This was so beautiful. I was thinking of revisiting the old video I made with Strogatz about the Brachistochrone and Johann Bernoulli's solution, but this honestly does most of what I could have dreamed and so much more. Bravo!

This whole STEM education space has reached completely new heights because of the likes of you guys!!! I couldn’t be more thankful. Stuff like this will be truly world changing. (The hologram video was epic! Long format is incredible and the little secret vlog was the cherry on top. Thanks so much for your work!)

"I recognize the lion by his claws" is such an epic quote Imagine being so legendary you don't have to sign off your letters/papers and people instantly know who wrote it

Counterpoint: “I have the most beautiful solution. Nobody has seen such a perfect solution, you wouldn’t believe it. You know it, I know it, everybody knows it. Don’t we have the best solutions?”

PLEASE, I BEG YOU - continue doing collaborations with Prof. Strogatz!! The combination of TWO of the greatest "explainers" of our time is producing absolutely compelling stories!!

One thing I adore about these videos is that they bring attention to history's forgotten heroes. Nakamura wasn't given the credit he deserved for the blue LED, and that video brought his contributions into the spotlight for millions. Now, Maupertuis has been given the spotlight and he can be recognized for his efforts alongside some of history's greatest mathematicians. If only he lived long enough to see this.

Those things always make me wonder what the people who denied the inventions so hard would say now when they see how much they pushed the world forward. What would the people who insulted Maupertuis for his idea would say after they see it proven right.

The way Euler was described as a “good guy” wanting to help and explain stuff brought tears to my eyes. My old math teacher was a HUGE fan of Euler and his face would light up every time he talked about him. To the point that some students mocked him behind his back for it. That teacher was very much invested in his students and whenever someone, who had struggled with a certain concept, finally grasped it, he would be overjoyed - much more than by someone effortlessly picking things up. If you genuinely worked hard to improve, you would be rewarded with grades on the same level as the naturally “gifted” kids. Only watching this video I just realized that Euler being his personal hero most likely had more to do with Eulers personality traits and empathetic teaching approach rather than his mathematical acumen. Truly a great teacher who had a lasting impact on my life.

Sometimes all it takes is one good teacher who loves and believes in their job to set you onto a path that really defines your life. Wish we had more of those. They are rare and the system doesn't really help finding them and keeping them around.

We don't a lot about Euler as he lived almost 300 years ago. But judging by what we know i am pretty sure he was one the greatest mathematician of all time not just because he produced a lot(and i mean a lottttttttt) of papers but because of his personality. He was probably a very nice man. Being friends with the bernoulli's who were seen as the bad guys certainly helped. He also played with his kids and grandkids and also did math with them! Euler is definitely one of my favorites!

I never had that experience as a math student, because I never had a math teacher with enough ambition to attempt to teach me something I didn't grasp almost immediately. Yes, the hard working dullards were awarded the same grade as I was awarded, but mostly because I was constantly forced to sit there in first gear, basically twiddling my thumbs. Math is endlessly full of things I would have found very difficult on first encounter at that age. But none of these things were on the dullard curriculum, so I got to sit there and goof off with my own projects and be the bright student my teachers mostly ignored.

Actually, forces do not describe all of physics. They are mainly a helper in classical mechanics. But you can not describe interference effects with forces. And in Langrangian mechanics you do not have explicit forces.

Would it not be more accurate to say force is a function of mass and acceleration? Newton's second law, F = ma, is traditionally seen as a static equation describing force as the product of mass and acceleration. However, life and complex systems are inherently dynamic, requiring a reinterpretation of this law as an interdependent relationship where force, mass, and acceleration are mutually dependent functions over time (defined as Einstein's Co-ordinate Time or the speed of light). Just as the electromagnetic field arises from the interactions of electrical and magnetic activities derived from matter and energy, Force dynamically interacts with mass and acceleration, creating a continuous feedback loop. External perturbations to a system's electromagnetic field influence its internal dynamics, and vice versa, through a process of field alignment at various levels. When matter and energy interact to produce information, or when information is applied to affect matter and energy, the resulting changes occur instantaneously across different field alignments. For example, information interactions at the matter and energy level generate electromagnetic interactions that, in turn, influence the information within the electromagnetic field itself. On a larger scale, the Earth's electromagnetic field interacts with that of the human body, affecting its internal dynamics and maintaining homeostasis-a state of equilibrium. This dynamic version of F = ma, measured continuously over a constant time frame, emphasizes the continuous, reciprocal relationships that sustain complex, living systems, illustrating how fundamental forces and properties are interconnected through time to maintain stability and balance.

I love these math videos because its so weirdly satisfying when you introduce another famous mathematician, and I'm like, "My man Euler was in this???". Its the same kind of excitement as the portal scene in Avengers endgame.

I'm a PhD physicist and I'm very grateful to you for this video. I'm amazed, I still have goosebumps. Best explanation I've ever seen. And all physicists and engineers know how difficult it is to understand this topic the first time during college, and you made it so easy. What an amazing trip it was!

Potential energy is dual to kinetic energy -- gravitational energy is dual. The Lagrangian is dual to the Hamiltonian synthesizes the principle of least action, The equations of motion (predictions) minimize the action in quantum mechanics. The Schrodinger representation is dual to the Heisenberg representation -- quantum mechanics is dual. Action is dual to reaction -- Sir Isaac Newton. "Aways two there are" -- Yoda. The equations of motion are predictions -- syntropic! Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics!

Watching this from Nigeria, and it's incredible how i can have access to this quality of information for basically free. I really love the internet sometimes.

It is something every person on the planet should have access too. It is the great knowledge equalizer. Allowing anyone from anywhere to learn anything.

I just saw another brazilian watching this video on the supermarket while waiting for his Uber. It was a somewhat old dude with his daughter. You've become massive, man. Great to see it.

@@ronaldderooij1774 If you raise your kids to be dumb, then yes, but my 11 years old daughter and 6 years old boy LOVE watching this and other science channels with me...

I generally dont leave comments. But I felt I had to write this down. 24 years ago when I took my physics class as a first year under grad student, I was quickly introduced to the Lagrangian and Hamiltonian in a physics class with just the equations thrown around. There were books in the library which provided tons of equations but never the intuition behind them. It was assumed that the reader knew why this had to be the case. I never got back to digging this deeper as my primary area of focus had shifted to other subjects. But after so many years I am finally happy to see the beautiful thought process behind them. Really appreciate you for making such valuable and interesting content.

Exactly!! Its degrading to teach how to use a formula without the story… the story and attempts through 4+ time periods are rich with lessons that can be applied all throughout life. Stories captivate an audience! Not formulas! Plus, you’ll only find independent thinkers at the forefront of discovery, I wonder how many greats fell short due to the rigidness of curriculum.

I’m 100% with you. I find people tend to learn best through story telling. Not “facts”. Understanding what lead people to a current understanding is far more powerful and sticks with you. It’s harder to do and takes more time and work, but I think it serves more.

This! Wouldn't it be much beter if all of those equations actually started as a story you'd follow through similarly as in this video? Wouldn't be much longer but way more meaningful and easier to learn and understand.

Please never stop making videos! You and your team make some of the best science communication content out there. Veritasium provides the education that public schools fail to do.

This was my favorite part of my intermediate mechanics course, except in the opposite direction. My professor would take F=ma and somehow turn it into a 2 class multi-page problem that in no way resembles the principles it had built from.

As a Mechanical Engineer I certainly knew the principles of Lagrangian and the Eulerian. I also knew Newton and Bernoulli's story. It touched my heart to learn about Euler's kindness and Maupertuis contribution. I never knew that. The human element was the most special. Thank you for sharing.

As a carpenter that watches math videos - knowing little about advanced equations - when I saw the outline of his profile it piqued my interest. I said to myself, "cool, he's back. There's something special about the E man." To discover he's also kind and generous, sorta made my day. Thanks Derek.

Maupertuis is, I feel, a guy that saw Bernoulli's work and had an intuitive vibe, but wasn't quite able to put into words correctly. People like him are invaluable for the process of discovery and creation, but hardly ever get the recognition they deserve because they're not the ones that bring it home.

@@Just_A_Dude People want to feel special by worshiping special individuals when advancements are always built on top of the previous shoulders. It's shoulders all the way down...

I have read that Gauss (according to Niels Henrik Abel, 1802 - 1829, a very short life) did not have Euler's kindness of writing clearly understandably, but rather like a sly fox who uses his tail to remove his tracks. Gauss: ".... Thus it follows, obviously, that ...", and you need 8 hours (or perhaps 5 days) to see the "obvious"...

OMG 23:23 to 25:57 - such beauty, eveything connects Also, phenomenal production values... The writing, the synchronization of the sound track to climax when F=ma shows up

Veritasium has now surpassed the quality of netflix docementaries. Really one of the best videos on math i have ever seen. Well done Ve. Cant wait for part 2

Netflix docus really have fallen lately. Moving more and more towards the formats of cable TV to desperately stretch out every single minute of content 3-6 times longer than necessary.

Im still waiting for the part 2 of their video about Thermite, and now Derek is making me wait for the part 2 of Action. They better release these sequels soon because im loving it

I’m a practicing mechanical engineer of 6 years now. Nearly 30 years old. In 2014 I discovered Veritasium and Smarter Every Day when deciding what to study. I cannot explain how instrumental these videos have been to my life. Thank you so much Derek!! Humanity is better off because of you

Im in school for engineering, but we haven't talked about this topic at all. Would this principle apply to classes like Dynamics and make it easier for me😅

@@elementalist1513You do generally cover it, idk in how much depth, it depends on your course structure and discipline. But if you ever take an advanced dynamics subjects you'll encounter them especially for shafts and machines with linkage mechanisms. Although nowadays most of this stuff is taught in conjunction with computational methods not strictly rigours math (at least where i study eng).

As a first year physics student, these types of videos are incredibly valuable! I legitimately cannot explain how incredible it is to walk the line of simple explaination vs specificity and detail that you and your team walk perfectly. Thank you so much, it makes me so happy that there are science educators such as yourself following in Euler's footsteps, teaching with empathy, clarity, and clear passion!

The video is interesting for sure, but it is technically little more than a history lesson. I wager you would not be able to solve even the simplest of problems using the fucntion you probably just saw for the first time in your life, after watching this video. Calling him a teacher for giving you a history crash course on a single formula is a disservice to anyone who is actually teaching, I think.

@@leviathan5207 While I understand where you are coming from, I never meant to undermine or disparage classical teachers and educators with my praise of Veritasium. Rather, and this was unstated, so there would have been no reason to assume this, I meant to call attention to the benefit of having various avenues and angles to education. To be sure, I am pursuing physics first and foremost because I had a fantastic high school physics teacher who ignited my initial passion and you are most definitely right, I likely would not be able to solve most simple problems using the function without help. However, I do not think that the value that Derek and his team provides is that of immediate practical application of the mathematical concepts they cover. Rather, as stated by many other people much smarter than myself, by teaching the history and rationale behind these mathematical concepts, one can make sense of them outside of just calculus and algebra. Additionally, I am calling Veritasium a teacher because, over the past couple years, I have learned a lot from this channel. I think that classical teachers are incredibly valuable (and often undervalued by most people), but I do not think one has to teach in a school to be an educator.

@@leviathan5207 my father tried to teach me to drive stick without explaining the principles behind it ("just do what I say when I say it"). Fortunately, he was a fast-hand on the emergency brake and I got to autograph the the skidmarks in our driveway. 🙂 Mom took over after that and learning what was happening in the engine as I pressed pedals kept that from happening again. Knowing _why_ helped me learn about "how". Having a conceptual underpinning and an understanding of how a concept was _developed_ gives you a framework to attach all the specific mathematical details to; something that simply throwing the final equation at you wouldn't provide. Context matters.

@@leviathan5207 I am also pursuing a physics degree. I'm in third year. While a large part of physics is, indeed, knowing how to solve formulae for solutions, simply knowing how to plug in numbers/manipulate an expression pales in importance compared to actually understanding the concept at hand. Where the equation comes from, what each term means, why certain cases yield certain solutions, etc.. Without this knowledge you are no longer doing physics, just math. Videos like this are invaluable when it comes to forming intuitive foundational understanding of these topics. Setting it all against the backdrop of the real history of the development of these concepts and ideas surely helps connect everything together. Also, Derek is Ph.D. in education research. I'd wager he knows more than most when it comes to education.

Your video deeply moved me, I have been wanting to go back to learning physics for a while now and your video reminded me of the sense of wonder I had in my freshman year. Thank you for creating something so special, I can’t wait for future videos like this one!

I wish he'd taken the time to impart a bit more intuition to those of us who haven't done calc in a long-ass time. But I'm certainly glad the rigor is there for those who can fully appreciate it.

I'm a theoretical physicist, and I'm astonished by how precise and well-presented the video is. It reminded me of the wonder I felt as an undergraduate attending beautiful lectures on classical mechanics. Thank you for creating such wonderful material for everyone on TH-cam.

