but I'll be thinking about that pyramid in a box for a while.
@@qwertyTRiG ViHart is indeed a good math communicator, although I would say they are better at drumming up interest for the subject rather than going into the technical details of why certain things are the way they are.
I'm an engineering student, when i study i always treat the demonstration as the most important thing-unless i'm REALLY late on an exam- and it is in fact the most fascinating part, making even a simple demonstration is so satisfying.
Totally agree with you. Im at my second year 9f engineering school, but decided yo switch to physics. When I'm studying any math branch I dwell with the topics given and I think of all the possibilities and whenever I have any unsolved question I invest my day on solving it. However, since professors don't teach with that in mind and only give formulas to memorize sometimes I need to rush a bit. It's so frustrating to ask these types of questions to then be answered "Why do you ask that, it's not included in the test next week"
Same, but the proof ideas can also helpful in the test. The proof ideas are very memorable, and sometimes you don't remember the formula they want us to memorize, but you can derive it mentally and keep going
The biggest thing I noticed about maths teaching was that the kids who had no trouble with maths were assigned the best teachers. The other kids were actively encouraged to do as little maths as possible. They had the worst teachers; teachers for whom maths was second or third fiddle at best. It suddenly struck me that this was the exact OPPOSITE of education: to NOT teach those who need teaching.
My school did exactly that, set one, ones who are the best at maths had the best teacher who taught them everything in depth and more and marked their work quickly, as you decreased in sets the teachers got worse, they didn’t really care much and were lazy with the marking. Very odd
“Fantasy remains a human right: we make in our measure and in our derivative mode, because we are made: and not only made, but made in the image and likeness of a Maker.”-J.R.R. Tolkien
I’m studying math at MIT, and I’ve just now thought about what math truly is to me. It actually makes me a bit sad to think that I’ve looked at math as the “opposite” of arts for my life, when that isn’t true at all.
I really started getting excited about maths when I started looking into the assumptions that we just made (for no apparent reason) before university maths, like "why is distance defined as c²=a²+b²", and then playing around with the idea of distance, seeing different weird shapes of voronoi cells that emerge if you don't use an L2 norm distance or whatever it's called, and then getting invested into this sort of idea of "I've been assuming thing X is always like that, what else can I find to try and break an assumption or play around with", that was one of those moments where my interest in maths really skyrocketed
My interest skyrocketed when I tried modeling the Magnus effect in a 3D soccer game I tried to make. Vector multiplication is almost black magic, more so quaternions.
@@OmegaF77 I'd definitely recommend 3blue1brown's videos on complex numbers and quaternions, I feel like I have a much better grasp on it conceptually than before!
As a teenager who is extremely passionate about mathematics, this video really hit home for me, and almost exactly describes my feelings towards math education. Incredible job!
That translates much of the feelings I had in highschool, and still have as a physics undergrad. In my case, a have to be very much self aware that "physics is not that" to keep the passion alive. Always hated mindless decorating rules and formulas.
Except they're not really mindless. Those rules and formulas comes from discoveries, from people trying to understand how the world works. Idk, I think it's pretty neat that we can describe the universe the best we can using rules and formulas. The fun thing about science is that you can test out those formulas for yourself (granted, some might be hard to test than others) and you can see for yourself if you think they're true.
@@missingno9 I agree with you. What I called mindless is the process of getting the formulas in their final form, and then applying then like robots, without knowing where they really come from, or what they really mean. Logically deriving equations from the fundamental theory, and them seeing if they agree (or not) with nature (knowing our limits of "knowing") is amazing, and gives me joy everytime I do it.
@@alexandreramos8484 I'm speaking from my experience, having finished my physics undergrad. Unfortunately, with time constraints and all that, giving students the time to really explore the theory behind stuff and letting them discover things on their own can be sometimes impossible. The university approach is to have the derivations already done for the students and to just work with (a lot of the times) contrived problems. I guess nowadays, people like Tibees and 3b1b are trying to change that by producing content that makes learning the foundations (like linear algebra) more insightful.
@@missingno9 They are absolutely mindless if you're never given the chance to explore them, and you're not usually given that chance. I don't have 40 hours in a day to explore them, I am pressed to get much more done so to me, I simply must skip over the interesting reasons in many cases because if I do not I will be paying for it with my academic performance. Maybe some people can sponge it all up but I don't know anyone that has. We all make sacrifices in understanding to perform the tasks as we need to, at the pace we are prescribed.
You're talking about physics courses... over in engineering school, asking the reason behind something is as good as frowned upon. You're bound to get some half assed garbage designed to shut you up 90% of the time. It grinds my gears. I'm not a proof person, but I find it painful how even the so called masters and professors fail to give convincing answers to fundamental questions. Thank God textbooks exist.
I grew up loving math, and i was good at it, and i got a big rush from solving math problems. by 6th grade i was being accused of cheating on tests all the time, my folks would have to come in and defend me. I did a lot of mental math, and had very sparse notes. in highschool they created a class called 'worldly math' and i think it was meant to teach balancing check books and stuff. but this teacher decided to teach the class the "correct" way to do mental math. He even showed us the "correct" way to SHOW YOUR MENTAL MATH WORK. After i failed this test, they held their ground. I then had to unlearn my natural math skills, and learn this teacher's "mental" math and put it on paper. at 16 years old this basically broke my brain, and I've never been good at math again.
RIP. My reply is worth infinite blessings. I hope you sue your teacher, win the case and receive a ton of compensation that you can use to by some paper and pencils to try and recover from that nightmare. (Note: Your teacher is bad at his job for he didn't teach math, but 'untaught it'. Give him what he deserves!)
I can palpably and manifestly discern that you genuinely care about mathematics and its educational dissemination. We need more profound, enlightened, and masterful professors like you. Thank. You. For. You.
The only reason people like Paul Lockhart have ever been blessed to see the beauty of math is the creative teaching methods of people like you. His lament is all about wishing there were more teachers like you. Teachers who make that vital connection between the rigorous rules of math and the exciting discoveries that fill the hearts of students with passion about the subject. Unfortunately, such gifted teachers are naturally very rare, even rarer than the gifted mathematicians.
I can listen to her whole day long. Just because of her voice but the fact that she is usually talking about physics or maths makes it even better lol.
"Good, he did not have enough imagination to become a mathematician". - Hilbert's response upon hearing that one of his students had dropped out to study poetry
@@ohnudes right? lets not compare dicks here. art and maths both have fascinating aspects that engage critical, logical and abstract thinking, visualization, pattern recognition, ability to come up with new ideas or to transform and reinvent new ones. i really dont see the point of comparing which one requires "more imagination". wonderwall required zero imagination, whereas poincares theorem required quite a lot to solove, i presume. 1+1 doesnt require a whole lot of imagination but ulysses did. not to mention postmodern texts where maths and literature intertwine and play around each other.
I've been fascinated by math since grade school when we started learning algebra. But I have been put down by the idea that math is only for certain people or only for those who truly "smart". However, I am slowly getting myself back into the love of it. I have taken Calculus 1-3 in the last year and it has given me so much happiness! I may not be great at math per se, but I do love learning it! I hope all future generations will come to love math and not discriminate for who can and cannot do math. Math is for everyone!!!
I hated Maths,until I met a Teacher who truly brings out the beauty of maths in his class in ways I didn’t even thought to be possible. Now it’s my favourite Subject!
