Pure Mathematics has it's own beauty. However, as an applied mathematics enthusiast, I have an inclination towards physics as well, including astronomy and space science.
@@shinzo5744Pure math is more proof heavy and doesn’t have as many applications to other fields yet. Applied Mathematics is more computation heavy and focuses specifically on math that are immediately applicable to another field of study. A computational mathematician might work on differential equations because they can model a variety of different things. A pure mathematician might try to prove some obscure conjecture in abstract algebra no one outside of math has heard of.
@@shinzo5744pure math = discovering new things that may not have any use, applied math = using these abstract things made by pure math, and try to use them in the real world
Fun fact, Richard Feynman was only 24 when he was part of the Manhattan project. He loved playing bongos and two scenes in Oppenheimer show him playing bongos, even though his character has no role in the arc of the movie. I spotted that immediately and knew whom that must have been a nod to. He was also the guy sitting in the car relying on the windshield for UV protection during the test. And there are newer editions that have been in print, even recently, although of lesser quality.
I studied chemistry and my son studied physics in college. I loved math and always did well in it. I have to admit that I did not enjoy physics in college because my interest was organic chemistry. I had to take 5 quarters of Physics at UC Berkeley in the late 70s. In those days Calculus series did not include vector Calculus so I taught myself vector Calculus from Div, Grad and all that to do E&M. Then I had to suffer Physical Chemistry for 2 quarters in my senior year which included basic Quantum Mechanics and Statistical Mechanics. I took a separate class in Thermodynamics taught by a Chemical Engineering professor. He stuck to the book so much that I only attended class to take quizzes and exams and got an A. While my son studied Physics, I told him to take engineering classes because most Physics majors ended up as software engineers or electrical engineers or even quants in financial analysis. He ended up working as an engineer at an Amazon subsidiary Lab 126 that made Alexa and has hired a lot of physicists to work for him. I always loved Feynman books, his life, personality and stories about him.
@@sentientartificialintelligence I think that much of it depends on attitude. One naturally gravitates to subjects that they enjoy and want to spend more time on those, but schools define the curriculum and employ professors with different specialties that then need students unless they only engage in research. Some of the better schools become more research focused and therefore are better for graduate students than teaching undergraduates. Since I wanted to graduate, if I had difficulty in a required subject I would work with my friends, go to prof. office hours, ask questions and had to spend more time to succeed in those subjects. Also, in the higher rated schools you will be competing with smarter students so you either sink or swim. Find a school that matches your ability. I hope this helps.
I am a mathematician first and foremost. I think physics is very cool, but I’m actually specializing in biological maths because I also love plants. My fellow botany friend is specializing in biophysics for a similar reason to me. I guess it’s whatever you end up developing an interest in.
My favorite Feynman video has to be his "Los Alamos from Below" lecture. It really highlights what you said, he seemed like just a goofy, charismatic guy who happened to be really good at physics
A friend of mine who was working on his PhD in Physics back in the 1970s told me some interesting stories about Feynman. I'm not sure, but one of them may have been repeated in one of Feynman's books. That is the one about teaching his dog to fetch socks laying around the house and dropping them in the laundry room. The dog would go on sock patrol. When he found a sock that needed to be taken to the laundry room, instead of picking it up and carrying it to the laundry room, the dog was taught to run out the doggie door in the back door, around the house to the front door, through that doggie door, to the sock, pick it up, run back through the doggie door in the front, around the house, in through the doggie door in the back, and to the laundry room where he would drop the sock. That was absolutely genius. Inspired by that, I tried to teach a dog something much simpler. In my company, I'm the only one who has never brought my dog to work (when I had one). My dog was very much an outdoors dog and didn't like to be inside. He would have hated to spend an entire day in the office. One woman here had a little Maltese who was quite smart. In the front of the office, we have doors on the south and north sides of the building to get up to the reception area. I tried repeatedly to get the dog to only use the south door, never the north. I tried everything I could think of, but he was still just as happy to use the north door as the south door. With all those dogs, the craziest thing was one falling through the ceiling tiles in my office while I was working. Nobody ever expects to find dogs falling through their ceiling. But that's another story. The physics grad student's second story about Feynman had to do with a topless bar/strip club near Cal Tech. Feynman would go there quite often for a break. Oddly enough, he didn't drink alcohol, just soft drinks or tea or something. At the time, there was some kind of investigation by the legislature wanting to shut down such businesses. One day the owner came up to quite a few of the regulars to try to get them to testify before the state legislature. According to the Physics student, Feynman was the only regular who did so. So he went to the hearing and they began their questioning. As surprised as they were when the witness identified himself as a professor at Cal Tech, they were even more surprised when they found out that he was a Nobel Prize Winner. And that he went nearly every day. The news picked up on this and the next day there were stories in the news about a Nobel Prize winning Physicist who went to topless bars/strip clubs. According to the Physics student, the owner of the bar was so grateful that Feynman got free drinks for life.