@@isodoubIet If you have data to "prove" that the principal of least action is wrong then do so but until then this forms the principal foundation of not just all of classical mechanics but the Feynman path integral and quantum field theory i.e. the standard model of particle physics. The burden of proof always falls onto the claimant when the weight of all human progress and knowledge in physics is at the heart of the subject.

@@Dragrath1 The principle of least (stationary) action is not wrong... _in classical physics._ It doesn't apply in quantum mechanics. In fact, quantum mechanics is what you use to prove exactly in which sort of situations the principle is a good _approximation._ The video goes so far as to state that quantum mechanics can be replaced by the least action principle, which is categorically nonsense. "but until then this forms the principal foundation of not just all of classical mechanics but the Feynman path integral and quantum field theory i.e. the standard model of particle physics" That is nonsense. Pop quiz! Explain in your own words how dimensional regularization is used to treat infinities arising from loop diagrams, why that doesn't present any conceptual problem for the theory, and why dimensional regularization is advantageous when compared with more simplistic schemes like cutoffs.

@@isodoubIet I thought you were trying to say the principal of least action was wrong, and yes the mechanical form of the action breaks down in quantum mechanics but the Feynman path integral shows quantum systems still follow the principal within probability or state space. I don't think you can really say that the Feynman path integral isn't part of the principal foundation of the standard model given that Feynman diagrams which are a computational tool for calculating these systems of possible interactions depend on this theoretical framework At this point though I think there is good evidence that this is a consequence of deeper more fundamental rules with Wolfram's computational emergent model of physics as a consequence of Turing complete computational constraints simultaneously iteratively acting on some informational system looks promising if they can come up with a solution for computing the continuous domain of dimensionalities which appear to be natural in that framework.

I took a class called theoretical mechanics, where we learned most of this. What was explained to me over 10 weeks was described infinitely more beautiful in this 30 minute video. I’m tearing up just thinking about it. Your channel is absolutely incredible for bringing math and physics to the average person, and even making the people familiar with the material think about it in a new way. Thank you

Last semester theoretical mechanics ended for me. I thought Lagrange's mechanics was just yet another way to describe moving things, except even more generalized and even more boring. I still do find it unintuitive, and i was genuinely hoping to see how this pops up somewhere else, but sadly we must wait for another video.

@@backspace345 Funny Lagrangian Mechanic saved me in my first Semester of theoretical physics. Could not get the hang out of classical Mechanik, but this gave me at once a tool set, i could appy. Esp. Double Pendulums (practical example: swinging bell) That and the Maxwell Equations are still the only parts of theoretical physics I like as a applied and Experimental physicist Even 20 year later and out of the scientific world

Personally, watching this 30 min video made me wish I had time to study the subject over a 10 week course. These videos are nice to learn about the history of physics, but if you don't study the math behind it you don't really understand any of it. You just accept an answer for the correct one.

A very fascinating video, this brings back painful memories which i have been enduring. My relationship of 6 years ended 3 months ago. The love of my life decided to leave me, I really love her so much I can’t stop thinking about her, I’ve tried my very best to get her back in my life, but to no avail, I’m frustrated, I don’t see my life with anyone else. I’ve done my best to get rid of the thoughts of her, but I can’t, I don’t know why I’m saying this here , I really miss her and just can’t stop thinking about her .

Parting ways with someone you deeply cherish is an agonizing experience. I understand firsthand, having encountered a parallel situation at the end of my 7-year relationship. Driven by an unyielding determination, I explored every avenue to salvage our bond. Seeking guidance from a spiritual counselor proved pivotal, as their intervention played a crucial role in rekindling our love.

A beautiful mix of history, physics, math, music, emotions and story telling. I am just blown away ! I remember terry tau's quote at this point that, we should teach our children the history behind the things, how it came and how much effort went to bring it in the form it is today. If we don't appreciate history then there is no way we can appreciate it's true essence. Thank you Derek and the team for their amazing efforts in STEM.

100 percent agree. I was always frustrated in college because I felt I was never "catching on" quickly enough... only to find out years later that the knowledge we were taught in one semester took humanity hundreds of years to figure out.

I hated history class because it seemed to be about learning these dates and names of dead people. Nowadays I love history because I can ignore exact dates and focus on the reasons and motivations of those people that came before me

It's worth noting that the history of a field is often more understood by those in its field than most historians. As a mathematics person, I have already heard of the Maupertuis, Voltaire and Frederick the Great drama from a biography of Leonard Euler, and have discussed the history of probability with professors while doing my honours thesis.

I am learning this right now in grad school and watching a Veritasium video about it and learning a little history of its origin is amazing! Makes me smile whole heartedly!

I attended a university lecture which covered Multi DOF Dynamic Systems, the Euler-Lagrangian Equation, and Double Pendulums this morning as a Mechanical Engineering student. Was completely baffled and confused about the theory behind all of it. Coming home exhausted at the end of the day watching this piece of art just made me tear up. Such an amazing coincidence that this video was released today. The moment everything came to F=ma was such an Eureka moment too! Thank you Derek.

I just had 8 weeks of my first course of mechatronics in technical university and this video was some what eye opening. I have been struggling with concepts of virtual work etc used in very hard and tidious matrice calculations used in equations of motion on multibody systems.

As a physics student in the 3rd semester this is a brilliant video to watch...literally goosebumps all the time. It is so satisfying to see what u have learned being illustrated in such a way. Just WOW really

I've been out of my engineering school for over a decade, but this video brought me back to my youth, lol I don't remember how to do all this math anymore but I recognize it and I think of my friends that went into math and physics

i always get goosebumps when i read about all those mathematicians, as they always somehow related to/connected another great mathematician, which i had no idea belonged to his timeline... and also contributed to the theory 🤯🤯

As of late, with each video you release I am struck by the sheer integrity and production value of your work. Since I discovered this channel I have been thoroughly impressed with your videos, but with each successive one you somehow still manage to reach new heights. It's not just production value, but also some other intangible factor I lack the vocabulary to express that gives your videos their unique and unmatched quality. I would not call it an exaggeration by any stretch to say that you are one of the greatest educators of the modern era.

Initially I was skeptical of the clickbaity title and the intro, but just after 3-4 minutes I was so *indulged* in it that I forgot to increase the video resolution to 1080p like I always do. Only later I realised that I watched 30 minutes of video that I was not going to watch. This is a testimony to how great this video is.

Same for me. I was going to watch this anyway because Veritasium always delivers, but I thought I'd put it to later and store the tab for a later day. But I saw a math equation, was intrigued and kept watching for a bit, then it was so interesting that pausing wasn't even on my mind.

It sound like clickbait, but it's true. Literally all of modern physics are derived from either lagrangian or hamiltonian mechanics, both of which are founded on the principle of stationary action

King of confusing for the laymen though😂. Imaging trying to understand this with highschool level understanding of math, I'm no genius in the subject so it was hard to say the least.

@@madamred3793 I think that wasn't really the purpose. by showing a wall of equations for 5 sec, you don't expect anyone to read it except of sb who hits the pause button and goes through all of it slowly.

@@madamred3793same man. I mean, ik basic differentiation and integration, some standard values, but the derivation for F = ma that he showed made me realise I should watch this a couple years later

We debated how to do this. We wanted to show all the math in case someone wanted to step through it, but we didn’t want to get bogged down in it and lose people so this was our compromise.

The fun of the history of math and your videos in particular is how when every time you bring up a new character I recognize their name from one of their laws/principles or just knowing them from another achievement in mathematics, reminds you how much everything is connected

Not one single channel on TH-cam can give you such detailed, contextualized and informative, yet so easy to follow and beautifully arranged video on what would seem to be just another part of curriculum you would go through in school or university. This makes me want to learn more about this topic, physics and everything in general which means this channel has achieved the true meaning of teaching. Inspiration and imagination. Kudos!

28:32 I remember when I was doing highschool physics olympiad, we treat Lagrange equations as some short of legendary weapon to handle meticulous oscillation problem 😂, because it is so hard to get the equation correctly using newtonian method. But we never knew why does it work and where does it came from. My mind has been blown 🤯.

It is easy to understand why this works. In the Langrange formula, the potential V is the cause and the energy of motion, the kinetic energy T, is the effect. The difference between the two must be zero all along the integration path, otherwise it means that we have missed either a cause or an effect, or both. Basically, the philosophy is that for every cause there is at least an identified effect. It is like the Newton law F is the cause and the acceleration is the effect, both are equal. The problem is that the Lagrangian assumes instantaneous transmission of causality, which is why it does not work in relativity. In Relativity the causality takes its share.

@@sanidhyapratapsingh-h7d "Instantaneous transmission of causality" means that there is no delay between a cause and the corresponding effect on a body. This is not the case in relativity.

The most beautiful thing about Science and Mathematics is you can just say "I don't know" for the thing which you really don't know and it doesn't impact your stature.

Ah, no. That's actually really far down the line. From my experience in university, the freshmen do like to play out the historic tropes of quarreling scientists fighting for each shred of credit. There are a lot of loner types entering maths and physics who are on a mission to show that they are the smartest. The way I experienced it, the physics course is deliberately structured to socialize such types of students towards a team spirit.

@@JoshuaNorton I studied physics in Australia and didn't get any of that. No one really cared how smart you were or how well you did, people just wanted to get through the day and hit up the bars. Also like half of the students were asians that only spoke broken english and kept to their own social groups, and that is half of an already very small class because not many people take physics. The asians were always good to get answers from if you can communicate with them though, much smarter than us and none of us even cared or tried to compete. We just wanted to pass

One thing missing? Connection to Noether's theorem. It is right there. Variation of momentum over space (Lagrange) vs variation of energy differential over time (Hamiltonian) 21:50

Hi Sir... I am Pranetha(remember from CFAL 2021 batch,druhan and pannaga's classmate in case you dont remember)....because of you I am still watching veritasium...currently in NITK final year ....hope you are doing great

Physics graduate here. You brought back a lot of good memories from my analytical mechanics course. I wasn't really able to appreciate the beauty of the principle besides its mathematical elegance. What you (and Strogatz) are doing with these videos is truly a gift to humanity. Thanks

Thanks for the video! It gave me an insight into Lagrangian as a high schooler in the final year. My Physics teacher once briefly mentioned about Lagrangians in class, that they’re a technique used to tackle mechanics problems using energy, and now I see exactly how! I can’t wait to learn more about this in detail in college next year!!

My son sent me to watch this. I'm already subscribed but so frequently when it's physics I get a bit wary, I'm very much not a maths person. You start throwing equations across the screen and my mind often just quits right there, lol. But this was fascinating. When he told me the name of the principle I blinked at him and said "You mean conservation of energy?" and he started hopping up and down going "NO! That's just the thing! Augh, go watch it Mom!" SO here I am! And I see what y'all are saying. Interesting to think about and I look forward to the next one!

Words cannot fully express how much this channel has transformed my perspective on learning. There are times when I feel completely lost with the concepts he talks about, yet instead of feeling intimidated, I’m inspired to watch the video multiple times and seek additional sources to deepen my understanding. The passion and effort he puts in helping people understand makes me not feel like I'm too dump to understand such complex concepts; instead, it sparks curiosity and a genuine hunger to extend my knowledge. I really appreciate you team Veritasium

Gripping screenplay ✔ Cinematic background score and camera angles ✔ Cameos by renowned (but dead) mathematicians ✔ Three-act structure, with the introduction of Euler's character placed perfectly at the mid-point of the video ✔ Spooky Halloween theme for the season ✔ Post-credit scene hinting at a sequel ✔ Forget blockbuster Hollywoood flicks, instead this video should be released in theatres and sent in film festivals!!

Probably one of the best science videos I've seen. So much where one can see where the math originated. Seeing the history of it is extremely fascinating and helps understanding it. Would have been interesting to see something like this in high school or the university to gain a deeper understanding.

I studied this as a third year physics undergraduate and you've really captured how at first it seems like pointless pushing algebra around until suddenly a profound revelation hits you. Our mind-blowing moment was the professor going on to show how you could picture every possible path between two end points as waves with neighbouring paths destructively interfering everywhere apart from along the true path where dS = 0, where the paths would be in phase. All of a sudden a ball moving under Newtonian motion looked a lot like a quantum mechanics. Eagerly waiting to see where this goes in the next video!

Maybe it should be dS = h instead of dS = 0. Euler might have made the initial error which led to the disagreement between quantum theory and relativity. The two may very well be in the analogous positions as the Rayleigh-Jeans and Wiens law formulas in the Blackbody radiation spectrum distribution plot. Both are accurate within the domain of applications but cannot bridge the gap. General relativity uses space-time continuum but quantum theory uses discretum of eigenvalues. Maybe space-time continuum of general relativity is incorrect but quantum theory's discretum of quantum states in the energy-momentum discretum is correct.