Although I never really had much trouble with school math. It didn't catch my interest beyond what I was required to do. Fortunately, in high school, I had a group of friends that created a sort of additional class powered by one enthusiastic teacher of ours which was dedicated to learn real maths. We were given complex problems and had time to think about them, discuss them and present our answers if we were able to formulate one given everything we did know so far. This experience really showed me what math is about, the simplicity of reasoning and creative thinking in tackling self-proposed idealized fantasies. I am very grateful to have had this opportunity and thankful for this because basically, it opened a whole other domain of creative exploration that previously was locked behind stiff bars. Currently, I do study a lot of maths just to get more ability in addressing some ideas/fantasies of mine concerning GRT and thus require a lot of algebraic geometry. There are moments when I prefer the simplicity of algebraic reasoning but the more profound ideas I have had insights that were purely geometric in nature which were just beautiful. Thanks for this wonderful video to remind me of the art that math really is.
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As a History of Art student, this is just beautiful.
Hi Tibees. This is Alessandro an Italian aerospace engineering PhD student. Your TH-cam videos are fun and entertaining but I think that somebody like you can give an enormous contribution to science. Big hug and stay safe.
As someone who has a B.S. in Math - abstract math. This hit home - I was good at math because I could not remember a formula unless I understood it - if then. I had to rederive spherical integration on a final exam. But because I understood it, I could teach it to someone I was tutoring thirty years later. I had one good math teacher before tenth grade - among other things, he taught us how to calculate square roots when I was eight. The other thing that completely messes up math learning is that kids (and adults) arrive at different levels of abstraction at different rates, and real math is abstraction. If a kid isn't ready for a concept, they are left behind, and it's very difficult for them to catch up. One thing that illustrated this clearly was that one of my math profs taught a section of the basic course required for university graduation every semester. From virtually every one of those classes, at least one person became a math major. Often they were older students - in their late twenties or thirties - who had thought they were bad at math from some point in school. My belief is that their brains matured to the point where they could think more complex, more abstract ways - but it took someone who made concepts come alive for them to light the flame. Something in me dies when I hear a person who is perfectly good at thinking about abstract issues say "I've never been good at math."
I was immediately caught by the title and had to watch. This is so true of the education system, that seeks to demand knowledge and supresses creativity as that is the anthesis of knowledge. I recall in a Maths lesson someone asking the teacher "What was the point of differentiation, they didn't need it to buy a Mars bar". We were being taught a process (to follow a pattern) before the relevance or time to consider why there was even a need to differentiate. In the end I recall the process therefore seemed onerous and ultimately the answers were meaningless.
My daughter took a lot of art classes, but never really liked it. And now I have the realization that her art classes were like her math classes. All techniques, and no original creativity. Thank you for sharing this essay.
@@rajarsi6438 well if you can do physics without math go grab your Nobel then, as far as we know math is THE tool we use to do science(if you want to play semantics and not call it a connection). In fact it is the only tool we can use to describe and test most of it.
@@rajarsi6438 Hah dude I guess you have to start reading more of his physics works and less of his philosophical bs, I dont care what einstein thought about reality. He made predictions which were confirmed and used math to do so. But you talking about "measuring relativities" tells me much about your understanding of his work..
@@rajarsi6438 actually I'm not good with production and there's plenty of good content here already, btw sorry for whining it seems it's bothered you But actually You should start producing some content about measuring relativities, I'm really curious about what's that never heard of it
You go through TH-cam searching for a good video. I don’t usually ever get satisfied, but this particular video is different. I feel like this video is what I have been searching for this whole time, and now I have finally completed my journey here.
I find beauty in math and I find beauty in music. And when I am playing music, I can't help but to see the math that is interwoven with the music that we are playing. The space that wants to be filled with beat, melody, and rhythm. And the beat that needs space to allow itself to be heard. The way melodies sing together and harmonize, by carefully calculated fractions. We notice how the beat is defined by the intervals of space. Two things that are so often seen as so different, art and math, rely on each other. Thank you for this video. This was a nice inspiration.
This video made my heart grow 10 times its size, and tears well up in my eyes. I connected so deeply with the phrase that "The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such." All of the joy I had when painting as a kindergartener with my fingertips, and tooting with a recorder... you mean I could have had that with mathematics too? I totally feel like that was stolen from me, and so many of my classmates. To all of us teaching mathematics (professionally or not) - we have to make sure that we never let the dogma of "curriculum" stomp on the freewheeling-ness of uninformed creativity. Thanks for the video :)
Everything amazes me . Starting from human body to the universe...every abstract,every profound thing amazes me....every creation, every history amazes me...list goes on..but what amazes me most is how some things give such perspectives which literally changes everything...hey Tibees you are one of my perspective alternators..thanks for living.. : )
OMG! Today I gave up studying for the math test I have in 2 weeks bcz it became so frustrating and I keep painting all day to distract myself but I had this realization after getting tired that math and art are not so different! And then you posted this video! What an amazing coincidence!!!✨ I'll get back to math now! :)
Once in college I was doing a test. I read one of the problems to be solved, worth 6 points. I realized I did not know how to solve the problem the way test wanted me to. But I thought about it, ran some numbers on a calculator, and in about 5-10 minutes I came up with the right answer, I knew it was the right answer. But I had no idea how to recreate the process of how did I get to that answer. I tried writing some stuff down, but I knew it was not good enough. When the test was later returned, I got 1 out of 6 points. I know why, but I still felt like " THERE IS ONLY ONE WAY TO DO THINGS" was just too much. From all the mathematics tests I did during my life, this is the only one I remember, because of this one problem. The less creative freedom there was in mathematics, the worse my grades got, from max grades down to less than halfway the scale. Thankyou so much for this video Tibees, it finally summed up what always bugged me about mathematics teaching in schools, I never could voice it out myself
Im a maths teacher and have experienced the math curriculum in Canada, South Africa, Bulgaria, Dubai and Australia. I believe the Australian system is the worst at just having kids memorise, excluding creativity & explorative thought (from this list). In Canada, I was taught way more conceptually, where I got to question, be creative and experience the beauty in math. Its very hard to carry that across though, especially to kids who have been taught to be little robots from the very beginning. I've had some great moments though, its always more interesting and natural. I describe the problem and let the students explain their attempts at solutions. Also, another challenge in teaching this way is that math is associated with the importance of success because it has been given a higher status in our society than the arts, and thus, you often don't have time in class to explore this way, because they have a list of formulas and techniques they need to know for their standardised test.
It’s very beautiful how you’ve described the “ art “ of mathematics , the inspired creativity that it is at its heart and how it can be / must be taught especially at those thirsty young ages . I’m a musician with a B.A. in music and after over 40 years - since my College years and being now 68 - of reflecting on how school , my parents etc. hadn’t seen what my truest loves and talents were , I too often lament , more deeply each day , at how much of my own artistic potentials were / remain untapped ... ever more so with mathematics given my passionate love of Physics 💔 Thank you for the inspiration .
I became entangled in this mess... Totally relatable... I cleared high school and pre university easily thanks to my memory... But during the lock down I came across many such videos... I did a grave mistake relying on the teachers in high school and pre uni... It sucks now... I'm in a UG uni now and it's the same... I feel terrible... Keep going Tibees.. I got inspired by your result sheet video and I particularly liked how you deducted the rapunzel dilemma... The van de graaf video showed me the concept in a few minutes which my teacher took a month to cover and still didn't teach it well... Sucks... But it's life. Not everyones got the same starting line.. It's every man for himself. Let's move on.. Now this might be an irrelevant comment.. But there must be people out there who would find an inspiration in you. Keep going. Good luck
As a former math teacher, I think you touch on a systemic problem in math education. Math teachers who love the subject are often pressured by their administrators to "teach to the test", and subsequently feel like they don't have time to share their love of the subject with their students, especially within the confines of a 45-50 minute class. I tried to push back against these pressures in my own classes, to show my students that there is often more than one way to solve a problem, which is where the creativity part comes in, and that making mistakes is not an indication of failure or stupidity, but rather an essential component of the learning process.
