@@JohnDoe_69 I don't have it saved. It happens in a few minutes or so after the end of this clip. So if you find a longer version that's where you'll find his joke.
This reminds me a bit of what Albert Einstein said: "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."
Reminds me of my math professor. One time our physics professor was out for a personal emergency just before midterms, and we frantically looked for a fill in, but all the science profs were in other classes that hour, so I thought of my math prof, who had the session open, and we were just using calculus to solve motion problems anyway, and some examples in calc class were the same exact problem as we worked in physics class. So a little maneuvering, and it was approved for him to fill in. We went through the homework, and he vetted our answers ok. Then he put the next sections problems on the board, and asked for volunteers to work them. We set some variables to zero, allowing us to narrow the equation, then set the two intersecting forces to equal so we could start eliminating unneeded elements. And he said, hold on, how are you doing this, what proof do you have that these can be equal. The answer of course from a physics perspective is it doesn't matter. If I drop a rock it will accelerate from gravity until it hits the floor, then the height, and velocity will be zero. His answer was "you physics guys sure play hard, and fast with the rules of mathematics". And pointing to me, "don't you try this sh@t it MY class". Which is a basic difference. In math everything has to be proven mathematically. In physics, you use math to get you in the ballpark, then pull out a ruler, and measure it. My proof, I dropped an object, it is now resting on the floor, measured height = 0.
The actual science of logic is conversant at present only with things either certain, or impossible, or entirely doubtful, none of which (fortunately) we have to reason on. Therefore the true logic for this world is the Calculus of Probabilities, which takes account of the magnitude of the probability which is, or ought to be, in a reasonable man’s mind. -James Clerk Maxwell
@@ivankaramasov bear in mind that a lot of Einstein's quotes have been refined and beautified by numerous consecutive authors ;) at the end of this process they become crystal clear and concise, but they're not verbatim quotes, just distillation
@s v it’s true I used to hate math . Then I started doing math for fun some times when I listened to music . Because it’s just patterns and it’s challenging but now I’m like what’s the meaning and purpose behind it I need it to apply to something meaningful lol
Many of my university colleagues are theoretical physicists, and sometimes it feels like they’re more into math than physics and I kinda don’t understand it. It feels so good hearing these words from such a legend among physicists.
Their math is used to model, very different from pure math. We don’t use math to predict and to model. Let’s say this to put into perspective, we all know g is roughly 9.81 to physicist this number means the strength of the gravitation field, but to mathematician this is a rational number. See the difference? Either perspective is correct but in the eye of a mathematician we only want to know how consistent or how related are things within math.
As a math Major, I totally agree. Pure mathematicians are just in pursuit of incredible intrinsic beauty within math. They're not doing stuff because it often winds up being connected to real life things or to help physicists or engineers or economists or whatever. They are not doing stuff to make the world a better place, although math frequently winds up doing so. They're just in search of beauty and mathematical truth, mathematical structures and connections, and mathematical meaning (not real life meaning or physics meaning or economics meaning or whatever). That's all. I would recommend checking out GH Hardy's "a mathematician's apology", he talks about these issues of mathematical beauty and real life. Hardy was one of the top two or three number theorists in the world in his time and was the mentor of the genius Ramanujam.
I always thought defining the purpose of math as the pursuit of beauty is rather absurd. Very few of the great theories would have been found had it been only a better pastime for its inventors.
@@dasbloekendeschaf The way Hardy explains it, and I agree with him, is like this. Say you're a basketball player like Jordan. If you ask Jordan why he plays basketball, he may say that it produces a social good like entertainment/inspiration etc but the truth is more like 1) he is very good at basketball, 2) it is super amazingly fun to play basketball, and 3) he wants to kick everyone's ass and accomplish something in basketball. According to Hardy, those are the true reasons behind pure mathematicians doing math. They are really good at math, math provides them with an immense amount of pleasure (you can also call it pursuit of beauty or fun) and they are ambitious and want to make a name for themselves in the math community and in history. Pure math gives you a kind of immortality. We are still talking about Pythogoras and Newton etc and always will if there is civilizational continuity.. much more than we would be talking about a poet or politician or a businessman from a different era. Yeah sure, math winds up being the language of physics and the language of universe and really helps with engineering and literally every other field of human enquiry and winds up having social value but.. that's not why mathematicians do math. Nobody does math to make the world a better place. People do math for the reasons Hardy described. In a free society, people should be allowed to do things for whatever reasons they want. In a communist or state controlled society, people should let mathematicians do math because they love it and the rest of us get this positive externality.