For me, one of the best introductions (albeit a bit old-fashioned at times) to the principle of least action is Landau and Lifshitz's volume on Mechanics. They also properly give Mapertuis his share of the credit. Also interestingly, they go on to explore how the equations change when you relax the constraints a bit (for instance, by not fixing the final point) and what this teaches us and how to use it. Simply marvelous.

Not specifying the endpoint is an interesting concept. It must allow ranges of answer that likely produce probability distributions. Odd way to get towards wave functions and their quantisations.

When Veritasium summarized Physics Grad first semester in half hour! Impressive work, you literally summarized the first semester of Physics Grad lecture series in one video. As Richard Feynman said great teacher knows how to communicate complex subjects in the least amount of action. Impressive! Even second semester on Thermodynamics, third semester on Electromagnetism, and fourth semester on QED would be extra episodes on least action principle topics. I am guessing eventually Veritasium might show how the least action principle works on Einstein's General Relativity. It's TH-cam channel like this that helps me explaining Physics to my kids. Thank you Veritasium.

Your first sentence should be a giant red flag to you. If you are capable of critical thought, so much info being compressed into 30 minutes should be a red flag that the info is at minimum, incomplete.

This channel is the first source that has taught me the origin and meaning of the Principle of Minimum Action in an intuitive way. I can only thank you for spreading so much knowledge. Long live Veritasium.

Indeed, even Newton said "If I have seen further than others, it is by standing upon the shoulders of giants.", so no important mathematician, physicist or scientist (or natural philosopher, how they used to be called) has single handily invented or discovered anything from scratch, all discoveries in physics has been a human group effort.

I think this was a meant to be a really funny double meaning line, since in real life we are very close and approaching Halloween. If not, that is a hilarious coincidence.

This video made me pick my Feynman lecture series book back out. The mathematics of all this is calculus of variations. I taught myself this once, and it was one of the most profound insights I’ve ever had mathematically. Thanks Derek, you are truly this days Feynman in terms of making complex concepts approachable and fun!

Your channel reminded me that I loved maths in school, and calculating moment of inertia of weird shapes was almost a hobby. Got myself an applied maths book to rekindle what lay dormant all this time. Thanks a lot for your work.

I remember this blowing my mind when we learned about it as a physics undergrad. These days I forgot most of this but had always thought if it as “lagrangian mechanics” since it used the lagrangian. But now I distinctly remember a chapter on Hamiltonian mechanics. Man I miss those days where ever single lecture just completely blew your mind. I suffered through learning math just so that I could have the tools to learn more physics

I really love it when I watch a veritasium video, because one of 2 things happen: 1) The content is completely new to me extremely exciting to learn 2) I already know most of what's about to be said and I'm pausing and predicting what Derek will say next. It gives me a new perspective with some wholesome details, and a nice ego boost. This was one of the latter, and it's an absolute masterpiece of production value. FLAWLESS

To be honest I wasn't shocked. I won't ever call myself to be smart, but I looked at this this way: if we initially use some formulas, isn't it normal that we can manipulate it to the already known equations? The "m*a" already popped out in integral, just "a" was written in terms of second derivative of displacement. I just think it's kind of rewriting the same thing in different terms. If you take a look at 24:45, they started with (1/2)*mV^2. It is already strictly connected to F=ma.

How satisfied would not Mr Maupertuis be, were he still alive, if he could see the principle of least action applied to highest degree of dignity to which it is susceptible.❤❤❤

I've experienced bliss by the end of the video. Feels like it filled a small void in me that was present from the time I started using the Lagrangian formulation at school, as I was busy on the practical applications but never really took time to explore the reasoning. Thank you Veritasium

I started watching Veritasium 13 years ago about a Slinky dropping and we're now here with pretty complex formulas (for me), I feel like Derek is giving us a STEM degree without us even noticing. I learned so much in these 13 years. Thank you.

You need to stop implicitly trusting people simply because they appear to know what they're talking about and have a higher production value. Veritasium does not make very trustworthy claims.

@@cherriberri8373 im not saying you are wrong with the advice about not trusting people just because they appear trustworthy, but could you give me an example of Veritasium making untrustworthy claims?

@@cherriberri8373what claims specifically is it you don't find trustworthy? Everything Derek presented here is either historical facts where you can look up the sources on every single person, or pure physics. The few times Derek has made bold claims without all the facts laid out, there has been an outcries from physicists in the comments. The fact that the comments are full of praise is because all the physicists watching recognize all the facts and are blown away by the genius way of presenting it. I dare you to point out a single factual error in this video.

I love Strogatz! I was fortunate enough to take his class on nonlinear dynamics and chaos, it was the most interesting class I'll pretty much never use!

Teaching school physics for over 30 years I love how you have embellished the maths & physics with the history of those men who contributed to the theory’s development. A coruscating delivery; your presentation makes it so interesting that there would be so many more physicist & mathematicians by teaching that way. These optimisation problems solutions are found in the "Calculus of variations". Like a chain hangs freely its shape is derived as a hyperbolic cosine curve or a hole drilled through the earth from one side to the other & a ball dropped through it to minimize time is a cycloid. The shortest distance between 2 point! Yes, one of the simplest problems takes such complex maths technique to solve it!

Veritasium's most impactful aspect is Derek and his team's storytelling and visual presentation. I'm not a math person, and I never have been, but you still keep me watching your videos from start to finish! If I had a math teacher who could explain like this, I’d probably be good at math.

Same here. In fact, I think I'm lost even a bit earlier: "So if you took a tiny step to the left or the right, the value of the function basically doesn't change". What does that mean? So does the value change or not? I think it does, I don't see why it wouldn't. And then, if you were to change the path of least action by "adding a tiny bump here or flattening it out there", why "the action basically shouldn't change"? It seems obvious to me that it would change. They even say a few moments later that "any other path must have more action". So why this altered path doesn't have more action? I would really appreciate an explanation.

This has to be the best and most expansive crossover ever. Spanning over centuries of eras, involving almost every major mathematician, uniting various branches of maths to solve multiple problems over many fields, creating a unique new unit which sparks innovation for an entirely new and uncharted area of physics. BRILLIANT! I was legit fanboying over the entry of every mathematician and the reveal at the end equating to Newton's Second Law of Motion had me actually pause the video to really scream and grasp the mind blowing connection. Amazing work by Derek and the amazing Veritasium team. As always, awesome work and thank you for this masterpiece.

I am an engineer and actually found this to be the best explaination of both schools of thinking. I always enjoyed applying the Langrangian and watching fellow students frown over their arrows and angles 😂

When I studied these topics during my college major, they didn’t impact me the way they do now. I’m just flabbergasted at how simply you explained such a complex problem in modern mechanics-it blew my mind!

25:38 This is why I love math. When it was revealed that under all of that derivation and derivation results in an equation that we're all too familiar with, I just gasped.

Because every formula or equation you know is just the simplification of its integral and derivative. Or in the quote of a famous Mathematician "Simplicity is hidden beneath the mask of Calculus"

Condensed into 30 minutes. Yeah, I'm sure someone without background knowledge understood the topic, there are plenty of comments from people like you. But there are even more from people who simply just memorized an extremely short summary that leaves out so much that should and would be covered in an actual class.

I'm glad. I read Goldstein's CM book about 3 years ago, in the 2nd year of college for my CM101 course. You did it, you brought the history along with the elegance of these pronciples. Thank you!!

I love these types of math/physics history videos. They really put in perspective that we are standing on shoulders of giants. They also make me nostalgic about the time I was learning these things in college for the first time.

It also really humanizes these figures, at least for me. We were all taught that Newton was a genius and the impact of Euler's work. But hearing about the social dynamics between these people and their relationships really brings them down to earth and reminds you that they were just people. Brilliant, yet flawed people.

god these are my favourite types of veritasium videos (e.g the video about the invention of imaginary numbers and the video talking about black holes) where they explain maths/physics but also fuse lore and story into it, so immersive and entertaining, keep it up! :-)

26:05 why this feels like an avengers movie , when every hero is defeated and we feel lost but then that one hero out of nowhere comes as an savior , the geniuses of Newton , hats off to my guy maupertuis, and shout out to euler and lagrange truly one of homie , wish i was part of this gang.

The best explanation I never thought I would get for the action. There I was studying in the lecture hall for the first time, thinking why it is not intuitive, what i am missing. Thanks for reminding me why I always loved Physics. Cheers!

Reminds me of one particularly interesting physics lecture in which my professor started with Heisenberg's Uncertainty Principles, which were reasonably easy to imagine, and performed the derivation to produce E=MC^2. The professor's intention, revealed at the last moment, made me wish I could see it all again. In light of my rather low-grade mathematical talents, I remain immensely grateful for your catalog of scientific delights... available to me on repeat... and to many others as an inspiration to remain ever hungry and thirsty for such knowledge. Your channel is a blessing and a gift. 🙏

Veritasium has now surpassed the quality of netflix docementaries. Really one of the best videos on math i have ever seen. Well done Ve. Cant wait for part 2

The principle of least action genuinely is one of the most underrated theories when it comes to explaining general relativity. Thank you so much for exposing more people to this theoretical masterpiece ^^

🤯 I’ve taken advanced classical mechanics (my favorite class in grad school) and I couldn’t tell you the number of times I wrote down langrangians and Hamiltonians for different systems. It took me 20mins into the video to realize where this was going. This is very elegantly put and I wish a lot of scientific concepts would be taught this way. The building blocks and thought processes that went into developing the least action principle as we know and use it today aren’t well dispelled when we learn them.

@3blue1brown8 วันที่ผ่านมา^{+22201}This was so beautiful. I was thinking of revisiting the old video I made with Strogatz about the Brachistochrone and Johann Bernoulli's solution, but this honestly does most of what I could have dreamed and so much more. Bravo!

@tanvirzawad8 วันที่ผ่านมา^{+257}Peace be on them who follow the guidance. Nice to see you here!

@ModernWizardx18 วันที่ผ่านมา^{+205}your videos are pretty good 3b1b i always enjoy them!

@LearningAccount-e5x8 วันที่ผ่านมา^{+418}This whole STEM education space has reached completely new heights because of the likes of you guys!!! I couldn’t be more thankful. Stuff like this will be truly world changing.

(The hologram video was epic! Long format is incredible and the little secret vlog was the cherry on top. Thanks so much for your work!)

@JadMustafa8 วันที่ผ่านมา^{+32}Indeed, surpasses the limit of education - absolutely beautiful.

@felix00038 วันที่ผ่านมา^{+3}wowie

@artbryanmoldon8 วันที่ผ่านมา^{+11979}Man! Euler is that superhero backup that arrives just in time when all hope is lost!

@threeuniquefingers8 วันที่ผ่านมา^{+319}Indeed! He was like Dr Strange in Avengers Endgame! Summoning Langarange as the ultimate support lol

@derroz31578 วันที่ผ่านมา^{+47}U LER-NING is the real superhero :D

@Game_Masters8 วันที่ผ่านมา^{+123}14:02 I am like: Not this guy again.. I swear XD

THE MAN - THE LEGEND

@tturi28 วันที่ผ่านมา^{+17}I've already used his stuff in solid mechanics

@johnimusic128 วันที่ผ่านมา^{+97}Euler = GOAT

@RENO_K8 วันที่ผ่านมา^{+11247}"I recognize the lion by his claws" is such an epic quote

Imagine being so legendary you don't have to sign off your letters/papers and people instantly know who wrote it

@joelspaulding59648 วันที่ผ่านมา^{+155}This is quite possible and common in art and music.

@ahsaasinator28408 วันที่ผ่านมา^{+41}Let’s go another science banger !!!

@ares3958 วันที่ผ่านมา^{+262}@@joelspaulding5964 Try doing that with Science.

@cgonz88 วันที่ผ่านมา^{+98}Counterpoint: “I have the most beautiful solution. Nobody has seen such a perfect solution, you wouldn’t believe it. You know it, I know it, everybody knows it. Don’t we have the best solutions?”

@jmalmsten8 วันที่ผ่านมา^{+10}That's basically how Richard Bachman was revealed. :P

@kevinboles38855 วันที่ผ่านมา^{+580}PLEASE, I BEG YOU - continue doing collaborations with Prof. Strogatz!! The combination of TWO of the greatest "explainers" of our time is producing absolutely compelling stories!!

@TheMoikero4 วันที่ผ่านมา^{+6}At university I have heard a lecture about non linear dynamics. Based on his book. It was the best lecture I have had

@Kyriancdb3 วันที่ผ่านมา^{+1}I agree!

@cocoji3214วันที่ผ่านมาTotally agree with you

@nolanthedude8 วันที่ผ่านมา^{+4439}One thing I adore about these videos is that they bring attention to history's forgotten heroes. Nakamura wasn't given the credit he deserved for the blue LED, and that video brought his contributions into the spotlight for millions. Now, Maupertuis has been given the spotlight and he can be recognized for his efforts alongside some of history's greatest mathematicians. If only he lived long enough to see this.