I'm studying to be a philosophy teacher, and everything mentioned in this video about math is true for my field as well. What is engaging and worthwhile in philosophy is exactly the joy and beauty of well-thought out argumentation. It is about developing an examinative and understanding approach, so that we may be better, fuller people. Studying is not supposed to be practical. Schools need to be refuges, places where students can come to see and learn the beauty and joy that is to be found in the world, in the knowledge we collectively have acquired, in doing activities for their own sake and most importantly, in themselves.
I cried watching this. I'm a Math major myself, but often I found myself fumbling to answer questions from the past syllabus. I'm only great at answering of what I currently learning and remember.
Lockhart's lament is my lament. So many ideas that I try to communicate as a math teacher are expressed here. I deeply resonate with the part of it where he extols the virtues of playing with the math, just because. I believe in my heart of hearts that the greatest key to any success that I have had as a mathematician has been that I play with it.
Your reading of that poem was so touching. I'm an Economist and I felt identified with the lament in the sense that there is something wrong with teaching: rather than creativity, trial, error and success, it's just about repeating steps on mandatory classes. Who wants that? But there is a lot of beauty in math when we actually think through it!
This is some kinda of intellectual ASMR delight, and I don't enjoy even enjoy 'normal ASMR'. Thanks Tibees, this captures my feelings about mathematics so well. I wish I had maintained and nurtured the flame of my love for maths better, which only is able to keep flickering into existence because of people like you and 3B1B, who understand the value of communicating one's passion and love for a subject.
I have always struggled with mathematics and to some extent I blame it on those who are teaching the subject. They're are those who know what they teach and then there is the much rarer breed...those who can teach what they know. Self taught, 73 and struggling through the calculus of variations. Love your videos Tibees, you are a gentle creature, stay safe.
Students are taught some checkpoints along the complete line of reasoning that built math theory in the first place. It's like you teach a child to walk by carrying it and letting it touch the ground in a few spots along the way. It learnt where to go, but not how to get there without support.
I just solved Bellman's lost in the forest optimization problem with an oblong spheroid using abstract thinking, but i don't know how to formalize it, so i used chatgpt to create the formal definitions and function. Essentially the best movement is the inverse of all other possible movements. That's how you find the best path out of the oblong spheroid.
As I watch this video, I realize that so much of what was being said, here, was "inflicted" upon me. Particularly, the idea of being convinced that I was not good at math because, rather than memorizing formulae, I was better at conceptualizing ideas, and figuring out those formulas as needed, kept me for years from realizing that I am, in fact, a "math person," and that I enjoy math. That said, as a university-level music educator, I can confirm that most of what Lockhart wrote about attitudes toward the learning of music is actually true. Rather than being a "nightmare scenario" showing the differences between attitudes toward the learning of music and math, I recognized in it the actual attitudes of my non-musician students. In particular, the statement that, "most of them couldn't care less about how important music is in today's world; they just want to take the minimum number of music courses and be done with it," rings too true. The one biggest difference, though, is that music education is NOT mandatory.
This one was very deep, dear Tibees. I like when you talk about "philosophical" (sorry, I cannot find another word xD) aspects of mathematics, in this case about the teaching
@@rajarsi6438 They never argued that mathematics was to do with science or philosophy. Philosophy is just thought about [usually] fundamental questions: the fundamental question in this case is "What is mathematics". You can't answer that question with mathematics alone, although you may arrive at the answer if you are a mathematician and think about what it means to you.
@@rajarsi6438 Also, you never explained why, you just said it's got "nothing to do with philosophy and science", which I agree with to some extent, mathematics is independent from those two, but you were saying it in response to someone talking about the philosophy of mathematics, which is very much a real thing.
@@rajarsi6438 Why do you keep on writing that in the comments? Nobody knows what you’re talking about. Perhaps there’s some truth to it, but you’d have to elaborate.
@@rajarsi6438 This sounds to me like a gross simplification of mathematics (but I could be wrong). Maybe a counterargument: why have we chosen our current set of axioms and the scheme in which we do proofs? One can argue that mathematicians where inspired to pick this set of axioms by experiencing reality itself. Continuing this reasoning, you could argue that mathematics is actually shaped by reality and it could explain why its language is this useful to science. It would mean that mathematics is strongly related to science, at least. Note: Within mathematics it is not even clear which set of axioms is the right one. Some mathematician do not agree with proofs by contradiction, for example.
first minute i thought ill close the video again.. but i stayed and i really enjoyed the whole thing through. glad i didnt close it. Thanks for this video!! makes me try to be aware of how i percieve things in general
6:10 or so as a Computer Science graduate who loves programming, I'm so used to model the world in a software-like way that my mindset is developed such that I describe to myself almost everything (human interactions, things to do, recipes for cooking and performing every common action like balancing myself while dancing) using either physics-like formulas (precise or approximative, no matter), set-and-preposition-like relations and definitions or lists of "programming instructions". (I'm sorry if this explanation is messy and confusing, I hope You, the reader, will understand) Therefore, I'm not just "good at following instructions", because I "see", model and understand the World around & inside me in a mathematical-like way. I'm sure that You, @Tibees , are at least as good as me in doing so, thus You are not a "simple, cold and arid machine who just do the job". Thank you SO MUCH for sharing this "lament", I think is critical/fundamental that everybody should be aware of what Math really is and the beauty and power of this __language__.
Denying self-exploration in maths is similar to parents saying to their child: "Don't ever travel the world, it's dangerous! Here at home you can just watch series all day long in which you can see anything about the world you'd like to see!"
@@monotronfan1 “useless”-stop viewing everything in life as some sort of strict value judgement. different people have different reasons for traveling, to assume that you know the unique perspective and priorities of everyone is simply arrogant
I don't really watch your videos much, but I had to click on this one because Lockhart's views on mathematics education changed me forever. Your rendition of his words was very touching. Thanks for that!
I rarely comment on youtube videos. But I'm making an exception here because this video really captures what I have found so special about mathematics. I'm sure I will share this video with many of my students. So many of them suffered so much in their grade school and high school math classes and have rejected the whole idea of mathematics being beautiful or exciting or enlightening. This is so sad.
YES! THIS! I have been struggling to explain this very idea to friends and family for my entire high school and college career and no one really listens or seems to understand. THANK YOU!
That was just beautiful. I'd come across the comparison between maths and music before but you took it far beyond my previous understanding. As I see it, there are two forms of mathematics. There's the practical, which everyone needs to make change, or a shelf.That's the slog that many people think of. Then there's the artistic, which is to the slog what playing a symphony is to playing scales. Unfortunately, many people never get beyond the slog because they can't 'hear' maths.
This is so true!!! I really really love Math and Physics but what they teach us in school bores me. I still want to learn more but I can’t because our entire education system is just based on rote learning and full marks🥺
Thanks for making this iconic article more widely known. I had known the earlier versions and also bought the book when it came out a few years later. The connection with art and creativity and especially music, or poetry is often no more appreciated. Schools these days often are pressured `to force more applications" or ``build in messy data analysis parts" to give math more more purpose. Especially the competition with applied math or stats puts pressure on remaining relevant. It is important to see it also as an art. Since art is closely related to creativity, this can also make it harder to teach and motivate. It is important to point out that many mathematical topics which were done entirely void of applications like properties about prime numbers later became very applied like for cryptology. But it is in the nature of pure mathematics not to worry too much about applications at first. And that makes pure math so pure! By the way, the Thales theorem round minute 9 in your movie is much more interesting when the base of the triangle is not the diameter. The angle stillremains constant when moving on the circular arc. This brings in a moment of surprise and makes the theorem much more interesting. The diameter case can be proven as you illustrated with symmetry. It needs a bit more creativity to find a proof of the general case. I teach this theorem since many years in a course and still have always seen that the class was able to figure out a proof in the more general case (despite that most have not seen the general case). I myself do no more agree with the pessimism of Lockart. Especially if you look what is around also on youtube (like also your channel) makes some aspects of math more accessible. S lot has happened since 2002 when the article was written. I'm sure that if Lockart would rewrite the essay today, he would agree. The last two decades have also produced msny fantastic math books for more general audiences as well as quite many movies and documentaries illustrating the beauty of the subject. Certainly the pamphlet of Lockart had a good deal to do with it.