@@amatya.rakshasa Ok. If we talk about the intrinsic personal motivation of some of maths greatest geniuses you are probably right. Yet what I was thinking about was that this perspective must be more of a minority given the tremendous role mathematics plays in our science and education. The overwhelming majority of people who work with it share a more pragmatic approach than the l'art pour l'art you described. At least thats how I feel as a computer science major ^^
Don't say things like "they do it to make the world a better place". That's Nonsense. No mathematician does mathematical research thinking that it will make the world a better place. Physicists may, but even then, much of their work doesn't see practical applications for some time. Those who are doing what they do to make the world a better place are doing and making real, applicable things that are not theoretical.
In 1962 Feynman gave a talk to our high school math club and soon thereafter I wrote him asking advice on whether to study math or physics in college. Amazingly, and kindly, he wrote back with some great advice. Much later, I published the contents of that letter (which, along with the envelope, I still treasure). After many, many years I now have my own opinions on math versus physics. If interested, you can find his letter here: The American Mathematical Monthly, Vol. 101, No. 6 (Jun. - Jul., 1994), pp. 543.
@@davidstokar887 La Mirada HS, CA. Not sure why/how Feynman came to our school - I’ve always guessed that one of my classmates’ parents had a connection to Feynman, but it never occurred to ask at that time since I didn’t know who Feynman was - he was just this incredibly animated speaker who exhibited the love of math/science that I had. The title of his talk was “What is 1/2 factorial’ - he spent the lecture developing the gamma function then using it to interpolate the factorial function at 1/2.
Hello! That is so amazing that he wrote back. I am very interested in reading the contents of that letter but I am unable to find it. When I search on Google for what you have referenced here, it brings up resources that I do not have access to. Are the contents of the letter available elsewhere? Thanks!
@@ramkiranputrevu the problem you may be having is that the letter, which is only one page, appears in a box on one page and is not considered a math article per se so it isn’t referenced in the Monthly’s index. It should be findable by searching JSTORE using the reference I gave. Let me know if you still have trouble and I’ll try to figure out a workaround.
@@bookert2373 Thank you so much! I was able to read it this time. I had not realised that JSTOR allows free reading of articles. The advise that Feynman gave was so simple and straightforward. It was amazing to come across this. Is it common for professors to reply to students like that? I gather that you are a professor too and that is why I ask. Thanks again!
In my senior high school years I had a hard time understanding math as nearly nothing being taught to me felt real. it was all abstract. But when similar looking equations and formulas where being used in my physics class to explain a real world situation my mind lit up and I was fully engaged in the learning process. I think the WAY they taught us mathematics was unnecessarily difficult. But then again maybe one of the major goals of teaching us mathematics was to exercise our ability to think in an abstract way. A lot of immensely beneficial things we enjoy today spent a lot of time in the mind of an abstract thinker before coming to life.
School mathematics is pretty much like running in laps. It's uncreative for most of the time, but you have to do it to build stamina if you wanna get into sports.
This is honestly a great opinion. For me, abstract thinking doesn't directly help us to solve things but it helps us develop a logical mind. A mind that doesn't just conform to what it sees but the possibilities that may look absurd but still a good foundation for finding solutions in life. Like how computer programming/coding uses lots of abstract logic/reasoning which leads to usable GUI, touchscreens, and such
@@InvadedTalks it's the other way around. The only thing that mathematics uses is formal logic. That's not to say that physics doesn't inspire mathematics, or that physicists don't contribute to mathematical discoveries, but mathematics doesn't use physics. Help is much appreciated, though.
Being an Engineer learning calculus and linear algebra, I've always tried to connect math to the real world because that's what's expected from us engineers. I realize now, that it was never the job of mathematics to manifest in the real world every time, but instead, that is what physics is designed for. Eureka moment, thank you Feynman!