@entitledOne8 วันที่ผ่านมา^{+144}Those things always make me wonder what the people who denied the inventions so hard would say now when they see how much they pushed the world forward. What would the people who insulted Maupertuis for his idea would say after they see it proven right.

@Player_is_I8 วันที่ผ่านมาSo true

@sottonk8 วันที่ผ่านมา^{+6}Poor Ibn Sahl

@TheAntira8 วันที่ผ่านมา^{+26}I'm not sure I'd call a Nobel prize laureate a forgotten hero

@julioaurelio8 วันที่ผ่านมา^{+67}@@TheAntira The company he worked for thoughout most of his life dumped him and refused to give him the compensation he deserved. A real injustice.

@raktimaryabiswas31828 วันที่ผ่านมา^{+3410}Waiting eagerly for the next part.

Please take the least possible time !

@krishnarajput35158 วันที่ผ่านมา^{+462}but ironically bring the maximum action

@yarodi8 วันที่ผ่านมา^{+11}😂

@nicezombie80548 วันที่ผ่านมา^{+13}The maximum effort so the maximum work, doesn’t necessarily necessitate the most action, but actually… make it cause the most action

@drttgb49558 วันที่ผ่านมา^{+5}@@nicezombie8054 Government in the equation = less action.

@TravisTellsTruths7 วันที่ผ่านมา^{+1}Bam @@krishnarajput3515

@DataIsBeautifulOfficial8 วันที่ผ่านมา^{+17130}Physics is just old guys arguing over who invented the best shortcut.

@lulairenoroub38698 วันที่ผ่านมา^{+908}"The difference between science and screwing around is writing it down"

-A guy Adam Savage was hanging around with. Then Adam Savage.

@JeffreyBenjaminWhite8 วันที่ผ่านมา^{+129}fastest shortcut ;.)

@lazyphoton8 วันที่ผ่านมา^{+184}True, but that's also because nature takes the best shortcut too!

@XILikeTrainsX8 วันที่ผ่านมา^{+139}So trackmania

@Truth4Lyf8 วันที่ผ่านมา^{+41}Math also uses this same principle

@caifasvaca94514 วันที่ผ่านมา^{+219}The way Euler was described as a “good guy” wanting to help and explain stuff brought tears to my eyes. My old math teacher was a HUGE fan of Euler and his face would light up every time he talked about him. To the point that some students mocked him behind his back for it. That teacher was very much invested in his students and whenever someone, who had struggled with a certain concept, finally grasped it, he would be overjoyed - much more than by someone effortlessly picking things up. If you genuinely worked hard to improve, you would be rewarded with grades on the same level as the naturally “gifted” kids. Only watching this video I just realized that Euler being his personal hero most likely had more to do with Eulers personality traits and empathetic teaching approach rather than his mathematical acumen. Truly a great teacher who had a lasting impact on my life.

@nokta73732 วันที่ผ่านมา^{+11}Sometimes all it takes is one good teacher who loves and believes in their job to set you onto a path that really defines your life. Wish we had more of those. They are rare and the system doesn't really help finding them and keeping them around.

@blazedinfernape886วันที่ผ่านมา^{+3}We don't a lot about Euler as he lived almost 300 years ago. But judging by what we know i am pretty sure he was one the greatest mathematician of all time not just because he produced a lot(and i mean a lottttttttt) of papers but because of his personality. He was probably a very nice man. Being friends with the bernoulli's who were seen as the bad guys certainly helped. He also played with his kids and grandkids and also did math with them!

Euler is definitely one of my favorites!

@afterthesmash23 ชั่วโมงที่ผ่านมา^{+1}I never had that experience as a math student, because I never had a math teacher with enough ambition to attempt to teach me something I didn't grasp almost immediately.

Yes, the hard working dullards were awarded the same grade as I was awarded, but mostly because I was constantly forced to sit there in first gear, basically twiddling my thumbs.

Math is endlessly full of things I would have found very difficult on first encounter at that age. But none of these things were on the dullard curriculum, so I got to sit there and goof off with my own projects and be the bright student my teachers mostly ignored.

@ctoid8 วันที่ผ่านมา^{+6036}It's truly an Eureka moment when all the things just came out to be F=ma

@happygood188 วันที่ผ่านมา^{+287}Yeah, my mind was blown. I did not expect that!

@steffenbendel60318 วันที่ผ่านมา^{+123}Actually, forces do not describe all of physics. They are mainly a helper in classical mechanics. But you can not describe interference effects with forces. And in Langrangian mechanics you do not have explicit forces.

@csgas08 วันที่ผ่านมา@@steffenbendel6031🤓

@Unmannedair8 วันที่ผ่านมา^{+83}But it never does describe f=ma... That's just a very special case. F=dI/dt.... di/dt only equals ma for cases where mass is constant.

@liamweavers92918 วันที่ผ่านมา^{+34}Would it not be more accurate to say force is a function of mass and acceleration?

Newton's second law, F = ma, is traditionally seen as a static equation describing force as the product of mass and acceleration. However, life and complex systems are inherently dynamic, requiring a reinterpretation of this law as an interdependent relationship where force, mass, and acceleration are mutually dependent functions over time (defined as Einstein's Co-ordinate Time or the speed of light). Just as the electromagnetic field arises from the interactions of electrical and magnetic activities derived from matter and energy, Force dynamically interacts with mass and acceleration, creating a continuous feedback loop. External perturbations to a system's electromagnetic field influence its internal dynamics, and vice versa, through a process of field alignment at various levels. When matter and energy interact to produce information, or when information is applied to affect matter and energy, the resulting changes occur instantaneously across different field alignments. For example, information interactions at the matter and energy level generate electromagnetic interactions that, in turn, influence the information within the electromagnetic field itself. On a larger scale, the Earth's electromagnetic field interacts with that of the human body, affecting its internal dynamics and maintaining homeostasis-a state of equilibrium. This dynamic version of F = ma, measured continuously over a constant time frame, emphasizes the continuous, reciprocal relationships that sustain complex, living systems, illustrating how fundamental forces and properties are interconnected through time to maintain stability and balance.

@xxvimilia8 วันที่ผ่านมา^{+4768}I love these math videos because its so weirdly satisfying when you introduce another famous mathematician, and I'm like, "My man Euler was in this???". Its the same kind of excitement as the portal scene in Avengers endgame.

@skoogy78 วันที่ผ่านมา^{+642}They say that theorems are named after the second mathematician who discovered them because the first was probably Euler.

@robspiess8 วันที่ผ่านมา^{+211}@@skoogy7 Euler's got his thumb up in everyone's business.

@threeuniquefingers8 วันที่ผ่านมา^{+219}@@robspiess Euler with his thumb and Newton with his nose poking in every flippin field in math and physics lol

@matercan56498 วันที่ผ่านมา^{+47}fr, the same mathmeticians discovered everything

@kallewirsch22638 วันที่ผ่านมา^{+168}First guesses: If it wasn't Euler, then it was Gauss.

@ahwe1737 วันที่ผ่านมา^{+1111}veritasium changed my life, from almost quitting school to mechanical engineering

@AlanTheBeast1007 วันที่ผ่านมา^{+4}Then 2B2B should be your math guide (if it wasn't).

@Waiter19867 วันที่ผ่านมา@@AlanTheBeast100 3b1b?

@gustavosantiago15437 วันที่ผ่านมา^{+45}@@AlanTheBeast1002 bedrooms 2 bathrooms?

@discursively7 วันที่ผ่านมา@@gustavosantiago1543 @3blue1brown

jj

@vitofodera36153 วันที่ผ่านมา^{+67}I'm a PhD physicist and I'm very grateful to you for this video. I'm amazed, I still have goosebumps. Best explanation I've ever seen. And all physicists and engineers know how difficult it is to understand this topic the first time during college, and you made it so easy. What an amazing trip it was!

@hyperduality283813 ชั่วโมงที่ผ่านมาPotential energy is dual to kinetic energy -- gravitational energy is dual.

The Lagrangian is dual to the Hamiltonian synthesizes the principle of least action,

The equations of motion (predictions) minimize the action in quantum mechanics.

The Schrodinger representation is dual to the Heisenberg representation -- quantum mechanics is dual.

Action is dual to reaction -- Sir Isaac Newton.

"Aways two there are" -- Yoda.

The equations of motion are predictions -- syntropic!

Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics!

@SochWrld8 วันที่ผ่านมา^{+1356}Watching this from Nigeria, and it's incredible how i can have access to this quality of information for basically free. I really love the internet sometimes.

@nemesiswes4267 วันที่ผ่านมา^{+46}It is something every person on the planet should have access too. It is the great knowledge equalizer. Allowing anyone from anywhere to learn anything.

@SochWrld7 วันที่ผ่านมา@@nemesiswes426 amen to that

@Gpacharlie7 วันที่ผ่านมา@@nemesiswes426Elon is working on that.

@iceteazen7 วันที่ผ่านมา^{+24}we need this kind of content to dominate most of the internet.

@sozzled30537 วันที่ผ่านมา^{+2}The best thing about it… you can look up the different concepts brought up in this as well. It’s the perfect source for going down the “rabbit hole”.

@arthurcuesta60418 วันที่ผ่านมา^{+1045}I just saw another brazilian watching this video on the supermarket while waiting for his Uber. It was a somewhat old dude with his daughter. You've become massive, man. Great to see it.

@dpatts8 วันที่ผ่านมา^{+106}Q: How many viewers does this video have?

A: More than a brazilian

@ronaldderooij17748 วันที่ผ่านมา^{+1}That was a fun father (NOT).

@joseivan23378 วันที่ผ่านมาTwo Brazilians! Guilty

@kawafernandes70258 วันที่ผ่านมา^{+12}Que legal!

@aboriani8 วันที่ผ่านมา^{+37}@@ronaldderooij1774 If you raise your kids to be dumb, then yes, but my 11 years old daughter and 6 years old boy LOVE watching this and other science channels with me...

@MrNpr8 วันที่ผ่านมา^{+1596}I generally dont leave comments. But I felt I had to write this down. 24 years ago when I took my physics class as a first year under grad student, I was quickly introduced to the Lagrangian and Hamiltonian in a physics class with just the equations thrown around. There were books in the library which provided tons of equations but never the intuition behind them. It was assumed that the reader knew why this had to be the case. I never got back to digging this deeper as my primary area of focus had shifted to other subjects. But after so many years I am finally happy to see the beautiful thought process behind them. Really appreciate you for making such valuable and interesting content.

@AbyssRein8 วันที่ผ่านมา^{+56}Exactly!! Its degrading to teach how to use a formula without the story… the story and attempts through 4+ time periods are rich with lessons that can be applied all throughout life. Stories captivate an audience! Not formulas! Plus, you’ll only find independent thinkers at the forefront of discovery, I wonder how many greats fell short due to the rigidness of curriculum.

@UniverseSpeck8 วันที่ผ่านมา^{+28}I’m 100% with you. I find people tend to learn best through story telling. Not “facts”. Understanding what lead people to a current understanding is far more powerful and sticks with you. It’s harder to do and takes more time and work, but I think it serves more.

@erikziak12498 วันที่ผ่านมา^{+4}Same here.

@guigoinz1128 วันที่ผ่านมา^{+4}Yeah, I need the story in order to make me abaorb the info, otherwise it’s too stale for my brain to remember😅

@semsuddin8 วันที่ผ่านมา^{+6}This! Wouldn't it be much beter if all of those equations actually started as a story you'd follow through similarly as in this video? Wouldn't be much longer but way more meaningful and easier to learn and understand.

@ethanboulter28834 วันที่ผ่านมา^{+10}Please never stop making videos! You and your team make some of the best science communication content out there. Veritasium provides the education that public schools fail to do.

@McBobtheruggaman7 วันที่ผ่านมา^{+842}Mechanical engineer here:

You took us on a winding journey and brought it all back to F = ma. Subbed for life.

@Guy-z6o6 วันที่ผ่านมา^{+10}F= (far out...or fark all) etc.) we agree.

@evanmika9055 วันที่ผ่านมา^{+8}The long and winding road

@JEEtube-f5g4 วันที่ผ่านมา^{+4}@@evanmika905 Definitely not the road with the least action.

@CitroenDS234 วันที่ผ่านมา^{+7}There's a new rickroll in town. We've all been been FMAd.

@cellofellow51152 วันที่ผ่านมา^{+1}This was my favorite part of my intermediate mechanics course, except in the opposite direction. My professor would take F=ma and somehow turn it into a 2 class multi-page problem that in no way resembles the principles it had built from.

@SalilShahane8 วันที่ผ่านมา^{+2457}15:34 the smile on Derek's face when he was compared to Euler made my day.

@akarshiaaryan59528 วันที่ผ่านมา^{+19}😂

@arskiz8 วันที่ผ่านมา^{+20}Euler angles

@realracing3specter2958 วันที่ผ่านมา^{+2}👌

@ludnix8 วันที่ผ่านมา^{+30}prof Strogatz was really channeling The Dude when he said that too!