I love your channel so much, and this is one of your best videos. I taught math for 40 years, and maybe occasionally managed to do what you're describing here. I love that proof about the triangle and the circle! So beautiful.
It's really nice to have these kinds of sources available for free, but I'd think that the people who watch these videos are the ones already interested in maths.
Those who believe themselves superior with their ego games try to enslave humanity in a state where they reject their own spirituality. This so called elite despises spirituality and try to force others into their view of life. You see, negating your spirituality is negating your inner creativity and mind power to enhance all life naturally and your own self.
What a funny coincidence... I stumbled upon this essay a while ago (funnily enough it was recommended by a music youtuber) so I saved it, but I never got around to reading it. Thanks to this video I could just sit back and relax without having to read the thing, and I got some extra comments as a bonus. Also, the visuals and music make it sooo relaxing (even though the message is not that great...). Great video!
If you wrote a book on math and science, I'd buy it and read it too my future kids. You do such a great job opening up the field and making it approachable through informative kindness.
Hi! I'm from Brazil, and that's the same thing. It happens to the most of the students, I always thinked that I was really good at math, but Math, at the most of the cases, is a subject that is introduced yo you just to make exercices, despising your creativity.
It's such a nice intuitive explanation from a 7th grader. Few years back I read "How to Solve it" by G. Polya. It delves into this idea of how to motivate students, when to give the right nudge and encouragement. It was really eye opening for me and has since encouraged me to really engage with math problems. Every now and then, I re-read the book and it still blows my mind.
Lockhart's essay is profound. He makes a very persuasive case for the "artistic view" of mathematics and I think I will never be able to turn my back on this. If anyone is interested in getting a taste of how Lockhart would teach math, you can get his book called "Measurement". I'm slowly working through it and it is honestly amazing!
This is superb! The point that letting students make discoveries for themselves is the golden nugget of teaching math - that is spot-on! There's just no describing the elation of that - it has to be experienced. Fred, a mathematician/physicist (retired)
As someone who decided to become a mathematician because I explored chaos theory after reading Jurassic Park, this essay has resonated with me! I have always felt that I had learned what "real math" is outside the classroom, rather than in it. (And this, despite enjoying my math classes in school.)
I have a pure linguistics background, but I confess I do think about the mathematical aspects of almost every and any problem, challenge or issue in my life. It is another form of light that always illuminates something important. Every time.
Thank you for this beautiful and important video. I used to think of myself as "not a maths person", and more of a creative person- assuming these things were opposites. I struggled through school maths, having been told I was not good at math by placement tests that I believed had accurately judged me. In university though I stumbled into an abstract algebra class and I remember having to prove that 0+0=0, and falling in love. Maths, it turns out, isn't an about memorising algorithms, it's about getting to the heart of why things are true. There's no recipe for that, and there's no comparison to the feeling of discovering a mathematical truth. It's such a pity most students never get to have that experience.
so why is 0+0=0?
OMGGGG YOU TWO HAVE TO MAKE VIDEOS TOGETHER PLSSS, kisses from Brazil
@@citrus4419 from the existence of an additive identity in a field (there exist 0 such that x+0=x for all x, in a field) which is unique(0=0+0'=0' after assuming two zeroes 0 and 0') and combining these two ideas by taking x=0
@Nadr Jomha the literally part got me😂😂 but on a serious note it is intuitive to us but to incorporate it into maths we need to derive them from some general axiom(field axioms) which deals with various systems apart from the reals(like complex numbers, numbers modulo some prime etc)
@Nadr Jomha glad to have been of help. Also I don't make a living working with numbers yet I am just a student but I wish to one day...thanks for the motivation!
That kid's proof of the second problem was brilliant.
It blew my freaking mind
Fact. Very impressive. Imagine that kid researching 12 dimensional space.
What kid?
@@real_michael that kid
@@FriedrichBoettger Forget what he *could* be like if xyz, just revel in the genius presented before you.
Not gonna lie, these videos are much better that most documentaries.
Lying isn't good anyways!
🧢
This is the real thing
Jajaj el Maquiavelico
I thought this comment was too big of a praise when I read it but after watching I agree with you.
20 years after my high school observation "It is not math nor science at this class, It's just following the pattern" I found you. Thank you for this
This video is heart-touching - from a Asian high school student who is obsessively interested in Maths but be totured by the maths class in school.
@@wizardo9226 Asian high schools tend to focus on the relatively less "elegant" side of math. More focus is put on engineering math instead of pure mathematics. A lot of memorization is involved too. This is partly due to the fact that most Asian countries are still undergoing large scale industrialization and can't afford to do basic science research (physics, chem, pure math etc). So they put a higher emphasis on applied math and speed compared to American or British education which put emphasis on a lot of theory, "elegance" and understanding.
@@unoriginalusernameno999 oh I see. I misunderstood it as an "asian kid from high school'. thx
I had creative and rule based math teachers. And during my high school career, I explored the whole spectrum of grades in math, from being best in class to abysmal. I was retested in my final exams, because my result was two grades better than my teachers expectations. (A- in fact)
When I was best in class I was fortunate enough to have the most inspirational and genius teacher I can imagine.
I feel so much for you!
@@unoriginalusernameno999 lmao, why did you treat him seriously, the dude mentions rice as if it isn't the more civilized of foods, he should be counting his blessings that europe wasn't exterminated when others had the chance
sorry for the 405th like
As a young artist, I had the impression that Math was the opposite of art. Now that I've gotten a bit older, I wish that people didn't see a separation between the two. I've been taking small steps of teaching myself what I missed out on.
I can relate to this. Here in the Far East with the culture of respect and obedience, education is more along memorization. Schedules are really tight and teachers need to cram into the student's brains. Meanwhile, students don't really care as long as they can get the correct answer and pass their exams. They memorized the formulas and theories and just practise, practise, practise.
Back in high school I felt like an outlier as I liked to ask questions like this video. If I get stuck on a certain question, or get something wrong all the time, I'd try to draw it out, sketch it out, and try to understand it deeper. I often get reprimanded by it, saying don't be weird, or, you're wasting your time.
But for some reason this inquisitive nature hasn't really left me. I brought it along with me when I teach other things like maths, history and engineering. The students are still affected by the culture and they most often don't care, as usual. A few do have the initiative to ask questions. I just want the youngsters to learn something about the world that could be useful to them, and in a fun way.
Keep it up! You're the change the youngsters need 😄.
I'm at around the same place as you, and I can't express my approval well enough through text. Wouldn't you absolutely abhor it when people keep telling you to "not waste your time" when it's really everyone else that's wasting theirs? What's the point of manipulating variables when you don't know what you're really doing? It's nothing but suppression of outward expression, curiosity, and the foundations of every great mathematician's most important traits-ignorant sabotage is what it really is.
You have no reason to feel called out. You're one of only two people, in my three decades of life, who's managed to get me interested in these things. Back in school it was cold dead memorization. I remember none of that, but I'll be thinking about that pyramid in a box for a while.
Is the other person 3Blue1Brown?
@@ideallyyours For me , Yes!😌
Pyramid in a box is quite a good problem to think through
@@ideallyyours Vi Hart is also most excellent.
@@qwertyTRiG ViHart is indeed a good math communicator, although I would say they are better at drumming up interest for the subject rather than going into the technical details of why certain things are the way they are.
I'm an engineering student, when i study i always treat the demonstration as the most important thing-unless i'm REALLY late on an exam- and it is in fact the most fascinating part, making even a simple demonstration is so satisfying.