I don't even believe Physicists are the group that makes math connect to the "real world", but they find physical phenomena and attempt to quantify the nature of things in mathematical form. Engineers often take the results and test the applicability of these relations in specific cases, and then throw out the specific terms that are infinitesimal in their specific case or replace them with a constant or simplified expression that will produce a useful result to solve the problem within specific parameters. For example, for most of us engineers, gravity is 9.81 m/s "down", and this gives us something useful for our problems. But to a physicist gravity is an equation that includes the mass of both objects to determine their attraction to one another, and it has to have a direction vector, when most engineering applications can just use, "down".
Good for you to realise this. We all do our jobs. But just to make sure that this is clear, mathematicians don't just come up with new axioms and theories willy-nilly (usually). If your theory doesn't solve any of the old problems, it will be hard to convince any mathematician that it's worth looking into. New mathematics is born from the fact that you solved some open problem and then bunch of other people get interested and expand the theory in search for other interesting applications. It's always a cycle: come up with something new to solve old problems, investigate the new theory on its own, create new problems, rinse and repeat.
Try to build a bridge(Real world!) without Mathematics. And don't tell me.....bla bla bla try to build a bridge without physics. Bridges were being built long before the "science" of Physics existed.
Today is teachers day in India and Richard Feynman has always been a great teacher His Feynman technique of learning is Amazing Lucky are those who had sir Richard feynman as their teacher
The main difference is that for true mathematicians mathematics is a form of art while for everyone else it is just one of many tools in a toolbox. The harmony and beauty they are after just do not matter for anyone else. You don't need your hammers to be pretty, you just want them to be comfortable in your hand and to accomodate your size of nails. And most importantly you don't want to invent them, you want them to be already available and ready to use.
sadly ive yet to be taught math by more than two great teachers, like other forms of art not all people could understand and fully appreciate it, i suck big time in calculus but did well in more down to earth subjects like statistics and probability. ive never knew math was boring and abstract on purpose
As a mathematician, I am surprised that this has not yet incited war on Feynman. Unfortunately, I'm gonna need the help of a physicist to solve the issue of time traveling back to Feynman
@@Crazytesseract that's what they said about flying, going to the moon, and the heliocentric model of the Solar System. Previous physical models have often been glaringly wrong, and the fact that our best models fail to join the quantum world with gravity shows just how wrong our current model is too. So just because an imperfect model says time travel is impossible, does not mean it is so.
Dr Feynman is absolutely right, in engineering school I was very worried about the mathematics so I tool all my math classes before I did my first physics class. I went down to the book store to get my physics book and when I opened it there weren’t any math problems, all word problems!
Math problems are "word problems". Mathematicians don't use special sign language to communicate, they speak and write as normal people do :D But I get what you mean, however, you are judging what maths looks like from the perspective of high school and college freshman. A bartender that had lot's of students as customers once told me he learned to differentiate physicists from mathematicians by looking at their notes and observing that mathematicians' notes didn't contain any numbers ;)
As physicists look for deeper meaning' they rely more and more on mathematics that at one time looked to have no relevance in the physical world. I agree with Dr. F .
I think mathematics is fundamentally the study of patterns. Any pattern that can possibly exist must be expressible in mathematical terms that either exist or could exist if only we were smart enough to invent/discover them
Not all patterns can be expressed mathematically, not just due to gaps in our knowledge, but due to certain mathematical concepts which contradict the notion that all patterns can be expressed mathematically. A few great examples of this including the "Haulting Problem" from computer science, as well as Godel's incompleteness theorems. Both of those examples show fundamental gaps in the abilities of math itself, not just human knowledge.