I've always understood that in physics, you not only have to understand the necessary math, but you have to be able to identify what math you should apply to specific real world situations, which can be a significant challenge in itself, as this pairing may not be immediately obvious.
Of course Feynman was a math genius as well. He switched from a mathematics major to physics at MIT after asking his math adviser what use all this "fancy" mathematics had, at which point his advisor suggested that if he had to ask that question, perhaps he should switch is major to something more "useful" like physics. Feynman despite being a physics major was recruited to the MIT Putnam team, and won first prize (in the country) by a wide margin. In terms of sheer computing and math power - before the age of people like Witten a Field's medal winner - only Schwinger was his equal (if not his superior). Someone once asked Murray Gell-Mann why in his quantum field theory course they couldn't use the Feynman approach - and Gell-Mann replied that Feynman's approach was to write a problem down on the blackboard - stare at it intensely for a couple of hours, and then write down the answer - his intuition was astounding. Feynman also in one of his lectures on gravity in the early '60's once started by saying that "now I too will show that I can write down incredibly complicated equations that no one can solve" referring to his work on "ghosts" and non-abelian gauge theory.
Not only did Feynman win the Putnam math competition, he beat the rest of the field by such a wide margin so CONSISTENTLY that he got bored of doing it and stopped. I think he won it three years in a row or something; and I believe he still has the record for widest margin of victory in the competition. Oh and he still has the highest EVER grade recorded on Princeton's notoriously difficult physics graduate exam to enter their doctoral program. I haven't checked if any student has since broken it but as of 7 years ago, the last time I checked, he still had the record. 100% a math genius with, apparently, only a "115" IQ - which means either the IQ test is silly, or it cannot measure genius. He was 1000% a genius. Period. End of story. His scientific abilities are up there with any scientist that has ever lived - he was at the Manhattan Project at 24!! That's crazy. 24? Yeah. Prodigy. Apropos "only Schwinger was his equal," I disagree. Dirac, Von Neumann and Weyl were all absolute geniuses of the highest order. Even lesser known names like David Bohm were prodigies with incredible raw ability. Von Neumann was legendary - the last polymath. Weyl knew as much mathematics as virtually any mathematician who has ever lived. Dirac essentially created quantum field theory (or what became QFT). And Einstein, well, Feynman said it best, "he was giant that the rest of us look up to." De Broglie essentially copied the same equations Einstein had derived for photons and applied them to electrons and called them matter waves, but the underlying physics reasoning was almost copied verbatim from Einstein's 1909 paper on what is now referred to as wave-particle duality. Feynman was amazing and, had he so chosen to be "pure mathematician" could have won a Fields Medal. He had that kind of imagination and creativity but chose physics instead (because math was easy for him).
@@feynmanschwingere_mc2270 Well I mentioned Schwinger because he was Feynman's contemporary - in fact the exact same age. And by the way, I think both of them are exceeded by Witten (whom Feynman admired) in terms of math ability. Feynman chose physics as I mentioned above because he wanted his math to have meaning and be of use.
Matt Sands was my Senior Project advisor at UC Santa Cruz; he taught me to write physics properly. (He went through a lot of red pens!) Matt did most the writing and translation from Feynmanese to English for the Feynman Lectures.
Hello Maths Sorcerer, a high schooler here. I had severe math anxiety. Your channel has left no leaf unturned in providing not only helpful math videos but also supportive sensitive content ❤ ❤ thank u , i got this!