Totally agree with you. Im at my second year 9f engineering school, but decided yo switch to physics. When I'm studying any math branch I dwell with the topics given and I think of all the possibilities and whenever I have any unsolved question I invest my day on solving it. However, since professors don't teach with that in mind and only give formulas to memorize sometimes I need to rush a bit. It's so frustrating to ask these types of questions to then be answered "Why do you ask that, it's not included in the test next week"
Same, but the proof ideas can also helpful in the test. The proof ideas are very memorable, and sometimes you don't remember the formula they want us to memorize, but you can derive it mentally and keep going
The biggest thing I noticed about maths teaching was that the kids who had no trouble with maths were assigned the best teachers. The other kids were actively encouraged to do as little maths as possible. They had the worst teachers; teachers for whom maths was second or third fiddle at best. It suddenly struck me that this was the exact OPPOSITE of education: to NOT teach those who need teaching.
Some of the best mathematicians were self-taught, like Galois and Ramanujan.
My school did exactly that, set one, ones who are the best at maths had the best teacher who taught them everything in depth and more and marked their work quickly, as you decreased in sets the teachers got worse, they didn’t really care much and were lazy with the marking. Very odd
Good teachers aren't an unlimited resource. Someone has to train the good students.
I'd rather have a few brilliant kids than a class full of perfectly average students.
Actually, no one should have had the worst teachers.
“Fantasy remains a human right: we make in our measure and in our derivative mode, because we are made: and not only made, but made in the image and likeness of a Maker.”-J.R.R. Tolkien
Seriously, youtube needs more videos like this one.
The whole world does.
I’m studying math at MIT, and I’ve just now thought about what math truly is to me. It actually makes me a bit sad to think that I’ve looked at math as the “opposite” of arts for my life, when that isn’t true at all.
Mentioning your university adds nothing to the argument.
@@NachoSchipswhy so angry?
@@AymanPlayer cause I'm miserable
@@NachoSchips That wasn't an argument, that was a statement lmao stop fighting ghosts
I really started getting excited about maths when I started looking into the assumptions that we just made (for no apparent reason) before university maths, like "why is distance defined as c²=a²+b²", and then playing around with the idea of distance, seeing different weird shapes of voronoi cells that emerge if you don't use an L2 norm distance or whatever it's called, and then getting invested into this sort of idea of "I've been assuming thing X is always like that, what else can I find to try and break an assumption or play around with", that was one of those moments where my interest in maths really skyrocketed
My interest skyrocketed when I tried modeling the Magnus effect in a 3D soccer game I tried to make. Vector multiplication is almost black magic, more so quaternions.
@@OmegaF77 I'd definitely recommend 3blue1brown's videos on complex numbers and quaternions, I feel like I have a much better grasp on it conceptually than before!
As a teenager who is extremely passionate about mathematics, this video really hit home for me, and almost exactly describes my feelings towards math education. Incredible job!
That translates much of the feelings I had in highschool, and still have as a physics undergrad. In my case, a have to be very much self aware that "physics is not that" to keep the passion alive. Always hated mindless decorating rules and formulas.
Except they're not really mindless. Those rules and formulas comes from discoveries, from people trying to understand how the world works. Idk, I think it's pretty neat that we can describe the universe the best we can using rules and formulas.
The fun thing about science is that you can test out those formulas for yourself (granted, some might be hard to test than others) and you can see for yourself if you think they're true.
@@missingno9 I agree with you. What I called mindless is the process of getting the formulas in their final form, and then applying then like robots, without knowing where they really come from, or what they really mean. Logically deriving equations from the fundamental theory, and them seeing if they agree (or not) with nature (knowing our limits of "knowing") is amazing, and gives me joy everytime I do it.
@@alexandreramos8484 I'm speaking from my experience, having finished my physics undergrad. Unfortunately, with time constraints and all that, giving students the time to really explore the theory behind stuff and letting them discover things on their own can be sometimes impossible. The university approach is to have the derivations already done for the students and to just work with (a lot of the times) contrived problems.
I guess nowadays, people like Tibees and 3b1b are trying to change that by producing content that makes learning the foundations (like linear algebra) more insightful.
@@missingno9 They are absolutely mindless if you're never given the chance to explore them, and you're not usually given that chance.
I don't have 40 hours in a day to explore them, I am pressed to get much more done so to me, I simply must skip over the interesting reasons in many cases because if I do not I will be paying for it with my academic performance.
Maybe some people can sponge it all up but I don't know anyone that has. We all make sacrifices in understanding to perform the tasks as we need to, at the pace we are prescribed.
You're talking about physics courses... over in engineering school, asking the reason behind something is as good as frowned upon. You're bound to get some half assed garbage designed to shut you up 90% of the time. It grinds my gears. I'm not a proof person, but I find it painful how even the so called masters and professors fail to give convincing answers to fundamental questions. Thank God textbooks exist.
Mathematics the music of reason. Music the mathematics of emotion
interesting
Wow that's poetic
Music unfolds formulas into gestures, math folds gestures back up into formulas :)
I grew up loving math, and i was good at it, and i got a big rush from solving math problems. by 6th grade i was being accused of cheating on tests all the time, my folks would have to come in and defend me. I did a lot of mental math, and had very sparse notes. in highschool they created a class called 'worldly math' and i think it was meant to teach balancing check books and stuff. but this teacher decided to teach the class the "correct" way to do mental math. He even showed us the "correct" way to SHOW YOUR MENTAL MATH WORK. After i failed this test, they held their ground. I then had to unlearn my natural math skills, and learn this teacher's "mental" math and put it on paper. at 16 years old this basically broke my brain, and I've never been good at math again.
that's pretty sad, man
RIP. My reply is worth infinite blessings. I hope you sue your teacher, win the case and receive a ton of compensation that you can use to by some paper and pencils to try and recover from that nightmare. (Note: Your teacher is bad at his job for he didn't teach math, but 'untaught it'. Give him what he deserves!)
Sorry to hear that
Dude that so sad and relatable
My age is 16 and I am also much better at Maths than anyone I know of my age group , and this comment has scared me
I can palpably and manifestly discern that you genuinely care about mathematics and its educational dissemination. We need more profound, enlightened, and masterful professors like you.
Thank. You. For. You.
This made me cry a little... I love your videos, always so on point, honest, and inspirational.
The only reason people like Paul Lockhart have ever been blessed to see the beauty of math is the creative teaching methods of people like you. His lament is all about wishing there were more teachers like you. Teachers who make that vital connection between the rigorous rules of math and the exciting discoveries that fill the hearts of students with passion about the subject. Unfortunately, such gifted teachers are naturally very rare, even rarer than the gifted mathematicians.
I can listen to her whole day long. Just because of her voice but the fact that she is usually talking about physics or maths makes it even better lol.
ASMR tingles! ;)
Her slow articulate melodic voice is gorgeous. I agree with your sentiment. And she looks gorgeous too!
@@ianrobinson8518 I like her eyes..
"Good, he did not have enough imagination to become a mathematician".
- Hilbert's response upon hearing that one of his students had dropped out to study poetry
Poetry and math are very similar at a higher level of understanding. Math is a language that moves objects around, and so is poetry.
Hey nice, thats exactly the kind of elitist way of talking that keeps maths away of people, all to save a half assed pride
@New only sith deal in absolutes.
@@ohnudes right? lets not compare dicks here. art and maths both have fascinating aspects that engage critical, logical and abstract thinking, visualization, pattern recognition, ability to come up with new ideas or to transform and reinvent new ones. i really dont see the point of comparing which one requires "more imagination". wonderwall required zero imagination, whereas poincares theorem required quite a lot to solove, i presume. 1+1 doesnt require a whole lot of imagination but ulysses did. not to mention postmodern texts where maths and literature intertwine and play around each other.