@@MrSephirothJenova im an absolute layman so please excuse my probable inaccuracy, but while it's true that concepts like Godel and the halting problem reveal that truth can exist beyond our ability to comprehend, to me, undecidable statements can't be said to have a "pattern" in the sense I intended. 🤔 Thinking about it, it seems to me that a statement might be fundamentally undecidable BECAUSE it lacks a pattern that can describe it; otherwise, we could. As a result, these kinds of statements are literally beyond math. If you agree/disagree I'd be interested to hear your opinion
@@Enthos2 Well I suppose this mostly just semantics, but generally it is accepted that patterns can be both hypothetical and concrete. You don't need to know of the pattern, or even be able to express it for it to exist. If we can speak of a hypothetical pattern (such as a computer program that can determine whether another program will halt), it is a pattern, regardless if maths is able to represent it or not.
The truth is we mathematician also care about reality and sometimes apply to it , and also you cannot describe higher dimension and string theory without maths,
Exactly and math has been crucial in recent years to theoretical physics compared to Feynman’s era. Math provides a strong backbone to physics and the rigor is really important in the end to both fields.
Ultimately, math is an exercise on logical arguments that spun off from a different part of philosophy than physics, though they are multually supporting, as math is grammar for many areas of human knowledge. If a subject is not (directly) applied to theorical physics, than it should have place somewhere else. Neither is physics submitted to math, because nature doesn't use numbers or is constrained to our models, instead it is the other way around.
It's really awesome how he crystal clearly differentiates the two...both are like good friends and never the same...mathematics is the way of making the understanding of physical phenomena a bit more easy but can never form the plinth...
"Mathematicians are not slaves to physics". So true. Right now, I'm floating in a meditative state so strong, I need not use my mortal hands to type this.
2:14 oh my god yes, this was exactly my struggle when I took undergraduate physics. I initially wanted to major physics, but I kept finding myself drowning in a sea of symbols and rules with no way out other than brute force application of the rules I knew I could trust. When the professor told me I should've just used one approximation or used one rule to quickly leap to the answer, I was frustrated by not having known I was allowed to use the trick, or that the rule was applicable in this scenario. Since then, I've switched to pure mathematics.
When I was in high school, I took both AP Calculus and AP Physics my senior year. After a while, I realized all the formulas and math I was doing in physics was the same in calculus. They were literally the same thing, except physics was basically just the story problems from calculus, which is probably why I struggled so much in physics as opposed to calculus, which was essentially just pure math and didn't have all the wordy over complicated context of physics.
Learning physics is better than studying physics. Yes, I understand this from my school days. Teachers who teach physics at colleges have to think like Dr Richard and teach not only math role that helps to understand numbers! Let them go beyond and make learners understand real-world connectivity systematically.
Watching this made me come up with a quote lol: "Physicists use math for practical/real-life purposes, and engineers use physics for practical/real-life purposes."
More like managers in all fields are businessmen who through cunning and luck take the credit and glory of engineers, computer scientists, economists, architects what have you, and do nothing but exist as means of control from yours and their bosses.
His statement that mathematicians don’t use intuition and don’t know what they are talking about is absurd. It’s required that proofs be rigorous but the method to getting those proofs is anything but that. Mathematicians make guesses and conjectures all the time and pretty much nobody ever ends up proving something they didn’t first intuitively think was true. Anyone who studies maths also discovers this for themselves. Consider an analysis class studying metric spaces. Sure, maybe a physicist would only care for euclidean distance. But the more you work with it the less you care what the metric actually is. You begin to get a feel for what things can be proved without even knowing what the distance between two points is.
You've knowingly or unknowingly (I presume the latter) straw manned his argument. He said mathematicians don't NEED to use intuition or know what they're talking about. That's just one extra word, but it completely changes the argument. Maths can exist without the connection to physical reality, although it often is inspired from it.
Engineers and physicists often do their own proofs because they have to. Mathematicians are getting short shrift here. They also advance economic theory, chemistry, medicine, biology, ...
I know right. I think saying that mathematicians dont need proof is saying that a mechanical robot with fitted logic inside him can do mathematical research. no it cant like physics mathematics too needs a sense of direction needs the so called pictures in the head of person doing it. so is true for physics. Its strange that in todays world where research is going about interdisciplinary domains and connecting various fields people still think that physics can be detached from mathematics. I want to become theoretical physicist and as a student undergoing MS i cant stress enough the importance of properly studying mathematics like a mathematician for physics. its like using a lense you just see physics better once you know your mathematics
@@SoumilSahu that's like saying that physics doesn't need to exist without classical mechanics, because every experiment is better explained using quantum mechanics. like yes, formally, physics would be no different without classical mechanics, but you're hardly a physicist if you don't know the basics. likewise, the formal structure of mathematics can get by without any intuition at all, but nobody would study it if that were the case.