@Utoxin8 วันที่ผ่านมา^{+73}My jaw literally dropped. That's one of the highest complements I think I've ever heard.

@harananand8 วันที่ผ่านมา^{+761}As a Mechanical Engineer I certainly knew the principles of Lagrangian and the Eulerian. I also knew Newton and Bernoulli's story. It touched my heart to learn about Euler's kindness and Maupertuis contribution. I never knew that. The human element was the most special. Thank you for sharing.

@arunjangir57817 วันที่ผ่านมา^{+2}Yes, me too bro. 😅 its like revision.

@lawrencerisley72317 วันที่ผ่านมา^{+18}As a carpenter that watches math videos - knowing little about advanced equations - when I saw the outline of his profile it piqued my interest. I said to myself, "cool, he's back. There's something special about the E man." To discover he's also kind and generous, sorta made my day. Thanks Derek.

@Just_A_Dude7 วันที่ผ่านมา^{+21}Maupertuis is, I feel, a guy that saw Bernoulli's work and had an intuitive vibe, but wasn't quite able to put into words correctly. People like him are invaluable for the process of discovery and creation, but hardly ever get the recognition they deserve because they're not the ones that bring it home.

@dangerfly7 วันที่ผ่านมา^{+6}@@Just_A_Dude People want to feel special by worshiping special individuals when advancements are always built on top of the previous shoulders. It's shoulders all the way down...

@user-gr5tx6rd4h7 วันที่ผ่านมาI have read that Gauss (according to Niels Henrik Abel, 1802 - 1829, a very short life) did not have Euler's kindness of writing clearly understandably, but rather like a sly fox who uses his tail to remove his tracks.

Gauss: ".... Thus it follows, obviously, that ...", and you need 8 hours (or perhaps 5 days) to see the "obvious"...

@clutchmaticชั่วโมงที่ผ่านมา^{+1}OMG 23:23 to 25:57 - such beauty, eveything connects

Also, phenomenal production values... The writing, the synchronization of the sound track to climax when F=ma shows up

@st0rysphere8 วันที่ผ่านมา^{+974}Veritasium has now surpassed the quality of netflix docementaries. Really one of the best videos on math i have ever seen. Well done Ve. Cant wait for part 2

@Neverforget713248 วันที่ผ่านมา^{+11}Agree. A few years they did a reboot of "Cosmos" ... The production quality of these videos is at least as good as the Cosmos series.

@jmalmsten8 วันที่ผ่านมา^{+9}Netflix docus really have fallen lately. Moving more and more towards the formats of cable TV to desperately stretch out every single minute of content 3-6 times longer than necessary.

@jerrysoncallado87098 วันที่ผ่านมา^{+6}Im still waiting for the part 2 of their video about Thermite, and now Derek is making me wait for the part 2 of Action. They better release these sequels soon because im loving it

@Patterner8 วันที่ผ่านมา^{+4}too bad for netflix my first thought will always be "black Cleopatra"

@andrewandrus32968 วันที่ผ่านมา^{+2}Imo these have always been better

@Kampamba8 วันที่ผ่านมา^{+374}I’m a practicing mechanical engineer of 6 years now. Nearly 30 years old. In 2014 I discovered Veritasium and Smarter Every Day when deciding what to study. I cannot explain how instrumental these videos have been to my life. Thank you so much Derek!! Humanity is better off because of you

@elementalist15138 วันที่ผ่านมา^{+2}Im in school for engineering, but we haven't talked about this topic at all. Would this principle apply to classes like Dynamics and make it easier for me😅

@offabender27198 วันที่ผ่านมา^{+2}@@elementalist1513You do generally cover it, idk in how much depth, it depends on your course structure and discipline.

But if you ever take an advanced dynamics subjects you'll encounter them especially for shafts and machines with linkage mechanisms. Although nowadays most of this stuff is taught in conjunction with computational methods not strictly rigours math (at least where i study eng).

@thegr8malachite3707 วันที่ผ่านมา^{+1}2 of my favorite science channels! add tom scott to that and we're set 😊

@funnyname77738 วันที่ผ่านมา^{+580}As a first year physics student, these types of videos are incredibly valuable! I legitimately cannot explain how incredible it is to walk the line of simple explaination vs specificity and detail that you and your team walk perfectly. Thank you so much, it makes me so happy that there are science educators such as yourself following in Euler's footsteps, teaching with empathy, clarity, and clear passion!

@leviathan52078 วันที่ผ่านมา^{+4}The video is interesting for sure, but it is technically little more than a history lesson. I wager you would not be able to solve even the simplest of problems using the fucntion you probably just saw for the first time in your life, after watching this video. Calling him a teacher for giving you a history crash course on a single formula is a disservice to anyone who is actually teaching, I think.

@funnyname77738 วันที่ผ่านมา@@leviathan5207 While I understand where you are coming from, I never meant to undermine or disparage classical teachers and educators with my praise of Veritasium. Rather, and this was unstated, so there would have been no reason to assume this, I meant to call attention to the benefit of having various avenues and angles to education.

To be sure, I am pursuing physics first and foremost because I had a fantastic high school physics teacher who ignited my initial passion and you are most definitely right, I likely would not be able to solve most simple problems using the function without help. However, I do not think that the value that Derek and his team provides is that of immediate practical application of the mathematical concepts they cover. Rather, as stated by many other people much smarter than myself, by teaching the history and rationale behind these mathematical concepts, one can make sense of them outside of just calculus and algebra.

Additionally, I am calling Veritasium a teacher because, over the past couple years, I have learned a lot from this channel. I think that classical teachers are incredibly valuable (and often undervalued by most people), but I do not think one has to teach in a school to be an educator.

@emm60648 วันที่ผ่านมา^{+15}@@leviathan5207 my father tried to teach me to drive stick without explaining the principles behind it ("just do what I say when I say it"). Fortunately, he was a fast-hand on the emergency brake and I got to autograph the the skidmarks in our driveway. 🙂 Mom took over after that and learning what was happening in the engine as I pressed pedals kept that from happening again. Knowing _why_ helped me learn about "how".

Having a conceptual underpinning and an understanding of how a concept was _developed_ gives you a framework to attach all the specific mathematical details to; something that simply throwing the final equation at you wouldn't provide. Context matters.

@aitsfni8 วันที่ผ่านมา^{+17}@@leviathan5207 I am also pursuing a physics degree. I'm in third year. While a large part of physics is, indeed, knowing how to solve formulae for solutions, simply knowing how to plug in numbers/manipulate an expression pales in importance compared to actually understanding the concept at hand. Where the equation comes from, what each term means, why certain cases yield certain solutions, etc.. Without this knowledge you are no longer doing physics, just math. Videos like this are invaluable when it comes to forming intuitive foundational understanding of these topics. Setting it all against the backdrop of the real history of the development of these concepts and ideas surely helps connect everything together. Also, Derek is Ph.D. in education research. I'd wager he knows more than most when it comes to education.

@funnyname77738 วันที่ผ่านมา@@emm6064 Wow, what an eloquent way of putting it, thanks!

@mariamabdallah-u5x5 วันที่ผ่านมา^{+10}Your video deeply moved me, I have been wanting to go back to learning physics for a while now and your video reminded me of the sense of wonder I had in my freshman year. Thank you for creating something so special, I can’t wait for future videos like this one!

@StarFury28 วันที่ผ่านมา^{+424}16.5M subscribers, and still not afraid to show entire formula deriving process using calculus! Bravo!

@DanKaschel7 วันที่ผ่านมา^{+32}I wish he'd taken the time to impart a bit more intuition to those of us who haven't done calc in a long-ass time. But I'm certainly glad the rigor is there for those who can fully appreciate it.

@jackkerouac15237 วันที่ผ่านมา^{+1}Gay comment

@DanKaschel7 วันที่ผ่านมา^{+13}@@jackkerouac1523 oh noooo incel doesn't like the comment nooooo

@fernandoizaurieta72707 วันที่ผ่านมา^{+471}I'm a theoretical physicist, and I'm astonished by how precise and well-presented the video is. It reminded me of the wonder I felt as an undergraduate attending beautiful lectures on classical mechanics. Thank you for creating such wonderful material for everyone on TH-cam.

@asjordan0yt6 วันที่ผ่านมา^{+2}Here, here.

@isodoubIet3 วันที่ผ่านมาShouldn't a theoretical physicist know that the central claim of the video is completely wrong?

@Dragrath12 วันที่ผ่านมา@@isodoubIet If you have data to "prove" that the principal of least action is wrong then do so but until then this forms the principal foundation of not just all of classical mechanics but the Feynman path integral and quantum field theory i.e. the standard model of particle physics. The burden of proof always falls onto the claimant when the weight of all human progress and knowledge in physics is at the heart of the subject.

@isodoubIet2 วันที่ผ่านมา^{+1}@@Dragrath1 The principle of least (stationary) action is not wrong... _in classical physics._ It doesn't apply in quantum mechanics. In fact, quantum mechanics is what you use to prove exactly in which sort of situations the principle is a good _approximation._ The video goes so far as to state that quantum mechanics can be replaced by the least action principle, which is categorically nonsense.

"but until then this forms the principal foundation of not just all of classical mechanics but the Feynman path integral and quantum field theory i.e. the standard model of particle physics"

That is nonsense. Pop quiz! Explain in your own words how dimensional regularization is used to treat infinities arising from loop diagrams, why that doesn't present any conceptual problem for the theory, and why dimensional regularization is advantageous when compared with more simplistic schemes like cutoffs.

@Dragrath12 วันที่ผ่านมา@@isodoubIet I thought you were trying to say the principal of least action was wrong, and yes the mechanical form of the action breaks down in quantum mechanics but the Feynman path integral shows quantum systems still follow the principal within probability or state space. I don't think you can really say that the Feynman path integral isn't part of the principal foundation of the standard model given that Feynman diagrams which are a computational tool for calculating these systems of possible interactions depend on this theoretical framework At this point though I think there is good evidence that this is a consequence of deeper more fundamental rules with Wolfram's computational emergent model of physics as a consequence of Turing complete computational constraints simultaneously iteratively acting on some informational system looks promising if they can come up with a solution for computing the continuous domain of dimensionalities which appear to be natural in that framework.

@roodog18 วันที่ผ่านมา^{+816}I took a class called theoretical mechanics, where we learned most of this. What was explained to me over 10 weeks was described infinitely more beautiful in this 30 minute video. I’m tearing up just thinking about it. Your channel is absolutely incredible for bringing math and physics to the average person, and even making the people familiar with the material think about it in a new way. Thank you

@G36-9998 วันที่ผ่านมา^{+8}damn literally same here

@backspace3458 วันที่ผ่านมา^{+10}Last semester theoretical mechanics ended for me. I thought Lagrange's mechanics was just yet another way to describe moving things, except even more generalized and even more boring. I still do find it unintuitive, and i was genuinely hoping to see how this pops up somewhere else, but sadly we must wait for another video.

@Luicatus8 วันที่ผ่านมา^{+3}@@backspace345

Funny

Lagrangian Mechanic saved me in my first Semester of theoretical physics. Could not get the hang out of classical Mechanik, but this gave me at once a tool set, i could appy.

Esp. Double Pendulums (practical example: swinging bell)

That and the Maxwell Equations are still the only parts of theoretical physics I like as a applied and Experimental physicist

Even 20 year later and out of the scientific world

@gd10378 วันที่ผ่านมา^{+12}Personally, watching this 30 min video made me wish I had time to study the subject over a 10 week course. These videos are nice to learn about the history of physics, but if you don't study the math behind it you don't really understand any of it. You just accept an answer for the correct one.

@manuel05788 วันที่ผ่านมา^{+9}No it doesn’t. You’re not going to be able to do any calculations yourself after watching this video.

@paulatk444 วันที่ผ่านมา^{+420}A very fascinating video, this brings back painful memories which i have been enduring. My relationship of 6 years ended 3 months ago. The love of my life decided to leave me, I really love her so much I can’t stop thinking about her, I’ve tried my very best to get her back in my life, but to no avail, I’m frustrated, I don’t see my life with anyone else. I’ve done my best to get rid of the thoughts of her, but I can’t, I don’t know why I’m saying this here , I really miss her and just can’t stop thinking about her .

@JohnWicked-fx3cs4 วันที่ผ่านมา^{+1}Parting ways with someone you deeply cherish is an agonizing experience. I understand firsthand, having encountered a parallel situation at the end of my 7-year relationship. Driven by an unyielding determination, I explored every avenue to salvage our bond. Seeking guidance from a spiritual counselor proved pivotal, as their intervention played a crucial role in rekindling our love.

@paulatk444 วันที่ผ่านมา^{+1}That's fascinating! How did you come across a spiritual counselor, and what's the best way for me to contact her?

@JohnWicked-fx3cs4 วันที่ผ่านมา^{+1}Meet Suzanne Ann Walters, an outstanding spiritual counselor with the power to restore your relationship with your ex.