@@swavekbu4959 So are essays and fiction and film, according to the moving objects around definition.
I've been fascinated by math since grade school when we started learning algebra. But I have been put down by the idea that math is only for certain people or only for those who truly "smart". However, I am slowly getting myself back into the love of it. I have taken Calculus 1-3 in the last year and it has given me so much happiness! I may not be great at math per se, but I do love learning it! I hope all future generations will come to love math and not discriminate for who can and cannot do math. Math is for everyone!!!
I hated Maths,until I met a Teacher who truly brings out the beauty of maths in his class in ways I didn’t even thought to be possible. Now it’s my favourite Subject!
Me too🙂
Same
Although I never really had much trouble with school math. It didn't catch my interest beyond what I was required to do. Fortunately, in high school, I had a group of friends that created a sort of additional class powered by one enthusiastic teacher of ours which was dedicated to learn real maths. We were given complex problems and had time to think about them, discuss them and present our answers if we were able to formulate one given everything we did know so far. This experience really showed me what math is about, the simplicity of reasoning and creative thinking in tackling self-proposed idealized fantasies. I am very grateful to have had this opportunity and thankful for this because basically, it opened a whole other domain of creative exploration that previously was locked behind stiff bars. Currently, I do study a lot of maths just to get more ability in addressing some ideas/fantasies of mine concerning GRT and thus require a lot of algebraic geometry. There are moments when I prefer the simplicity of algebraic reasoning but the more profound ideas I have had insights that were purely geometric in nature which were just beautiful.
Thanks for this wonderful video to remind me of the art that math really is.
As a History of Art student, this is just beautiful.
Hi Tibees. This is Alessandro an Italian aerospace engineering PhD student. Your TH-cam videos are fun and entertaining but I think that somebody like you can give an enormous contribution to science. Big hug and stay safe.
Me: thinking you're you're solving complex mathematical equations.
You : drawing music icons.
As someone who has a B.S. in Math - abstract math. This hit home - I was good at math because I could not remember a formula unless I understood it - if then. I had to rederive spherical integration on a final exam. But because I understood it, I could teach it to someone I was tutoring thirty years later.
I had one good math teacher before tenth grade - among other things, he taught us how to calculate square roots when I was eight. The other thing that completely messes up math learning is that kids (and adults) arrive at different levels of abstraction at different rates, and real math is abstraction. If a kid isn't ready for a concept, they are left behind, and it's very difficult for them to catch up. One thing that illustrated this clearly was that one of my math profs taught a section of the basic course required for university graduation every semester. From virtually every one of those classes, at least one person became a math major. Often they were older students - in their late twenties or thirties - who had thought they were bad at math from some point in school.
My belief is that their brains matured to the point where they could think more complex, more abstract ways - but it took someone who made concepts come alive for them to light the flame. Something in me dies when I hear a person who is perfectly good at thinking about abstract issues say "I've never been good at math."
You just described elegantly the beauty of mathematics. The why behind loving math all my life and working as an artist. Thank you!
I was immediately caught by the title and had to watch. This is so true of the education system, that seeks to demand knowledge and supresses creativity as that is the anthesis of knowledge. I recall in a Maths lesson someone asking the teacher "What was the point of differentiation, they didn't need it to buy a Mars bar". We were being taught a process (to follow a pattern) before the relevance or time to consider why there was even a need to differentiate. In the end I recall the process therefore seemed onerous and ultimately the answers were meaningless.
"It's a sad race to nowhere" was the line that I felt called out on the most.
My daughter took a lot of art classes, but never really liked it. And now I have the realization that her art classes were like her math classes. All techniques, and no original creativity. Thank you for sharing this essay.
Lockhart's lament is one of my favorites. I've long had the idea of making an animation and read along. Great job.
The production value of this video is out of this world!
I like how you chose Debussy's as background music. Debussy's compositions contain a lot of mathematics.
@@rajarsi6438 but math IS connected to it, it appears in most sciences, it just isnt the same as science, it's independent.
@@rajarsi6438 well if you can do physics without math go grab your Nobel then, as far as we know math is THE tool we use to do science(if you want to play semantics and not call it a connection). In fact it is the only tool we can use to describe and test most of it.
@@rajarsi6438 Hah dude I guess you have to start reading more of his physics works and less of his philosophical bs, I dont care what einstein thought about reality. He made predictions which were confirmed and used math to do so.
But you talking about "measuring relativities" tells me much about your understanding of his work..
@@rajarsi6438 actually I'm not good with production and there's plenty of good content here already, btw sorry for whining it seems it's bothered you
But actually You should start producing some content about measuring relativities, I'm really curious about what's that never heard of it
@@rajarsi6438 Ooohhh ok I see everything is relative. But what is science then if not measuring and doing math?
You go through TH-cam searching for a good video. I don’t usually ever get satisfied, but this particular video is different. I feel like this video is what I have been searching for this whole time, and now I have finally completed my journey here.
This video hit me to my core... thank you
I find beauty in math and I find beauty in music. And when I am playing music, I can't help but to see the math that is interwoven with the music that we are playing. The space that wants to be filled with beat, melody, and rhythm. And the beat that needs space to allow itself to be heard. The way melodies sing together and harmonize, by carefully calculated fractions. We notice how the beat is defined by the intervals of space. Two things that are so often seen as so different, art and math, rely on each other. Thank you for this video. This was a nice inspiration.
This video made my heart grow 10 times its size, and tears well up in my eyes. I connected so deeply with the phrase that "The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such." All of the joy I had when painting as a kindergartener with my fingertips, and tooting with a recorder... you mean I could have had that with mathematics too? I totally feel like that was stolen from me, and so many of my classmates.
To all of us teaching mathematics (professionally or not) - we have to make sure that we never let the dogma of "curriculum" stomp on the freewheeling-ness of uninformed creativity. Thanks for the video :)
Everything amazes me . Starting from human body to the universe...every abstract,every profound thing amazes me....every creation, every history amazes me...list goes on..but what amazes me most is how some things give such perspectives which literally changes everything...hey Tibees you are one of my perspective alternators..thanks for living.. : )
OMG! Today I gave up studying for the math test I have in 2 weeks bcz it became so frustrating and I keep painting all day to distract myself but I had this realization after getting tired that math and art are not so different! And then you posted this video! What an amazing coincidence!!!✨ I'll get back to math now! :)
Once in college I was doing a test. I read one of the problems to be solved, worth 6 points. I realized I did not know how to solve the problem the way test wanted me to. But I thought about it, ran some numbers on a calculator, and in about 5-10 minutes I came up with the right answer, I knew it was the right answer. But I had no idea how to recreate the process of how did I get to that answer. I tried writing some stuff down, but I knew it was not good enough. When the test was later returned, I got 1 out of 6 points. I know why, but I still felt like " THERE IS ONLY ONE WAY TO DO THINGS" was just too much. From all the mathematics tests I did during my life, this is the only one I remember, because of this one problem. The less creative freedom there was in mathematics, the worse my grades got, from max grades down to less than halfway the scale. Thankyou so much for this video Tibees, it finally summed up what always bugged me about mathematics teaching in schools, I never could voice it out myself
Im a maths teacher and have experienced the math curriculum in Canada, South Africa, Bulgaria, Dubai and Australia. I believe the Australian system is the worst at just having kids memorise, excluding creativity & explorative thought (from this list). In Canada, I was taught way more conceptually, where I got to question, be creative and experience the beauty in math. Its very hard to carry that across though, especially to kids who have been taught to be little robots from the very beginning. I've had some great moments though, its always more interesting and natural. I describe the problem and let the students explain their attempts at solutions. Also, another challenge in teaching this way is that math is associated with the importance of success because it has been given a higher status in our society than the arts, and thus, you often don't have time in class to explore this way, because they have a list of formulas and techniques they need to know for their standardised test.