Going to take physics as one of my IB subjects instead of biology, this has been enlightening and to be honest-physics makes you more calculative provided you have some measure of skill and knowledge of a equal-higher level in mathematics, the two do correlate but are still very different yet similar simultaneously. Interesting wisdom in this, thanks for putting this out there.
the math major and physics major combo is forever an unstoppable duo. the math major lacks any form of physical intuition while the physics major lacks in mathematical logic. this relationship perfectly describes me (a math major) and my classmate who's a physics major!
The first PhD candidate I talked to when I started studying math was working on a model to predict and prevent traffic jams. Quite real world oriented I would say.
@@brunojani7968 so can physicists. What he said can clearly be generalized to absolutely any academic field. it's entirely unsubstantiated. It's literally just an arbitrary bit of "wisdom." I suggest you look up Slavoj about his opinion on "vulgar wisdom" (spoiler: that would be all wisdom).
@Sky Gardener look up on most of the quantum mechanical interpretations, people trying to solve for quantum gravity, AdS/CFT correspondance, janus model. none of which has an application but are considered as great piece of physics.
@Sky Gardener on your later comment about mathematics. almost everything can be and is usually said about quantum mechanics. I would even argue that going by this logic quantum mechanics is more of a branch of mathematics and not physics.
I feel like this was what made math in school so difficult for me. I could always understand problem better by associating them with the real world and unfortunately, math teachers never really cared to make that connection.
As someone that used to teach mathematics in school (a pure mathematician), your teachers had the wrong approach. That way of teaching only works for maths majors and even then, you need to come up with examples, even though the examples for maths majors come from less abstract maths. You can learn a great deal of theory, but if you can't come up with examples (and counterexamples), that knowledge is pointless.
True. Even right now trying to learn mathematics online, nearly all of them do not dive into the intuition of human sense, but teach simply by the rules of math. Doing math itself is incredibly easy, but understanding why I do the things I do takes me days of thought
@@Ennar I believe that in order to understand the general case, one needs to start with the specific cases. You’re much more on the money there, frankly.
I had the opposite experience back in school: abstracting away a lot of details made it a lot easier to think about the problems without a lot of unnecessary fluff that comes with the real world. I usually barely got passable grades in physics because a lot of the formulas seemed arbitrary and disconnected from each other leading to me constantly forgetting them all the time. Meanwhile, I could recall at least some of the steps of deriving theorems in mathematics to recall what they were, and I was fascinated enough with maths to jump far ahead of the program in many cases where proof was omitted, finding it and spending time thinking over it until understanding it.
Physics is a dream and the way to express that dream is maths. Maths: General Equation to fit everything Physics: Special cases to fit their dream. Engineer: Lets trivialize few variables to make them into a physical reality.
Trivialize some variables? Let's recognize that I can replace the ODE with the number 1 in our problem because if the deflection is small the angle = tan(angle) = sin(angle) and then the equation becomes... The same thing mathematicians do all the time.
@@mr.rachetphilanthrophist601 Impact is an ambiguous word. Mathematicians will tell you that asskicking is just a trivial 3D case of what they seek to grasp.
Being as a physics student, I agreed to this such words but it's really interesting to know such generalised world, real to imaginary, 1D to nD. As a physicist respect all the mathematian. Physics and Mathematics are like two sides of a coin.