A quote from Leon Lederman (Nobel award winner in physics) “the physicists defer only to mathematicians, and the mathematicians defer only to God (though you may be hard pressed to find a mathematician that modest)” The strength of your interest will determine your best avenue. The gap of knowledge makes one envious or fearful of the other discipline. Mathematician and physicist are like siblings that want to be right but in the long run depend on each other
Physics is harder than pure mathematics imo. Look at Einstein v Hilbert and the race for the final field equations of General Relativity. Hilbert was a mathematics god, with as strong an understanding of pretty much every area of mathematics as any human that as ever lived (at least in modern times). And Einstein beat him to the final field equations of General Relativity - even after teaching him the theory in a series of lectures at Gottingen (with Hilbert getting additional help on the physics from Emily Noether). And according to Ed Witten, the only physicist to ever win a Fields Medal, MANY mathematicians have problems understanding quantum field theory because of the density of the physics (not the mathematics), and that I find fascinating. If anybody would know about this particular intersection, it would be Witten. Plus, most physicists are just mathematicians who don't like writing proofs lol.
im a first year physics major, my calc professor is amazing and learning epsilon-delta proofs for things ive always taken for granted like limits, and the power rule and the chain rule, was one of the most satisfying things ever. and its absolutely perfect, you pick your axioms and assuming they are true, everything you say about it follows. feynman would be proud - the meaning of any statement is perfectly defined. meanwhile, physics is kicking my ass and I have no idea whats happening.
Mathematics, Physics and Computer Science form a powerful trifecta. Abstract, observe, compute! :D Study all three to the greatest depth time allows until they carry you out feet first. ⚰♾💪
Physics is done in a completely different style. While math, even when it's "hard," is often still vaguely straightforward on a large scale, physics is very much "all over the place," a pretty random collection of math problems that are applied to reality. It is very messy. If you take the time to understand the physics rigorously, like a mathematician and not like a physicist, physics becomes extremely beautiful and clever. Physics students (and often physicists) don't really understand the math they're doing, and just the way it's done can make it an enormous challenge for one used to more mathematical thinking. Sometimes in physics it pays to think *less*, to just take something at face value, warts and approximations and all, and just calculate with it. But I love physics. I continue to study it.
My education was in Physics and, if I could go back, I would probably choose math even if my grades were consistently slightly better in physics-related disciplines rather than in math-related ones. My experience is that learning and mastering the mathematical formalism will put a person in a better position when it comes the time to apply that formalism to Physics. The other way around lead to a somewhat more stressful experience in my opinion. For example, when a Physics student meets the Lagrangian and Hamiltonian formulations of classical mechanics for the first time, he/she usually has no knowledge of differential geometry, and as a consequence the whole theoretical construction is somewhat obscured and feels more like an ad hoc solution rather than a natural application of an elegant mathematical formalism to the description of the trajectories of a physical system. Same thing with Quantum Mechanics, General Relativity or Quantum Field Theory, where differential geometry, tensor fields algebra and group theory all play a very important role in anchoring the formulation of the theory to a well defined and rigorous mathematical formalism.
This is ironic because Ed Witten has been quoted as saying that from his experience he has found that a lot of mathematicians have problems understanding quantum field theory because of the physics not the mathematics. Fascinating.
I've seen Feynman's own copies of the Lectures books up for sale recently, going for a cool $175,000. 😮 Stop press: I goofed on the asking price, to the tune of $50,000. Apparently, they only want $125K. 😵💫
Oops! I got a bit carried away there: just checked the price again, and it's actually a snip at $125,000. Much more affordable! My own copy is heavily written over in the margins: I took about a year getting through just the first volume, taking the time to derive his results, and re-reading each chapter many times over until it sank in. One of the best experiences of my life.
I love physics, but everyone told me to study mechanical engineering instead. I'm almost done with my sophomore-level classes, and I'm going to transfer to ASU soon. Mechanical engineering is really cool. I found dynamics and circuits fun! However, I'm also a little sad that I will not be taking any more specific physics classes. Mad respect for physics and math majors!