It’s very beautiful how you’ve described the “ art “ of mathematics , the inspired creativity that it is at its heart and how it can be / must be taught especially at those thirsty young ages .
I’m a musician with a B.A. in music and after over 40 years - since my College years and being now 68 - of reflecting on how school , my parents etc. hadn’t seen what my truest loves and talents were , I too often lament , more deeply each day , at how much of my own artistic potentials were / remain untapped ... ever more so with mathematics given my passionate love of Physics 💔
Thank you for the inspiration .
I became entangled in this mess... Totally relatable... I cleared high school and pre university easily thanks to my memory... But during the lock down I came across many such videos... I did a grave mistake relying on the teachers in high school and pre uni... It sucks now... I'm in a UG uni now and it's the same... I feel terrible... Keep going Tibees.. I got inspired by your result sheet video and I particularly liked how you deducted the rapunzel dilemma... The van de graaf video showed me the concept in a few minutes which my teacher took a month to cover and still didn't teach it well... Sucks... But it's life. Not everyones got the same starting line.. It's every man for himself. Let's move on..
Now this might be an irrelevant comment.. But there must be people out there who would find an inspiration in you. Keep going. Good luck
Yes there must
As a former math teacher, I think you touch on a systemic problem in math education. Math teachers who love the subject are often pressured by their administrators to "teach to the test", and subsequently feel like they don't have time to share their love of the subject with their students, especially within the confines of a 45-50 minute class. I tried to push back against these pressures in my own classes, to show my students that there is often more than one way to solve a problem, which is where the creativity part comes in, and that making mistakes is not an indication of failure or stupidity, but rather an essential component of the learning process.
I'm studying to be a philosophy teacher, and everything mentioned in this video about math is true for my field as well. What is engaging and worthwhile in philosophy is exactly the joy and beauty of well-thought out argumentation. It is about developing an examinative and understanding approach, so that we may be better, fuller people.
Studying is not supposed to be practical. Schools need to be refuges, places where students can come to see and learn the beauty and joy that is to be found in the world, in the knowledge we collectively have acquired, in doing activities for their own sake and most importantly, in themselves.
I cried watching this. I'm a Math major myself, but often I found myself fumbling to answer questions from the past syllabus. I'm only great at answering of what I currently learning and remember.
Wow, this is so good, this gives me that feeling of beauty and wonder that I only used to get from 3b1b videos.
So true
@@daphenomenalz4100 lllll
@@daphenomenalz4100 l
Lockhart's lament is my lament. So many ideas that I try to communicate as a math teacher are expressed here. I deeply resonate with the part of it where he extols the virtues of playing with the math, just because. I believe in my heart of hearts that the greatest key to any success that I have had as a mathematician has been that I play with it.
When you forget to add +C at the end of integral
underrated comment
DEFINITEly ;)
Indefinite integral*
InDEFINITEly doesn't quite have the same response, does it? I prefer the pun nod.
@@limitingchaos ya😂
Your reading of that poem was so touching. I'm an Economist and I felt identified with the lament in the sense that there is something wrong with teaching: rather than creativity, trial, error and success, it's just about repeating steps on mandatory classes. Who wants that? But there is a lot of beauty in math when we actually think through it!
_And a special shout out to today's Patreon Cat Of The Day - a lawyer from West Texas._
This is some kinda of intellectual ASMR delight, and I don't enjoy even enjoy 'normal ASMR'.
Thanks Tibees, this captures my feelings about mathematics so well. I wish I had maintained and nurtured the flame of my love for maths better, which only is able to keep flickering into existence because of people like you and 3B1B, who understand the value of communicating one's passion and love for a subject.
Why do I become very relaxed and infinitely interested in whatever topic you do?!
I have always struggled with mathematics and to some extent I blame it on those who are teaching the subject. They're are those who know what they teach and then there is the much rarer breed...those who can teach what they know. Self taught, 73 and struggling through the calculus of variations. Love your videos Tibees, you are a gentle creature, stay safe.
Students are taught some checkpoints along the complete line of reasoning that built math theory in the first place. It's like you teach a child to walk by carrying it and letting it touch the ground in a few spots along the way. It learnt where to go, but not how to get there without support.
I just solved Bellman's lost in the forest optimization problem with an oblong spheroid using abstract thinking, but i don't know how to formalize it, so i used chatgpt to create the formal definitions and function. Essentially the best movement is the inverse of all other possible movements. That's how you find the best path out of the oblong spheroid.
Wow
You must make a series "Beauty in mathematics" .Take it serious you may be Carl Sagan Of Mathematics !
As I watch this video, I realize that so much of what was being said, here, was "inflicted" upon me. Particularly, the idea of being convinced that I was not good at math because, rather than memorizing formulae, I was better at conceptualizing ideas, and figuring out those formulas as needed, kept me for years from realizing that I am, in fact, a "math person," and that I enjoy math.
That said, as a university-level music educator, I can confirm that most of what Lockhart wrote about attitudes toward the learning of music is actually true. Rather than being a "nightmare scenario" showing the differences between attitudes toward the learning of music and math, I recognized in it the actual attitudes of my non-musician students. In particular, the statement that, "most of them couldn't care less about how important music is in today's world; they just want to take the minimum number of music courses and be done with it," rings too true. The one biggest difference, though, is that music education is NOT mandatory.
This one was very deep, dear Tibees. I like when you talk about "philosophical" (sorry, I cannot find another word xD) aspects of mathematics, in this case about the teaching
@@rajarsi6438 They never argued that mathematics was to do with science or philosophy. Philosophy is just thought about [usually] fundamental questions: the fundamental question in this case is "What is mathematics". You can't answer that question with mathematics alone, although you may arrive at the answer if you are a mathematician and think about what it means to you.
@@rajarsi6438 Also, you never explained why, you just said it's got "nothing to do with philosophy and science", which I agree with to some extent, mathematics is independent from those two, but you were saying it in response to someone talking about the philosophy of mathematics, which is very much a real thing.
@@rajarsi6438
Why do you keep on writing that in the comments? Nobody knows what you’re talking about. Perhaps there’s some truth to it, but you’d have to elaborate.
@@rajarsi6438
I am interested in elaboration.
@@rajarsi6438 This sounds to me like a gross simplification of mathematics (but I could be wrong). Maybe a counterargument: why have we chosen our current set of axioms and the scheme in which we do proofs? One can argue that mathematicians where inspired to pick this set of axioms by experiencing reality itself. Continuing this reasoning, you could argue that mathematics is actually shaped by reality and it could explain why its language is this useful to science. It would mean that mathematics is strongly related to science, at least.
Note: Within mathematics it is not even clear which set of axioms is the right one. Some mathematician do not agree with proofs by contradiction, for example.
first minute i thought ill close the video again.. but i stayed and i really enjoyed the whole thing through. glad i didnt close it. Thanks for this video!! makes me try to be aware of how i percieve things in general
To me, this channel is what Paul Lockhart was looking for, you're an excellent teacher!
6:10 or so
as a Computer Science graduate who loves programming, I'm so used to model the world in a software-like way that my mindset is developed such that I describe to myself almost everything (human interactions, things to do, recipes for cooking and performing every common action like balancing myself while dancing) using either physics-like formulas (precise or approximative, no matter), set-and-preposition-like relations and definitions or lists of "programming instructions".
(I'm sorry if this explanation is messy and confusing, I hope You, the reader, will understand)
Therefore, I'm not just "good at following instructions", because I "see", model and understand the World around & inside me in a mathematical-like way. I'm sure that You, @Tibees , are at least as good as me in doing so, thus You are not a "simple, cold and arid machine who just do the job".