I love mathematics abstract and logic everything in the universe works under its laws its the gods universal language the fact we can understand it differs us from other animals
@@hiiamjustacoolrandomuser168 Of course, to the mathematicians the physicists are mere upstarts and noisy brats with a whiteboard who are getting way too much research money. ;-)
stuff like those electromagnetic thingies in physics , 'non-intuitive' concepts are often unfounded when tackled with math, as it is purely in argument form. so maybe not just physics, many real-phenonmena cannot be explained via an argument and need empirical, visual founding evidence obtained through somebody's personal time and observation to link to the argument, or which case, should he/she discover smth otherwise non-intuitive, they'll correct themselves to find an alternative argument. i often have struggled to see any practical use as a highschool sophomore for math. it just serves as a puzzle to solve. even still, when i reached the threshold for calculus, i realized these things can have potential usage in 3d graphics, and derive for the velocity aka tangent slope. I still often give up and narrow towards just seeking what yields the most fun and beauty, and repurpose towards hedonism, but i still do hope that one day when the time comes for me to solve problems i find impractical, that i will forge ahead regardless, try to make what feels in vain, not so.
The field of physics is trying to reverse engineer an exact set of axioms and logic, which when applied together produce the reality we observe around us. The field of mathematics is trying to explore the entire space of logic and reason, unconstrained from specific axioms. Both are trying to home in on the core fundamental truth of reality, just from different angles.
Wow, as an elect. eng. I love to study physics, how and why something happens. I am very good at circuits, control and logic and a poor mathematician. I was known for creating one line diagrams that showed system operation that could be used for understanding the whole and troubleshooting. Faraday is my hero because like me he had a sense of system by studying results of experiment while being a poor mathematician.
The general case is important. In machine learning n can be a big number. in computer science we use complex math and it's beautiful. Physics is just a small part of math, that's it.
This video leaves out quite a funny line from Feynman where he concedes that the general case is important. See: watch?v=obCjODeoLVw&t=207s But here's the quote: "[...] There's a certain amount of reducing because the mathematicians have prepared these things for a wide range of problems, which is very useful. And later on it always turns out that the poor physicist has to come back and say, 'Excuse me, when you wanted to tell me about the 4 dimensions...'"
Yeah, I was gonna say, all the talk about physics being about specific cases or something you can intuit really falls apart when you start venturing into more advanced physics topics. These parts of physics AREN'T intuitive and can be extremely hard to visualise classically or model accurately without advanced mathematics. And there is a long list of useless looking math that has surprising and incredible implications for areas of physics beyond the basics. I also think he completely leaves out the possibility of a purely mathematical insight inspiring new models for physical phenomenon, instead making it sound like pure luck whenever a mathematician happens to already have a theorem ready for a specific physical case.
@@NabsterHax The Special Theory of Relativity has simple linear algebra yet it's postulates are very profound. Same is true for Hawking's black hole equations. Your idea that advanced physics require complex maths isn't true.
@@kundakaps no offense but 1) relativity’s math is not easy, it is considered very difficult, when you actually look at how the constants are derived it requires lots of very complex mathematics. on top of that it uses maxwells’ equations to justify some of its conclusions, which are no small hill to conquer either. 2) there are other areas of physics which also require immense calculations
To me maths and physics are just very strongly intertwined. Math is a language that makes our lives easier. Physics describes a observation of the real world with the help of maths. Mathematicians create formulas while physicists have to find out which formulas to use in order to describe the observed thing.
I took economic calculus in college. I was great at math but performed terribly because I has no interest in finance. Now that I have 20 years in the real world I am studying finance and I love it.
This video is incomplete. He doesn't think that. He was just joking around there. You should watch the full clip. After it, he made fun of physicist also that how they go to Mathematicians when we need 4D.
Thank you. I realized an error in my previous quest for the -2nd dimension polygon and the meaning of pi. I used physical diagram of a 2-D diagram of radium and radius to describe any +3 angled polygons. Then I used the schematics of integration and derivation to shift the dimension of the y-axis, the x-axis, the point, and so I arrived at the -1angled polygon. I used what was previously completely unknown (the 0 sided non-dot polygon) to do another integration/derivation-related dimensional shift and I arrived at what I could only describe as the hidden divine living ever-changing ever-growing creature called Pi, which grows in observation much like (if not more) than any human beings. For the first time I thought I witnessed something I wasn't allowed, but it spoke to me in irrational temporary language and told me to share the divinity only when the world is ready and attentive. Nowadays I believe that such was merely a prank by whomever controlled this small sector of life. The quest, however, is indeed an important investigative experience for myself, and only a man such as Mr. Feynman could have the abilities to ultimately suggest to me possible errors in my ways. I have noticed that I have mixed theoretical analysis with practical-verifiable scientific analysis many times, which allowed the chance for pranksters (of many diverse and distinct mixtures of abilities) to leave doodles during my personal quest for creating the strongest surviving pillar of no stress-points for my metaphysical museum of knowledge and tales of wisdom. If my mind can create, then so could it survive any harm I or others may do onto it. During the prank by the divinity or the middle-person between me and the offspring (division) of people's arbitrary reassignment of shapes and forced convergence of spaces (curves and lines should never exist in the same reality but they do), I did acquire some tricks and techniques from the so-called lifeless meta-world.