@paulatk444 วันที่ผ่านมา^{+1}I'm grateful for this valuable information; I've just taken a moment to find her online.

@Breach-Clear9 ชั่วโมงที่ผ่านมาaverage bot

@Lukav16 วันที่ผ่านมา^{+397}This is such a great transition:

Mapertui is bullied - depressing music playing

Euler mentioned - Boss battle music starts playing 🔥🔥🔥

@LuisSierra423 วันที่ผ่านมาEpic fight ensues

@One.Zero.One1013 วันที่ผ่านมาIt's like when the battle theme starts playing in Final Fantasy.

@DevRajyaguru-lx8pi8 วันที่ผ่านมา^{+649}A beautiful mix of history, physics, math, music, emotions and story telling. I am just blown away !

I remember terry tau's quote at this point that, we should teach our children the history behind the things, how it came and how much effort went to bring it in the form it is today. If we don't appreciate history then there is no way we can appreciate it's true essence.

Thank you Derek and the team for their amazing efforts in STEM.

@Neverforget713248 วันที่ผ่านมา^{+29}100 percent agree. I was always frustrated in college because I felt I was never "catching on" quickly enough... only to find out years later that the knowledge we were taught in one semester took humanity hundreds of years to figure out.

@chattiezzz8 วันที่ผ่านมา^{+5}couldn't agree more!!

@kirkbotingress36908 วันที่ผ่านมา^{+8}I hated history class because it seemed to be about learning these dates and names of dead people. Nowadays I love history because I can ignore exact dates and focus on the reasons and motivations of those people that came before me

@aseemlimbu76728 วันที่ผ่านมา^{+1}@@kirkbotingress3690 Loved the way you put it.

@btf_flotsam4788 วันที่ผ่านมาIt's worth noting that the history of a field is often more understood by those in its field than most historians. As a mathematics person, I have already heard of the Maupertuis, Voltaire and Frederick the Great drama from a biography of Leonard Euler, and have discussed the history of probability with professors while doing my honours thesis.

@notenoughmonkeys6 วันที่ผ่านมา^{+390}They should make a movie about this, Least Action Hero.

@vids79836 วันที่ผ่านมา^{+6}You talking about anime earth? Haha

@garybaldrick6 วันที่ผ่านมา^{+11}@@vids7983I think it’s either a reference to the movie Last Action Hero or the title of their sex tape.

@RolandoGarza4 วันที่ผ่านมา^{+1}Would the villains stumble and hit their face on Least Action Hero's fists?

@Gogeta704 วันที่ผ่านมา^{+3}@@RolandoGarza Yep, their faces would find the quickest path to his fist, every time.

@-unclebuck-4 วันที่ผ่านมา^{+1}@@vids7983 Last action hero is a movie.

@shriramjoshi6807ชั่วโมงที่ผ่านมาI am learning this right now in grad school and watching a Veritasium video about it and learning a little history of its origin is amazing! Makes me smile whole heartedly!

@skindalal11898 วันที่ผ่านมา^{+4098}This Comment is for Maupertuis.

@FScott-m1n8 วันที่ผ่านมา^{+183}_pours one out for Maup_

@lordbunbury8 วันที่ผ่านมา^{+79}I did it all for the Maupie

@kilgorezer8 วันที่ผ่านมา^{+3}hi

@mattmccallum20078 วันที่ผ่านมา^{+40}If you say his full name in a dark room four times fast…… you giggle

@henrikebbesen18388 วันที่ผ่านมา^{+54}The unit [kg*m**2/sec] of m*v*s ought to be called a Maupertuis, 1 Ma.

@tonytya8 วันที่ผ่านมา^{+216}I attended a university lecture which covered Multi DOF Dynamic Systems, the Euler-Lagrangian Equation, and Double Pendulums this morning as a Mechanical Engineering student. Was completely baffled and confused about the theory behind all of it. Coming home exhausted at the end of the day watching this piece of art just made me tear up. Such an amazing coincidence that this video was released today. The moment everything came to F=ma was such an Eureka moment too! Thank you Derek.

@kzeich8 วันที่ผ่านมา^{+1}It's beautiful

@tatsga8 วันที่ผ่านมา^{+3}I just had 8 weeks of my first course of mechatronics in technical university and this video was some what eye opening. I have been struggling with concepts of virtual work etc used in very hard and tidious matrice calculations used in equations of motion on multibody systems.

@whatTheblue7 วันที่ผ่านมา^{+3}Only if uni teachers were like this!!!

@blu_sevn8 วันที่ผ่านมา^{+383}As a physics student in the 3rd semester this is a brilliant video to watch...literally goosebumps all the time. It is so satisfying to see what u have learned being illustrated in such a way. Just WOW really

@ashleymorrissey1018 วันที่ผ่านมา^{+7}I've been out of my engineering school for over a decade, but this video brought me back to my youth, lol I don't remember how to do all this math anymore but I recognize it and I think of my friends that went into math and physics

@realracing3specter2958 วันที่ผ่านมา^{+3}i always get goosebumps when i read about all those mathematicians, as they always somehow related to/connected another great mathematician, which i had no idea belonged to his timeline... and also contributed to the theory 🤯🤯

@Pleasing_view8 วันที่ผ่านมา^{+1}Have you done Mathematical Physics yet?

@blu_sevn8 วันที่ผ่านมา^{+1}@@Pleasing_view just theoretical physics

@acron75598 วันที่ผ่านมา^{+5}I am a computer science student, i have a special place for physics, even though I left it for 4 years. This video revives those good ol' days.

@kingdolphin5104 วันที่ผ่านมาAs of late, with each video you release I am struck by the sheer integrity and production value of your work. Since I discovered this channel I have been thoroughly impressed with your videos, but with each successive one you somehow still manage to reach new heights. It's not just production value, but also some other intangible factor I lack the vocabulary to express that gives your videos their unique and unmatched quality. I would not call it an exaggeration by any stretch to say that you are one of the greatest educators of the modern era.

@pedrocasella13278 วันที่ผ่านมา^{+347}I just did an undergraduate research about Lagrangian in manifolds, and now I have to create a poster about it. Thank God. for this video right now!!

@PetraKann8 วันที่ผ่านมา^{+4}So you were asleep in class for all those years?

@Gokuk-oq3uk8 วันที่ผ่านมา^{+6}@@PetraKannwodent this video make his task easier

@roulzhq8 วันที่ผ่านมา^{+1}Bozhe moi

@rasmusturkka4808 วันที่ผ่านมา@@PetraKann yes, studying is for nerds who don't know anything

@PetraKann8 วันที่ผ่านมา^{+1}@@rasmusturkka480 listening and paying attention is not

@MasterReady128 วันที่ผ่านมา^{+262}Initially I was skeptical of the clickbaity title and the intro, but just after 3-4 minutes I was so *indulged* in it that I forgot to increase the video resolution to 1080p like I always do. Only later I realised that I watched 30 minutes of video that I was not going to watch.

This is a testimony to how great this video is.

@DornigeChance8 วันที่ผ่านมา^{+8}Do not think that you are a meassurment instrument for video quality! But I see what you(!) like.

@Egan4668 วันที่ผ่านมา^{+4}I have a plugin that auto set to highest quality all videos because TH-cam doesn't like anything above 1080p

@PROtoss9878 วันที่ผ่านมา^{+3}Same for me. I was going to watch this anyway because Veritasium always delivers, but I thought I'd put it to later and store the tab for a later day.

But I saw a math equation, was intrigued and kept watching for a bit, then it was so interesting that pausing wasn't even on my mind.

@ryukiiprimer53838 วันที่ผ่านมา^{+5}You should watch Derek's video on clickbait and why his video's title and thumbnail seem clickbaity when you'll actually get what you see.

@HunsterMonter8 วันที่ผ่านมาIt sound like clickbait, but it's true. Literally all of modern physics are derived from either lagrangian or hamiltonian mechanics, both of which are founded on the principle of stationary action

@gabberwhacky6 วันที่ผ่านมา^{+194}24:44 I appreciate that you don't shun away from showing derivations. Makes it much more enjoyable for the average physicist

@madamred37934 วันที่ผ่านมา^{+13}King of confusing for the laymen though😂. Imaging trying to understand this with highschool level understanding of math, I'm no genius in the subject so it was hard to say the least.

@madamred37934 วันที่ผ่านมา^{+3}But he did a great job of explaining ngl

@gabberwhacky4 วันที่ผ่านมา^{+11}@@madamred3793 I think that wasn't really the purpose. by showing a wall of equations for 5 sec, you don't expect anyone to read it except of sb who hits the pause button and goes through all of it slowly.

@Krazykahaan4 วันที่ผ่านมา^{+4}@@madamred3793same man. I mean, ik basic differentiation and integration, some standard values, but the derivation for F = ma that he showed made me realise I should watch this a couple years later

@veritasium3 วันที่ผ่านมา^{+33}We debated how to do this. We wanted to show all the math in case someone wanted to step through it, but we didn’t want to get bogged down in it and lose people so this was our compromise.

@jacoL812 ชั่วโมงที่ผ่านมาThe fun of the history of math and your videos in particular is how when every time you bring up a new character I recognize their name from one of their laws/principles or just knowing them from another achievement in mathematics, reminds you how much everything is connected

@jamesmiller17707 วันที่ผ่านมา^{+222}Not one single channel on TH-cam can give you such detailed, contextualized and informative, yet so easy to follow and beautifully arranged video on what would seem to be just another part of curriculum you would go through in school or university. This makes me want to learn more about this topic, physics and everything in general which means this channel has achieved the true meaning of teaching. Inspiration and imagination. Kudos!

@DanKaschel7 วันที่ผ่านมา^{+8}3B1B. And that channel knows its audience better, imo.

This was a cool video though.

@the_spicy_orange7 วันที่ผ่านมา^{+1}@@DanKaschel 😂 That's who I was gonna say.

@nephi2467 วันที่ผ่านมา^{+2}Kursgesagt is amazing like that too

@mugnuz7 วันที่ผ่านมา^{+1}@@nephi246 kurZ*

@nephi2467 วันที่ผ่านมา@@mugnuz Kurzgesagt*

@priyobayuramadhan12848 วันที่ผ่านมา^{+356}28:32 I remember when I was doing highschool physics olympiad, we treat Lagrange equations as some short of legendary weapon to handle meticulous oscillation problem 😂, because it is so hard to get the equation correctly using newtonian method. But we never knew why does it work and where does it came from. My mind has been blown 🤯.

@J.E.E.DESTROYER8 วันที่ผ่านมา^{+2}Very cool 😎😎

@fredericharmand8 วันที่ผ่านมา^{+16}It is easy to understand why this works. In the Langrange formula, the potential V is the cause and the energy of motion, the kinetic energy T, is the effect. The difference between the two must be zero all along the integration path, otherwise it means that we have missed either a cause or an effect, or both. Basically, the philosophy is that for every cause there is at least an identified effect.

It is like the Newton law F is the cause and the acceleration is the effect, both are equal.

The problem is that the Lagrangian assumes instantaneous transmission of causality, which is why it does not work in relativity. In Relativity the causality takes its share.

@Player_is_I8 วันที่ผ่านมา^{+1}Lol, now it is when it makes sense right

@sanidhyapratapsingh-h7d8 วันที่ผ่านมา^{+1}@@fredericharmand what does "instantaneous transmission of causality" mean, and what's different in relativity when this doesn't work.

@fredericharmand8 วันที่ผ่านมา^{+2}@@sanidhyapratapsingh-h7d "Instantaneous transmission of causality" means that there is no delay between a cause and the corresponding effect on a body. This is not the case in relativity.

@aseemlimbu76728 วันที่ผ่านมา^{+103}The most beautiful thing about Science and Mathematics is you can just say "I don't know" for the thing which you really don't know and it doesn't impact your stature.

@JoshuaNorton7 วันที่ผ่านมา^{+6}Ah, no. That's actually really far down the line. From my experience in university, the freshmen do like to play out the historic tropes of quarreling scientists fighting for each shred of credit. There are a lot of loner types entering maths and physics who are on a mission to show that they are the smartest.

The way I experienced it, the physics course is deliberately structured to socialize such types of students towards a team spirit.

@user-gr5tx6rd4h7 วันที่ผ่านมา^{+3}@@JoshuaNorton That must be AMERICAN students, I guess!

@DanKaschel7 วันที่ผ่านมา@@user-gr5tx6rd4hmy friend, you have much to learn of human nature

@MyNameIsSalo6 วันที่ผ่านมา^{+1}@@JoshuaNorton I studied physics in Australia and didn't get any of that. No one really cared how smart you were or how well you did, people just wanted to get through the day and hit up the bars. Also like half of the students were asians that only spoke broken english and kept to their own social groups, and that is half of an already very small class because not many people take physics. The asians were always good to get answers from if you can communicate with them though, much smarter than us and none of us even cared or tried to compete. We just wanted to pass

@ninjaasmoke4 วันที่ผ่านมา^{+2}25:46

when i realised what was coming, my mouth was wide open in disbelief! science if freaking beautiful! and how you present it is awesome!!!!!