I have a degree in ME. In the 2nd year there are basically no engineering classes. Only preparation courses which are just math and physics. So you can change easily if you want. But remember that engineering is just applied real world physics in many ways
@@devon9374 Yeah i've been noticing that in classes like circuits and mechanics of materials. Its physics applied to various applications. Yeah i'm only one class away where i could transfer as a physics major. University physics 3. It is tempting. I have also seen physics majors after getting a bachelor's go into a master's program for engineering.
@@tmann986 Ultimately, I don't think your major matters that much as long it's in this math/physics based realm. After years in industry, I became drawn to pure math and CS and that's what brought me to this channel. If I could go back I would have still done engineering (ME or EE) or my first love physics. I know I wouldn't have studied math because I realized I had to learn how to use and apply it first before appreciating it's depth and beauty. Now I'm learning Proofs and Discrete Math alongside low level programming
You have to find your "Knack". Maybe a STEM degree is the right path, maybe learning a trade. Experiment. Do. Be open-minded. Write down all of the things you'd like to try and sort them by "Job" and "Hobby". Do several iterations. It's the advice I give to my kids & they are doing well building lives for themselves. After clawing my way through High School Chemistry in my Junior Year, I gave Physics a shot since it was the last science course offered; if that fell apart, "Scientist" would get scratched off my list. During my Senior Year, Mr. "Nix" helped me *rediscover* Physics: I was all into gizmos and contraptions when I was a little kid. It was revolutionary to discover that a thing called a "Physics Major" existed! Out of all of the other possibilities I was considering, he collapsed my wave function and vectored me into Physics. It has served me well over the years. That was a while ago: "Against the Wind" by Bob Seger & The Silver Bullet Band was a hit. (We both have held-up pretty well!)
From my point of view as a chemist who had to struggle both with physics and math in his education, and very slowly liked to find them more appealing all the time since then, both are hard, but for different reasons. Math is hard because of its rigor and the fact that everything builds on top of each other, so missing out some basics will haunt you for years to come. Physics is hard too, but more because of the opposite, namely its lack of logic, because Nature is, what it is, regular and irregular, logical and illogical, which means that physical truth often has to be taken as is, also the ugly pieces are part of it.
If you know the math, the physics is far easier. The mistake most students make is in trying to learn the math and the physics at the same time. One semester in grad school back in the 1970s, my schedule was very light and I wanted to take something interesting and so I took their Classical Dynamics course. I had the math already and it was surprisingly not difficult to keep up. Most of the students, though, didn't have the math that they needed and were really struggling. On our first exam, there was 20 or 25 bonus points. With the bonus points, I made a 118 on the exam. The average in the class was in the 50s. I knew some of the students in the class and I know that several of them were definitely smarter than me. They just didn't have the math background they needed for the course. Unfortunately, I had a conflict and couldn't take the second semester of the course. After I graduated and finially had some money, one of my first things I did was to order two sets of books, Feynman's three "Lectures on Physics" books and Spivak's five "Differential Topology" books. By the way, one year I shared an office with a grad student in Math who had a BS in Physics and intended to earn a PhD in Physics. He felt that he really didn't know the Math he needed to really succeed in Physics. So he decided an MS in Math was the way to go. That year, he took both semesters of the graduate Real Analysis course using Royden's book on the subject. I always considered that to be the toughest course in the University. He worked hard and made A's in both semesters. Then, to celebrate his second A in the course, he got drunk and that night he threw up in his sleep and choked to death. That was a real tragedy.
Physics is mathematics , term mathematics is universal Physics, algebra, calculus etc this are names of the discipline and action of mathematics The highest form mathematics is word problems from basic to advanced and complex include mathematical proofs and logic with practical and applied to real world that aid us to be better critical Thinkers for advancement of the world Great job ! A intelligent person
Remember, physics is all word problems which make the subject harder. In solving word problems, the solver must understand the paragraph, understand the physics concepts to the problem, retrieve the formula from one's memory, come up with an expression, then solve the problem, mathematically at the very end...exhausting.
That's not how physics is above high school level (in my experience at least) - problems aren't usually presented as "word problems", formulae are usually provided and you're taught to frame things mathematically from the outset (not right at the end) - mathematics isn't an afterthought in higher level physics, it's utterly fundamental.
Physics at university is totally different than in high school. I was never interested in physics in high school, yet I did end up studying it at uni and it was goddamn amazing!