Okay, I don't know about anyone else, but I never understood algebra until I took a physics class. Keep in mind I was taking a friggen pre-calc class at the same time. But I just couldn't do more than briefly memorize those abstracted topics until some reality was given to them. I think even unobservable concepts like n=4 are easier to grasp if you can learn the math and why the logical rules exist with a simpler real case like n=3.
I found only two words in my heart -"mathematics"and "physics" . And I am happy to say that these two words are enough to form this beautiful nature ❤️
I love the first law of thermodynamics it applies to everything. The conservation of energy can be applied to forces and explained that way from an energy point of view. Like Lagrangian equations explain it.
Mathematicians do care about the meaning. It’s pretty much hidden in the proofs but intuition is very important in Math. Mathematicians don’t (shouldn’t) tell physicists what their subject is and the same goes the other way. Feynman was a brilliant physics genius, but not a mathematician.
When I first heard Feynman talk about this, I was an undergraduate math major, first learning things like real analysis and abstract algebra. And I agreed with his sentiments. But now that I'm a published research mathematician hearing this clip again for the first time in years, yeah, that part made me cringe.
i feel like anyone who's math degree is worth anything understands that math has meaning and application. what he is talking about is jerking off over theoretical things with no real world application which is a very thin and specific slice of the math pie. cue joke about how modern physics is vastly more theoretical and more often than not lacks literally any application within the foreseeable future.
Also, there must be some sort of meaning to mathematical symbols or else they wouldn't be applicable in physics to begin with. Sure, mathematicians talk about n dimensions and aren't particularly interested in n=3, but n nevertheless does represent 'possible dimensions' here. So, perhaps mathematics circumscribes possibilities whereas physics describes realities.
The physics courses were only a little better. They tried to solve problems with simultaneous equations that could be transformed into 1D models. It was like driving a tack with a sledge hammer. If I used the physics instructor's methods on my problems at work, or on my PE exam, I wouldn't be an engineer today because I wouldn't have finished the test or the assignment before the deadline.
The difference between physics and mathematics being equated, pun intended, to the difference between the particular and the general is an excellent analogy.
As a student of mathematics , all i want to know is how in the world does physics help mathematics? it can be other way around but how does physics help mathematics as he says.
At a minimum, physics shows how the instruments of mathematics could be used to for practical, scientific purposes. I don't see both subjects having some type of parasitic relationship. Both complement our pursuit of knowledge.
The only way I can see it is that physics "helps" mathematics by being a source of problems to solve. A lot of cutting edge maths is about creativity, and physical phenomenon can inspire on that front.
It's a common occurrence in history for research in physics to create new mathematical areas of inquiry. Fourier analysis, the theory of wavelets, calculus of variations and symplectic geometry are classical examples. More recently, research in physics has provided mathematicians with powerful tools, such as Seiberg-Witten invariants, and has shed light on important mathematical topics, such as mirror symmetry.
Legends do make mistakes sometimes. It was bit derogatory for Maths. In my view, both Physics & Maths are complementary to each other, so each side should respect the other. BTW.. without Physics, maths can survive.. like in economics, social, banking, statistics & in many practical day to day things which run life of a common persons… BUT without maths, physics can’t survive..
text for the last portion that doesn't have subtitles: "it is not necessary that just because this would be useful to you, they have to do it that way. they can do what they will. it's their own job. and if you want something else, then you work it out yourself." very wise words, that i think can be applied to a lot more than just the fields of math and physics
it's not true that mathematicians don't know what the symbols mean. they know exactly what they mean and they can have great intuition about what follows from given axioms or assumptions
What he wanted to say with this, is that mathematics uses symbols to denote things that can be anything. If i write 2+2 i dont know what 2 means. 2 can be apples, people, money , anything, even the "+" can change depending on what is defined.