@PrajwalDSouza8 วันที่ผ่านมา^{+296}One thing missing? Connection to Noether's theorem.

It is right there. Variation of momentum over space (Lagrange) vs variation of energy differential over time (Hamiltonian)

21:50

@perorenchino20368 วันที่ผ่านมาConvert to hinduism

@hata62908 วันที่ผ่านมา^{+21}maybe next video

@srujankumarmishra17688 วันที่ผ่านมาricebag

@toinfinityandbeyond20238 วันที่ผ่านมา^{+18}Hi Sir... I am Pranetha(remember from CFAL 2021 batch,druhan and pannaga's classmate in case you dont remember)....because of you I am still watching veritasium...currently in NITK final year ....hope you are doing great

@PrajwalDSouza8 วันที่ผ่านมา^{+3}@@hata6290 yes. I realised that towards the end. Hope the video goes deep into this topic.

Also, especially symmetries.

@niccolozanotti8 วันที่ผ่านมา^{+91}Physics graduate here. You brought back a lot of good memories from my analytical mechanics course. I wasn't really able to appreciate the beauty of the principle besides its mathematical elegance. What you (and Strogatz) are doing with these videos is truly a gift to humanity. Thanks

@matercan56498 วันที่ผ่านมา^{+275}The animation in these videos keep getting better and better, I love it.

@nclsb1428 วันที่ผ่านมาYeah It's a great addition to the content 😊

@theairaccumulator71448 วันที่ผ่านมา^{+1}Am I tripping? It feels like I've seen this exact video before. Years and years ago on 3B1B. Did they just recycle the whole script and animations?

@cherriberri83738 วันที่ผ่านมาYes, just let that production value keep convincing you to never be skeptical of watching these videos.

@CalculusSince133 วันที่ผ่านมาThanks for the video! It gave me an insight into Lagrangian as a high schooler in the final year. My Physics teacher once briefly mentioned about Lagrangians in class, that they’re a technique used to tackle mechanics problems using energy, and now I see exactly how! I can’t wait to learn more about this in detail in college next year!!

@Beryllahawk7 วันที่ผ่านมา^{+101}My son sent me to watch this. I'm already subscribed but so frequently when it's physics I get a bit wary, I'm very much not a maths person. You start throwing equations across the screen and my mind often just quits right there, lol. But this was fascinating. When he told me the name of the principle I blinked at him and said "You mean conservation of energy?" and he started hopping up and down going "NO! That's just the thing! Augh, go watch it Mom!"

SO here I am! And I see what y'all are saying. Interesting to think about and I look forward to the next one!

@meghanto6 วันที่ผ่านมา^{+2}this is so nice to see! thank you for watching and sharing his enthusiasm!

@DJTubeFactory6 วันที่ผ่านมา^{+1}Welcome. The next video will be interesting.

@marvelwizalamu5988 วันที่ผ่านมา^{+113}Words cannot fully express how much this channel has transformed my perspective on learning. There are times when I feel completely lost with the concepts he talks about, yet instead of feeling intimidated, I’m inspired to watch the video multiple times and seek additional sources to deepen my understanding. The passion and effort he puts in helping people understand makes me not feel like I'm too dump to understand such complex concepts; instead, it sparks curiosity and a genuine hunger to extend my knowledge.

I really appreciate you team Veritasium

@mikec.86048 วันที่ผ่านมา^{+5}same for me !

@mikeyb72638 วันที่ผ่านมา^{+3}The twinkle in Einstein's eyes was no accident.

@MrAnshulji8 วันที่ผ่านมา^{+160}Gripping screenplay ✔

Cinematic background score and camera angles ✔

Cameos by renowned (but dead) mathematicians ✔

Three-act structure, with the introduction of Euler's character placed perfectly at the mid-point of the video ✔

Spooky Halloween theme for the season ✔

Post-credit scene hinting at a sequel ✔

Forget blockbuster Hollywoood flicks, instead this video should be released in theatres and sent in film festivals!!

@thehardistdifficulty10508 วันที่ผ่านมา^{+5}We need more like you good person ❤🎉 math and science are everything ❤️ 💖

@LynxUrbain8 วันที่ผ่านมา^{+4}And what a cliffhanger at the end !

@natyalim3 วันที่ผ่านมา^{+1}Probably one of the best science videos I've seen.

So much where one can see where the math originated. Seeing the history of it is extremely fascinating and helps understanding it.

Would have been interesting to see something like this in high school or the university to gain a deeper understanding.

@ALJCpalaeozoic6 วันที่ผ่านมา^{+47}I studied this as a third year physics undergraduate and you've really captured how at first it seems like pointless pushing algebra around until suddenly a profound revelation hits you. Our mind-blowing moment was the professor going on to show how you could picture every possible path between two end points as waves with neighbouring paths destructively interfering everywhere apart from along the true path where dS = 0, where the paths would be in phase. All of a sudden a ball moving under Newtonian motion looked a lot like a quantum mechanics. Eagerly waiting to see where this goes in the next video!

@solconcordia43152 วันที่ผ่านมาMaybe it should be dS = h instead of dS = 0.

Euler might have made the initial error which led to the disagreement between quantum theory and relativity.

The two may very well be in the analogous positions as the Rayleigh-Jeans and Wiens law formulas in the Blackbody radiation spectrum distribution plot. Both are accurate within the domain of applications but cannot bridge the gap. General relativity uses space-time continuum but quantum theory uses discretum of eigenvalues. Maybe space-time continuum of general relativity is incorrect but quantum theory's discretum of quantum states in the energy-momentum discretum is correct.

@kilimanjarocruz6607 วันที่ผ่านมา^{+29}For me, one of the best introductions (albeit a bit old-fashioned at times) to the principle of least action is Landau and Lifshitz's volume on Mechanics. They also properly give Mapertuis his share of the credit. Also interestingly, they go on to explore how the equations change when you relax the constraints a bit (for instance, by not fixing the final point) and what this teaches us and how to use it. Simply marvelous.

@richardchapman159223 ชั่วโมงที่ผ่านมาNot specifying the endpoint is an interesting concept. It must allow ranges of answer that likely produce probability distributions. Odd way to get towards wave functions and their quantisations.

@AdithiaKusno8 วันที่ผ่านมา^{+120}When Veritasium summarized Physics Grad first semester in half hour! Impressive work, you literally summarized the first semester of Physics Grad lecture series in one video. As Richard Feynman said great teacher knows how to communicate complex subjects in the least amount of action. Impressive! Even second semester on Thermodynamics, third semester on Electromagnetism, and fourth semester on QED would be extra episodes on least action principle topics. I am guessing eventually Veritasium might show how the least action principle works on Einstein's General Relativity. It's TH-cam channel like this that helps me explaining Physics to my kids. Thank you Veritasium.

@cherriberri83738 วันที่ผ่านมา^{+1}Your first sentence should be a giant red flag to you.

If you are capable of critical thought, so much info being compressed into 30 minutes should be a red flag that the info is at minimum, incomplete.

@diegopg71864 วันที่ผ่านมา^{+1}This channel is the first source that has taught me the origin and meaning of the Principle of Minimum Action in an intuitive way. I can only thank you for spreading so much knowledge. Long live Veritasium.

@oberlurch-handimations86288 วันที่ผ่านมา^{+175}The thing I love the most about science is that it's like a cooperative undertaking spanning thousands of years

@farrel_ra8 วันที่ผ่านมา^{+3}Agree

@Argoon19818 วันที่ผ่านมา^{+25}Indeed, even Newton said "If I have seen further than others, it is by standing upon the shoulders of giants.", so no important mathematician, physicist or scientist (or natural philosopher, how they used to be called) has single handily invented or discovered anything from scratch, all discoveries in physics has been a human group effort.

@aldrinmilespartosa15788 วันที่ผ่านมา^{+3}@@Argoon1981 man, imagine these poeple who are separate in time in the same room.

@samagraarohan25138 วันที่ผ่านมา^{+3}cooperative for only as long as no one brings up a challenge to the views

@donmacquarrie91618 วันที่ผ่านมา^{+4}Giants standing on the shoulders of Giants....

@HeisenbergFam8 วันที่ผ่านมา^{+510}You know its deadly serious when Veritasium says "we are approaching spooky teritory"

@0Senzuu8 วันที่ผ่านมา^{+1}😂😂😂

@DrDeuteron8 วันที่ผ่านมา^{+7}"spooky" is such a loaded term in physics.

@giovanni_vaz_cardoso8 วันที่ผ่านมา^{+1}@@DrDeuteronEinstein effect.

@dVTHoR8 วันที่ผ่านมา^{+4}I think this was a meant to be a really funny double meaning line, since in real life we are very close and approaching Halloween. If not, that is a hilarious coincidence.

@naejelangelogonzales66238 วันที่ผ่านมาGhosts are explained by physics from this video right now😊

@benjamincraig71988 วันที่ผ่านมา^{+57}This video made me pick my Feynman lecture series book back out. The mathematics of all this is calculus of variations. I taught myself this once, and it was one of the most profound insights I’ve ever had mathematically. Thanks Derek, you are truly this days Feynman in terms of making complex concepts approachable and fun!

@דודקופלוביץ8 วันที่ผ่านมา^{+5}Expect Feinmann to make an appearance in the sequel video.

@ivanjelenic56278 วันที่ผ่านมาAs the previous comment to your comment said, you wouldn't want to miss the next video then.

@wag-on7 วันที่ผ่านมาDefinitely a path integral on its way.

@InAMinMaths3 วันที่ผ่านมาDefinitely getting QED vibes here

@calanguteb3 วันที่ผ่านมาYour channel reminded me that I loved maths in school, and calculating moment of inertia of weird shapes was almost a hobby. Got myself an applied maths book to rekindle what lay dormant all this time. Thanks a lot for your work.

@natetrice81948 วันที่ผ่านมา^{+76}Literally did the cycloid problem in my intermediate mechanics class yesterday. The timing is crazy!!

@paulbizard34938 วันที่ผ่านมา^{+5}... They are among us ...

@adnan76988 วันที่ผ่านมา^{+8}You mean the timing is optimal?

@aqibramzan97428 วันที่ผ่านมาMe too

@Flesh_Wizard6 วันที่ผ่านมา@@paulbizard3493amogus

@johnchessant30128 วันที่ผ่านมา^{+69}14:01 Euler!!

@Weeksmistro8 วันที่ผ่านมา^{+11}Euler came in and said: “On your left.”

@ngcool41127 วันที่ผ่านมาOiler

@somethingforsenroวันที่ผ่านมาwhen euler's on your side, you know you're right. god damn

@SnackPack9138 วันที่ผ่านมา^{+34}I remember this blowing my mind when we learned about it as a physics undergrad. These days I forgot most of this but had always thought if it as “lagrangian mechanics” since it used the lagrangian. But now I distinctly remember a chapter on Hamiltonian mechanics. Man I miss those days where ever single lecture just completely blew your mind. I suffered through learning math just so that I could have the tools to learn more physics

@wissamkadamani3 วันที่ผ่านมาI really love it when I watch a veritasium video, because one of 2 things happen:

1) The content is completely new to me extremely exciting to learn

2) I already know most of what's about to be said and I'm pausing and predicting what Derek will say next. It gives me a new perspective with some wholesome details, and a nice ego boost.

This was one of the latter, and it's an absolute masterpiece of production value.

FLAWLESS

@Miftahul_7868 วันที่ผ่านมา^{+96}25:53 I can’t lie.. I may or may not have gotten goosebumps

@plwadodveeefdv7 วันที่ผ่านมา^{+5}dam right when there's an emotional crescendo in the music? that's crazy

@marwanfakhradin25437 วันที่ผ่านมาI certainly did

@PinkeySuavo6 วันที่ผ่านมาTo be honest I wasn't shocked. I won't ever call myself to be smart, but I looked at this this way: if we initially use some formulas, isn't it normal that we can manipulate it to the already known equations? The "m*a" already popped out in integral, just "a" was written in terms of second derivative of displacement.

I just think it's kind of rewriting the same thing in different terms. If you take a look at 24:45, they started with (1/2)*mV^2. It is already strictly connected to F=ma.

@Miftahul_7866 วันที่ผ่านมา^{+1}@ Yeah yeah I get that it’s just beautiful to see it in its final form and with the crescendo of the music it was just 🤌🏼

@bernard0camp0s8 วันที่ผ่านมา^{+34}Man, seeing what all these geniuses were up to way back when, sometimes in their spare time, is truly humbling.

@ultraokletsgo8 วันที่ผ่านมา^{+1}My understanding is they were fighting off bears a lot of the time.