That story about him rolling around on the ground to solve problems is interesting. My uncle would do this when he was in school too. He's a family physician.
During my engineering degree I realized how engineering topics are hard without advanced math, and how engineering could be creative with advanced math, that’s why I am starting next year my second bachelor in math major so help me God
For me, one of the notable features of physics vs math is that in physics, when you work with measuring units, you don't follow the same algebra of numbers. For example, if m is the unit meter, then you have m + m = m and not 2m. In the same way, m - m = m, and not 0. But this allows you to check if your equations are correct, especially with long and complicated expressions.
Indeed. That's called "dimensional analysis" and it's a great way to check your work in physics (and even to derive the general structure of equations from first principles). The key thing from an "algebra" point of view is, we're only interested in the _type_ of quantity, not the amount. So when you add or subtract, as you note, the units stay the same BUT when you multiply or divide they change (so m x m = m^2 and m/m = 1 i.e. the unit disappears, this is now a _dimensionless_ quantity) because a metre is a different _type_ of quantity to a square metre (one is a length and the other's an area) but one metre is the same _type_ of quantity as two, ten or a million metres (they're all still lengths). (and I agree it's notable BTW but from a slightly different perspective. Units _make_ quantities _physical_ - a dimensionless number by itself doesn't mean much in physics, it doesn't tell us anything about the universe. Whereas of course numbers by themselves are intrinsically meaningful in mathematics)
In my humble opinion the chance of getting through phisics problems can not be possible with out a strong base on math . here when the buty appear . the buty of transition between them. man that's wonderful. as an example in the topic of Shells. Rays, withdrawal, and also require integrations with an astronomical way . Maybe this is obvious but stunning don't you think
Could a single geometrical process square ψ², t², e², c², v² forming the characteristics of mathematics? We need to go back to r² and the three dimensional physics of the Inverse Square Law. Even back to the spherical 4πr² geometry of Huygens’ Principle of 1670. The Universe could be based on simple geometry that forms the potential for evermore complexity. Forming not just physical complexity, but also the potential for evermore-abstract mathematics.
Hey math sorcerer hope you're doing awesome , so i recently completed my grade 12 and have developed a keen interest in quantitative finance. I’ve decided to embark on a journey of self-study and am seeking your guidance on the best path to follow. Could you please recommend some books that would be beneficial for a beginner like me? Additionally, any advice on the sequence of topics to study, online resources, or practical exercises would be greatly appreciated. I’m eager to learn and am committed to building a career in this field without attending college. Your guidance would be invaluable to me.
I have a book recommendation for you, I came to posses this book by chance when my University decided to give some books away from their library. It's called Mainstreams of Mathematics by Fraleigh. It's quite old and possibly rare, but if you don't have it in your collection yet it's a really great read, very different than most math books because of the scope of subjects it covers. (love your videos btw)
Thanks for the book rec! Any other recommendations? I think it would be great to have an exhaustive list. I'd like to learn more physics and mathematics.
I have been wanting to learn more physics as of late. But I barely have enough time to keep up with what my graduate program requires of me. So it will have to be a project for another time
Dear Math Sorcerer, Firstly, thank you for another excellent video! When you say, at around 6'19", that you don't think the Feynman Lectures books were meant to be for beginners, but for 'good students who already know some math', I think you might be wrong; I believe the Feynman Lectures WERE meant for BEGINNERS in physics who might also have only quite basic (pre-calc) maths knowledge (at least volume one was)! If you read the preface in volume I, Feynman states "These are the lectures that I gave last year and the year before to freshmam and sophomore classes at Caltech." Admittedly, the academic calibre of Caltech freshmen probably meant that the material could be pitched at a higher level than might be usual for freshman physics at other universites. Feynman does state that in devising the lectures he was concerned to "maintain the interest of the very enthusiastic and rather smart students coming out of the high schools and into Caltech." That being said, many of the students taking Feynman's two-year physics course were NOT majoring in physics, as it is the academic tradition of Caltech that ALL students must at least minor in physics, regardless of what they are majoring in! So many of the students in Feynman's classes were actually studying things like Biology, History, English Literature or whatever other undergraduate courses Caltech might offer. Therefore, Feynman's lectures needed to be sufficiently elementary - at least in the freshman year classes - to be accessible for students with hardly any previous background in physics OR maths! I believe it is partly this fact