Thank you SO MUCH for sharing this "lament", I think is critical/fundamental that everybody should be aware of what Math really is and the beauty and power of this __language__.
Your content is so interesting and your voice is so calming! Thank you!
P.S.: the proof of the last theorem was really elegant!
Her voice calms me down. Kinda helps me focus too.
Denying self-exploration in maths is similar to parents saying to their child: "Don't ever travel the world, it's dangerous! Here at home you can just watch series all day long in which you can see anything about the world you'd like to see!"
No, traveling is mostly useless. For most a waste of time, money and resources. traveling is not a personality trait, or skill, but that’s my opinion
@@monotronfan1 Not the point though. woooosh
@@monotronfan1 “useless”-stop viewing everything in life as some sort of strict value judgement. different people have different reasons for traveling, to assume that you know the unique perspective and priorities of everyone is simply arrogant
@@monotronfan1 travelling is very useful to learn about humans.
I don't really watch your videos much, but I had to click on this one because Lockhart's views on mathematics education changed me forever. Your rendition of his words was very touching. Thanks for that!
I rarely comment on youtube videos. But I'm making an exception here because this video really captures what I have found so special about mathematics. I'm sure I will share this video with many of my students. So many of them suffered so much in their grade school and high school math classes and have rejected the whole idea of mathematics being beautiful or exciting or enlightening. This is so sad.
How did your students react?
YES! THIS! I have been struggling to explain this very idea to friends and family for my entire high school and college career and no one really listens or seems to understand. THANK YOU!
Strangely featured on my homepage, TH-cam is doing strange things again.
Consider yourself fortunate that this superb video has found you...Shame that people are so lazy that they don't appreciate real talent and learning..
not quite strange, the text on thumbnail with author image is quite a trend for 2021 however the font may be updated to serif style.
@@jayzee6617 yes so true !
Not strange, TH-cam is trying to send you a subtle message but you have not understood it yet.
That was just beautiful. I'd come across the comparison between maths and music before but you took it far beyond my previous understanding.
As I see it, there are two forms of mathematics. There's the practical, which everyone needs to make change, or a shelf.That's the slog that many people think of. Then there's the artistic, which is to the slog what playing a symphony is to playing scales. Unfortunately, many people never get beyond the slog because they can't 'hear' maths.
Books respectively on the shelf, TH-cam reward on the floor.
Got ma Respekt
This is inspiring as a homeschool educator! Now I'm off to read Lockhart's Lament!
This is so true!!! I really really love Math and Physics but what they teach us in school bores me. I still want to learn more but I can’t because our entire education system is just based on rote learning and full marks🥺
I use Trig at work - it solves so many problems for me. It is quite an elegant device. This was a Very Beautiful video. Thank you.
Thanks for making this iconic article more widely known. I had known the earlier versions and also bought the book when it came out a few years later. The connection with art and creativity and especially music, or poetry is often no more appreciated. Schools these days often are pressured `to force more applications" or ``build in messy data analysis parts" to give math more more purpose. Especially the competition with applied math or stats puts pressure on remaining relevant. It is important to see it also as an art. Since art is closely related to creativity, this can also make it harder to teach and motivate. It is important to point out that many mathematical topics which were done entirely void of applications like properties about prime numbers later became very applied like for cryptology. But it is in the nature of pure mathematics not to worry too much about applications at first. And that makes pure math so pure! By the way, the Thales theorem round minute 9 in your movie is much more interesting when the base of the triangle is not the diameter. The angle stillremains constant when moving on the circular arc. This brings in a moment of surprise and makes the theorem much more interesting. The diameter case can be proven as you illustrated with symmetry. It needs a bit more creativity to find a proof of the general case. I teach this theorem since many years in a course and still have always seen that the class was able to figure out a proof in the more general case (despite that most have not seen the general case). I myself do no more agree with the pessimism of Lockart. Especially if you look what is around also on youtube (like also your channel) makes some aspects of math more accessible. S lot has happened since 2002 when the article was written. I'm sure that if Lockart would rewrite the essay today, he would agree. The last two decades have also produced msny fantastic math books for more general audiences as well as quite many movies and documentaries illustrating the beauty of the subject. Certainly the pamphlet of Lockart had a good deal to do with it.
This article was an eye opener for me back in my school days. It is probably my inspiration to keep a for a better explaination and learn from it.
Everytime a Mathematician forgot to add units to their answers:
Mathematician: Video Thumbnail
think you mean physicist
@@tibees I second. Also, hi!
Lucky you got reply from tibees❤️
Math is unitless. It's the real world that requires comparatives.
@@rajarsi6438 Math can be used to describe entropy.
I love your channel so much, and this is one of your best videos. I taught math for 40 years, and maybe occasionally managed to do what you're describing here. I love that proof about the triangle and the circle! So beautiful.
I really think the situation is improving, mainly due to all the Math-TH-camrs out there! Keep it up!
Agree with you.
It's really nice to have these kinds of sources available for free, but I'd think that the people who watch these videos are the ones already interested in maths.
@@milandavid7223 you‘re right
Well done! You do so well as an educator. Your way of explaining math through creative means is a wonderful talent. Please do not doubt yourself.
This says a lot about society.
We live in a
Bottom text
when the
Those who believe themselves superior with their ego games try to enslave humanity in a state where they reject their own spirituality. This so called elite despises spirituality and try to force others into their view of life. You see, negating your spirituality is negating your inner creativity and mind power to enhance all life naturally and your own self.
What a funny coincidence...
I stumbled upon this essay a while ago (funnily enough it was recommended by a music youtuber) so I saved it, but I never got around to reading it. Thanks to this video I could just sit back and relax without having to read the thing, and I got some extra comments as a bonus. Also, the visuals and music make it sooo relaxing (even though the message is not that great...).
Great video!
I feel like Tibees has solved Lockhart’s issue through her amazing videos
I am completely amazed at both the wisdom in the content and the quality of the presentation hats off Toby hats off i just adore ur channel
all my exams got over today and ive decided to binge watch Tibees today 😊
When that which one loves to do, becomes that which one has to do, it is such that one cannot bear to do it any longer
"logic takes you from A-B imagination takes you everywhere"
If you wrote a book on math and science, I'd buy it and read it too my future kids. You do such a great job opening up the field and making it approachable through informative kindness.
Hi! I'm from Brazil, and that's the same thing. It happens to the most of the students, I always thinked that I was really good at math, but Math, at the most of the cases, is a subject that is introduced yo you just to make exercices, despising your creativity.
It's such a nice intuitive explanation from a 7th grader.
Few years back I read "How to Solve it" by G. Polya. It delves into this idea of how to motivate students, when to give the right nudge and encouragement. It was really eye opening for me and has since encouraged me to really engage with math problems. Every now and then, I re-read the book and it still blows my mind.
Lockhart's essay is profound. He makes a very persuasive case for the "artistic view" of mathematics and I think I will never be able to turn my back on this.
If anyone is interested in getting a taste of how Lockhart would teach math, you can get his book called "Measurement".
I'm slowly working through it and it is honestly amazing!
This is superb! The point that letting students make discoveries for themselves is the golden nugget of teaching math - that is spot-on!
There's just no describing the elation of that - it has to be experienced.
Fred, a mathematician/physicist (retired)
As someone who decided to become a mathematician because I explored chaos theory after reading Jurassic Park, this essay has resonated with me! I have always felt that I had learned what "real math" is outside the classroom, rather than in it. (And this, despite enjoying my math classes in school.)
I have no idea why this appeared in my recommendations, but I'm glad I clicked on it when it did. Excellent. Well done :)
This is so insightful and eye-opening! Thank you, Toby!
I have a pure linguistics background, but I confess I do think about the mathematical aspects of almost every and any problem, challenge or issue in my life. It is another form of light that always illuminates something important. Every time.