@Help-jr1mq8 วันที่ผ่านมา^{+24}25:38 you know it just got real when music changes

@glengarryglenross71276 วันที่ผ่านมา^{+3}No - it's the words 'but wait'

@Conormedy6 วันที่ผ่านมา^{+2}😂

@wendjys5662 วันที่ผ่านมาI love how u are slowly getting more detailed in ur explanation and showing and proving the equations

This was really beautiful

@noddynorthside8 วันที่ผ่านมา^{+64}How satisfied would not Mr Maupertuis be, were he still alive, if he could see the principle of least action applied to highest degree of dignity to which it is susceptible.❤❤❤

@AyoolaLadapo-hg7vs8 วันที่ผ่านมา^{+2}I wonder who Not Mr Mapertuis is?

@AyoolaLadapo-hg7vs8 วันที่ผ่านมา@@noddynorthside Just a joke bro😂🤲

@noddynorthside8 วันที่ผ่านมา@@AyoolaLadapo-hg7vs 😅😅

@RitikMaurya078 วันที่ผ่านมา^{+56}Now I understood how my dog feels when I talk to him.

@prithvibharadwajmellacheru11217 วันที่ผ่านมา^{+14}I've experienced bliss by the end of the video. Feels like it filled a small void in me that was present from the time I started using the Lagrangian formulation at school, as I was busy on the practical applications but never really took time to explore the reasoning.

Thank you Veritasium

@troik8 วันที่ผ่านมา^{+35}I started watching Veritasium 13 years ago about a Slinky dropping and we're now here with pretty complex formulas (for me), I feel like Derek is giving us a STEM degree without us even noticing. I learned so much in these 13 years. Thank you.

@cherriberri83738 วันที่ผ่านมาYou need to stop implicitly trusting people simply because they appear to know what they're talking about and have a higher production value.

Veritasium does not make very trustworthy claims.

@philipingram15638 วันที่ผ่านมา^{+1}Such a mental journey, awe inspiring...

@dog4me8 วันที่ผ่านมา@@cherriberri8373what is bro smoking?

@DootyDuck8 วันที่ผ่านมา@@cherriberri8373 im not saying you are wrong with the advice about not trusting people just because they appear trustworthy, but could you give me an example of Veritasium making untrustworthy claims?

@Tjeran7 วันที่ผ่านมา^{+1}@@cherriberri8373what claims specifically is it you don't find trustworthy? Everything Derek presented here is either historical facts where you can look up the sources on every single person, or pure physics.

The few times Derek has made bold claims without all the facts laid out, there has been an outcries from physicists in the comments. The fact that the comments are full of praise is because all the physicists watching recognize all the facts and are blown away by the genius way of presenting it.

I dare you to point out a single factual error in this video.

@akhasshativeritsol19506 วันที่ผ่านมา^{+11}I love Strogatz! I was fortunate enough to take his class on nonlinear dynamics and chaos, it was the most interesting class I'll pretty much never use!

@deanjericevic89126 วันที่ผ่านมา^{+27}Teaching school physics for over 30 years I love how you have embellished the maths & physics with the history of those men who contributed to the theory’s development. A coruscating delivery; your presentation makes it so interesting that there would be so many more physicist & mathematicians by teaching that way.

These optimisation problems solutions are found in the "Calculus of variations". Like a chain hangs freely its shape is derived as a hyperbolic cosine curve or a hole drilled through the earth from one side to the other & a ball dropped through it to minimize time is a cycloid. The shortest distance between 2 point! Yes, one of the simplest problems takes such complex maths technique to solve it!

@Zibonnn7 วันที่ผ่านมา^{+10}Veritasium's most impactful aspect is Derek and his team's storytelling and visual presentation. I'm not a math person, and I never have been, but you still keep me watching your videos from start to finish! If I had a math teacher who could explain like this, I’d probably be good at math.

@Pritchie458 วันที่ผ่านมา^{+154}19:16 This is when I got lost.

@architektradim8 วันที่ผ่านมาSame. Did he mean the sum of areas constrained by trial path above and below the true path is zero?

@inksansdemon51818 วันที่ผ่านมา^{+4}same.. not quite sure what they meant on that part🤔

@cursedlycan99258 วันที่ผ่านมา^{+1}Its Simple integral calculus. And a few classical mechanic's formula for Kinetic and Potential energy

@architektradim8 วันที่ผ่านมา^{+7}@@cursedlycan9925 And how about the part when visible difference becomes zero difference?

@bazylicyran77278 วันที่ผ่านมา^{+16}Same here. In fact, I think I'm lost even a bit earlier: "So if you took a tiny step to the left or the right, the value of the function basically doesn't change". What does that mean? So does the value change or not? I think it does, I don't see why it wouldn't.

And then, if you were to change the path of least action by "adding a tiny bump here or flattening it out there", why "the action basically shouldn't change"? It seems obvious to me that it would change.

They even say a few moments later that "any other path must have more action". So why this altered path doesn't have more action?

I would really appreciate an explanation.

@muhammadsheheryaarghayas29687 วันที่ผ่านมา^{+13}This has to be the best and most expansive crossover ever. Spanning over centuries of eras, involving almost every major mathematician, uniting various branches of maths to solve multiple problems over many fields, creating a unique new unit which sparks innovation for an entirely new and uncharted area of physics. BRILLIANT! I was legit fanboying over the entry of every mathematician and the reveal at the end equating to Newton's Second Law of Motion had me actually pause the video to really scream and grasp the mind blowing connection. Amazing work by Derek and the amazing Veritasium team. As always, awesome work and thank you for this masterpiece.

@schuetzm56912 วันที่ผ่านมา^{+1}I am an engineer and actually found this to be the best explaination of both schools of thinking. I always enjoyed applying the Langrangian and watching fellow students frown over their arrows and angles 😂

@crazypyro7777 วันที่ผ่านมา^{+15}Having a mathematician say you are like Euler must be one of the highest possible praises.

@TheThoughtfulInsight8 วันที่ผ่านมา^{+8}When I studied these topics during my college major, they didn’t impact me the way they do now. I’m just flabbergasted at how simply you explained such a complex problem in modern mechanics-it blew my mind!

@anapalone8 วันที่ผ่านมา^{+106}25:38 This is why I love math. When it was revealed that under all of that derivation and derivation results in an equation that we're all too familiar with, I just gasped.

@peter116128 วันที่ผ่านมา^{+1}It wasnt hard to spot earlier in the video 11:35

@justno9848 วันที่ผ่านมาhow tf did you not know this?

@Lq323328 วันที่ผ่านมา@@justno984how tf are you this condescending? 🤡

@roelsvideosandstuffs15138 วันที่ผ่านมา^{+2}Because every formula or equation you know is just the simplification of its integral and derivative.

Or in the quote of a famous Mathematician

"Simplicity is hidden beneath the mask of Calculus"

@scotth.hawley15603 วันที่ผ่านมา^{+1}Great timing! This is precisely what we're covering this week in my mechanics class. Assigning this video as required viewing.

@nmpspiky7 วันที่ผ่านมา^{+51}0:22 bro, am I the only one who thought this video is about Entropy? After seeing del (S) = 0 😂 Entropy generation for reversible adiabatic process

@guilhermefavaro20895 วันที่ผ่านมาI thought too 😂

@RaushanKumar-qb3de4 วันที่ผ่านมาUniversal

@MansukhchainSingh2 วันที่ผ่านมา^{+1}Me too

@Edarnon_Brodie2 วันที่ผ่านมาYes you're the only

@manshikumari536919 ชั่วโมงที่ผ่านมาSame here

@iamsh4r1068 วันที่ผ่านมา^{+74}00:29 compression going crazy lmao

@lazymidas42628 วันที่ผ่านมา😭

@0maeWaMou8 วันที่ผ่านมาWhat're you even talking about

@Wm7forthewin8 วันที่ผ่านมา^{+1}@@0maeWaMouthe million ducks

@0maeWaMou8 วันที่ผ่านมา@@Wm7forthewinelaborate

@Brunoenribeiro8 วันที่ผ่านมาwent brrrrrrrr

@TzarHiroki108 วันที่ผ่านมา^{+85}This is everything I learned in my 4 years of college calculus class (and never understood). Well explained!

@bituniverse86778 วันที่ผ่านมา^{+2}I can feel the pieces falling into place too

@cherriberri83738 วันที่ผ่านมาCondensed into 30 minutes. Yeah, I'm sure someone without background knowledge understood the topic, there are plenty of comments from people like you.

But there are even more from people who simply just memorized an extremely short summary that leaves out so much that should and would be covered in an actual class.

@lackdejuranez70845 วันที่ผ่านมาI'm glad. I read Goldstein's CM book about 3 years ago, in the 2nd year of college for my CM101 course. You did it, you brought the history along with the elegance of these pronciples. Thank you!!

@markus91478 วันที่ผ่านมา^{+11}I love these types of math/physics history videos. They really put in perspective that we are standing on shoulders of giants.

They also make me nostalgic about the time I was learning these things in college for the first time.

@TherapyGel8 วันที่ผ่านมาIt also really humanizes these figures, at least for me.

We were all taught that Newton was a genius and the impact of Euler's work. But hearing about the social dynamics between these people and their relationships really brings them down to earth and reminds you that they were just people. Brilliant, yet flawed people.

@erthane8 วันที่ผ่านมา^{+44}god these are my favourite types of veritasium videos (e.g the video about the invention of imaginary numbers and the video talking about black holes) where they explain maths/physics but also fuse lore and story into it, so immersive and entertaining, keep it up! :-)

@walaraubo8 วันที่ผ่านมา^{+6}Sometimes I come back and rewatch those. I’ve probably seens the Gödel/Hilbert video 10 times

@whyandhowdaushitenande7 วันที่ผ่านมา^{+6}26:05 why this feels like an avengers movie , when every hero is defeated and we feel lost but then that one hero out of nowhere comes as an savior , the geniuses of Newton , hats off to my guy maupertuis, and shout out to euler and lagrange truly one of homie , wish i was part of this gang.

@nikhilgupta57333 วันที่ผ่านมาThe best explanation I never thought I would get for the action. There I was studying in the lecture hall for the first time, thinking why it is not intuitive, what i am missing. Thanks for reminding me why I always loved Physics. Cheers!

@jd27576 วันที่ผ่านมา^{+6}Reminds me of one particularly interesting physics lecture in which my professor started with Heisenberg's Uncertainty Principles, which were reasonably easy to imagine, and performed the derivation to produce E=MC^2. The professor's intention, revealed at the last moment, made me wish I could see it all again. In light of my rather low-grade mathematical talents, I remain immensely grateful for your catalog of scientific delights... available to me on repeat... and to many others as an inspiration to remain ever hungry and thirsty for such knowledge. Your channel is a blessing and a gift. 🙏

@mismis31533 วันที่ผ่านมาDo you still have that derivation ?

@du_nut_tuch_me42308 วันที่ผ่านมา^{+68}12:52 When you are so wrong that your close friend wrote an entire book just to ridicule you for how blasphemous your work is

@mekosuji_facemask7 วันที่ผ่านมา^{+6}bro yells at you over voice chat for dying in a game (18th century version)

@AntonHdz4 ชั่วโมงที่ผ่านมา^{+1}Thanks for the ride into this fascinating world! I didn't understood any of it but it was beautiful nonetheless

@EthelJung-j5w7 วันที่ผ่านมา^{+62}Veritasium has now surpassed the quality of netflix docementaries. Really one of the best videos on math i have ever seen. Well done Ve. Cant wait for part 2

@hotflame_editz8 วันที่ผ่านมา^{+130}We saw veritasium dropping 4 videos in a month before GTA 6🗿🎯

@MashLimit8 วันที่ผ่านมา^{+2}You measure time via GTA releases? Interesting...

@ashukun8 วันที่ผ่านมา@@MashLimit and when it comes out the world is gonna end

@Dakkyun8 วันที่ผ่านมา^{+1}@@ashukun

We measure it like how we use Christ to measure time, BGTA6 and AGTA6

@wolfxzen8 วันที่ผ่านมาXD

@arktic31408 วันที่ผ่านมา^{+12}The principle of least action genuinely is one of the most underrated theories when it comes to explaining general relativity. Thank you so much for exposing more people to this theoretical masterpiece ^^

@tahntongkfen136010 ชั่วโมงที่ผ่านมา🤯 I’ve taken advanced classical mechanics (my favorite class in grad school) and I couldn’t tell you the number of times I wrote down langrangians and Hamiltonians for different systems.

It took me 20mins into the video to realize where this was going. This is very elegantly put and I wish a lot of scientific concepts would be taught this way. The building blocks and thought processes that went into developing the least action principle as we know and use it today aren’t well dispelled when we learn them.

@How19.8 วันที่ผ่านมา^{+14}who needs enemies when you've got friends like maupertuis's friends

@billdicklechips8 วันที่ผ่านมา^{+6}Learning the calculus of variations was my favorite part of classical mechanics in undergrad. It's cool to learn more about the history of it.

@emanueleluzio4846 วันที่ผ่านมา^{+4}This was by far the best explanation of principle of least action i ever seen. Please, consider a I video on the maximum likelihood principle too!