that marks out the Feynman Lectures as both a unique experiment and a remarkable achievement in physics pedagogy, along with the style of exposition which, as you remark, is very different from a typical textbook because of its somewhat informal, discursive, story-telling format. On a personal note, I own all three volumes of the Feynman Lectures (they have been treasured possessions for 40 years), having purchased and read through them all prior to commencing my own degree course in theoretical physics in 1982 (and they were an absolute JOY to read!). Unusually, I was also completely self-taught to undergraduate level in most of the branches of mathematics I would need for my physics degree by this point, too. The reason for this is that my path to higher education was somewhat unusual, as was my preceding school career. I learned and/or remembered almost nothing of my school maths (other than perhaps factoring and expanding quadratics) because I made the switch from 'Arts-stream' subjects (e.g. music, English, art, etc.) to the sciences and maths only around the age of 14. And then my school career had ended prematurely due to tragic family events (that I won't go into). But it was at that point that I became fascinated by mathematics to the point of obsession, and set about devouring books on mathematics pretty-much 24/7 (I also used it as a form of therapy, to help me deal with the trauma of the aforementioned tragic events - for which it proved very effective). Some of the books were from my local library (which I made copious notes from before returning them), but most I purchased with my allowance (and later my wage from my first job pre-university). I still have all those books arrayed proudly on my bookshelves, and they are all very precious to me. They are an ever-present reminder of my life-long passion for mathematics and also a link to my past and my exciting early years of mathematical discovery. I still buy yet more books on maths and physics to this day, as my love for both subjects is as strong in my early 60s as it was in my teenage years. But I have run out of bookshelf space and so must now stack them in piles on any horizontal surface... I am also toying with the idea of becoming a maths writer for the popular science market, and also a maths tutor when I finally leave my current career in IT. For these reasons I am also revisiting books that I read many decades ago in order to refresh my memory of the more elementary maths I was learning back then - which is still a very enjoyable exercise. Of course, now we have the internet as an incredible resource for learning maths (and so much else), and I take full advantage of it. There are many fine mathematicians and lectures on TH-cam (and university outreach websites, such as Stanford and MIT), and I can happily sit through hours of lectures on mathematics, some of it already familiar but also some that is excitingly new and fresh to me. Maths is an endlessly fascinating subject, the most stimulating and absorbing intellectual pastime I can think of (yes, perhaps even moreso than theoretical physics!), and I thank the day that picked up that first maths book and thought 'Hey, this looks cool!'. Regarding maths channels on TH-cam, your channel is one of my favourites (this is no false flattery). I really like the different approach you take in your videos, which convey a lot of the fascination that I feel for maths, and also put a human face on a subject which many people can find alienating and intimidating. Well done, and please do continue the good work; you are an ambassador for our subject! Finally, regarding Feynman's Lectures, this is an article I wrote on Quora a few years ago, addressing the question of how best to learn physics from books: www.quora.com/What-are-some-books-that-a-non-trained-physicist-should-read-in-order-to-get-a-better-understanding-of-science/answer/Steve-Denton I mention the Feynman Lectures, of course. I also include a link to the online .pdfs of the books, which have been made available free-to-read in the past few years (thank you, Caltech!). (This is a Quora article I wrote in a similar vein about learning mathematics from books - a subject about which I consider myself something of an expert... (actually one of my most popular answers):www.quora.com/If-you-had-to-teach-yourself-math-from-basic-algebra-to-high-level-mathematics-what-would-be-your-strategy/answer/Steve-Denton)
I think if someone is good in Mathematics he should have no problem in understanding Physics. The concepts of Physics are not hard to understand but translating them to Mathematics and then working with them is much harder.
I'm not an expert or even competent in either math or physics but in my experience with both, I think math is harder. I think people perceive difficultly differently depending on their own skill set.
While they are closely related, math for scientists, including physicists, becomes a language that describes physical reality. What does this mean? I think it comes down to, in part, it being used to describe physical events, to suss out physical laws, to make repeatable predictions. Mathematicians have a different focus. The laws of Mathematics seem to be their own thing, describing its own realm, often unrelated to observable phenomena. The Ven diagram between the two subjects share an inscribed area, but most of the laws governing each system are to me mostly unrelated. Have you done any work covering Gödel's incompleteness theorem? I believe it may serve to illustrate my point, somewhat.