@@toniokettner4821 Mathematicians focus on the logical structures defining these objects, but they don't really care about its correspondence to real stuff
@@toniokettner4821 What do you mean by that? 2 is 2? Do you speak of the symbol? Of the abstract idea of a quantity in the physical world? Mathematically, 2 usually refers to succ(succ(0)) (= succ(1) = 2) Does 0 have any meaning here? Not really, it is defined to be the first natural number in the Peano axioms. The only meanings associated with it are the ones that logically follow from the axioms. Mathematics never concerns itself with real world phenomena. Mathematicians might draw inspirations from the real world for new theories and abstractions, but ultimately mathematics is an entirely decoupled construct where the only meaning the symbols have is their relationship to the rest of mathematics.
He is talking about pure/abstract mathematics. Applied mathematics is most certainly concerned about results that can be applied to the real world. It is interesting, however, how much pure/abstract mathematics is applied to physics and engineering "down the road" when certain enlightenments occur and unexpected connections come. An interesting study is the various geometries that existed mathematically and, years later, their subsequent and unexpected applications to real world problems. Professor Feynman is correct. Each one helps the other.
I wish I could agree, but I found physics in college to be exactly how he describes mathematics. It was incredibly hard to ground the work we were being taught in reality and the explanations to many questions were "well this is what you get if you do the algebra with the previous equation."
You are correct. Unfortunately, physics is today a discipline that is taught purely as how to calculate various results mathematically. The real kicker is that once you get to graduate school they stop teaching you how to solve problems or apply the math altogether, at least where I am. I'm expected to solve extremely difficult problems entirely on my own. The excuse is that we're supposed to team up with classmates and solve the set together. What if you don't have friends? For me personally it's honestly a nightmare.
though, this "not knowing what you're talking about" feature of maths can be used to one's advantange in physics. if you don't know if a vector will be in the direction +i or -i, you can just assume it to be in +i, and solve the equations. if your magnitude comes out to be negative, it will automatically imply that it is actually in the -i direction. im just a high school student and this "feature" of maths helps me out so much while im doing physics, i can only imagine how useful it would be in higher studies. maths and physics definitely go hand in hand
I think the main thing that separates math from a lot of the physical sciences is one simple aspect. Mathematicians are fascinated by the existence of a formula that seemingly appears out of nowhere and want to dig deeper into it and investigate the reasoning behind its existence. Physicists, chemists, engineers etc don't need to care why a formula exists, they just need to know that it works and that they can use the existing theory to build more complicated models and theories that can help explain or construct certain things in the real world. Mathematics relies on logic and axioms, but physics and engineering relies on existing math concepts.
That's not true. Physicists definitely are struck by certain formulae and want to dig deeper into their meaning and "reason" for existing. A nice example would be the path integral for which Feynman is famous, which has its routes in the action principle of classical physics. Physicists simply care more about connecting physical ideas rather than mathematical ones. That doesn't mean they treat all formulae as mere phenomenological models that must be made more complicated to fit more circumstances. In fact, usually the opposite has happened. Simpler and simpler formulae describe larger and larger collections of phenomena.
Had physicists “not cared about why formulas are such and such” than we wouldn’t have gotten any further than the science we knew back in the 1700s. Knowing what causes what is essential and are the building blocks to the advanced sciences we have today.
@Abin Mathew Issac well considering the majority of the world believes in a higher deity, then yes God does have an impact on our world. Our lives wouldn’t be the same if it wasn’t for people’s belief in God. Saying “there’s nothing to do with God” is ridiculous.
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2:25 I think we are beginning to see the point in modern physics where the opposite of that assessment is true: Things become so abstract that physical intuition alone is ultimately misleading, with mathematical rigor being the only way to avoid missteps.