You gotta be the kind of guy that would get stumped by a inelastic/elastic collision in physics 1, yet look at something like switching between operater formalism to path integrals in QFT; and have little or no difficulty understanding it. Generalized thinker. Like Brian from the Breakfast Club, you built the elephant in shop class and the light didn't come.
The lectures are trivial to get. Upper division physics and what I’ve seen in my graduate physics texts shows it to be something of an early adopter of pure mathematics: Clifford and Lie algebras, etc. Cryptography of course being another adopter because of number theory. It’s all good and each has its brain-warping aspects: physics demands we attempt to interpret the math’s implications on the nature and behavior of reality in particular. Beyond recognizing where one’s personal strengths lie, it makes no sense to pick sides about which is “better” or “harder”.
Hi, I'm an engineer with a decent BS in Applied Mathematics. I want to teach myself Classical Mechanics. Somehow, I didn't learn either Lagranian or Hamiltonian Mechanics. If I did, it was hidden under the cover of the class. Can you recommend a textbook? Thank you, Baruch
what do you think is better for training your brain to be better at general problem solving and understanding for any other kind of field? physics or math?
hi, this is a off topic question but why is it important to be able to represent a number as a rational number, And is there any pratical applications of it?
Sir I am 18 year old computer science guy who has no bg in maths as go futher I realised that I lack problem solving skills and that is also because I dont know maths at advance level and one more thing I can do maths but it just mindless remembering of maths tables and formulas, can you recommend me where should I get started
My issue with physics is that every single physics model looks like some kind of crude stick-figure approximation of what's actually happening in an extremely complex natural world. I could never wrap my mind around the 'cut-off point" for this simplification process ... it seems purely subjective and physical science should not be an exercise in subjectivity. It is supposed to be objective. This is still a huge frustration. I really don't like it.
Which one is harder? I guess there a more derailed maths guys while physics guys are still on track. Women don’t take neither except some, and those don’t go full theoretically the respective fields.
I study physics but it’s disappointing the lack of mathematical rigor. Physics is absolutely nothing without mathematics, but there’s plenty of mathematics without physics.
If you're worried about mathematical rigour you may prefer studying... mathematics :). Mathematics is a tremendously important tool in physics but it's not _everything_ - the universe is the sine qua non of physics, so long as you have that and the capacity to examine it you can do physics (a _much_ less powerful, cohesive version compared to the one we've known for the last 400 ish years but still, physics). (i'm leaving aside the "it from bit"/"mathematics is the foundation of everything" philosophical position which _could_ be true but is currently _highly_ contestable)
I always wonder what people mean when they mention mathematical rigor. Is it the proofs, which I absolutely hate. I just visualize the mathematics and can see the truth in them.
@@michaelpieters1844 Yes, mathematical rigor implies proofs, which are absolutely important and necessary for the development of mathematics. No truths would be uncovered in mathematics if it weren't for the truths
Unfortunately I find the Feynman lectures very outdated. They are taught considering a 1960's (1970's?) audience...I personally don't like his methodology. I suggest you look at the Walter Lewin lectures, they are beyond amazing! Unfortunately, he had to exit MIT because of a sexual misconduct allegation and his lectures were, officially, taken down. You can still find copies around though.
@@einstein6285 Agreed. It's the equivalent of "PC vs Mac". No serious person cares about (or even believes in) some made-up "mathematics vs physics" competition. Just pick whichever you like best and study that, both are interesting, valuable fields. (does anyone "brag" that "without French there'd be no French literature" or make spurious claims like "if you know French you know French literature" ??)
“If I were again beginning my studies, I would follow the advice of Plato and start with mathematics.” - Galileo Galilei This quote resonates with me, as I wish to get my PhD in a field of theoretical physics - however I found that having a solid foundation in math is essential. It is because of this realization that I switched my undergraduate major to Math from Physics.
Sure, likely true for theoretical physics (which is more abstract) and its resonance for yourself is what matters. Not so true for e.g. astrophysics though IMO (where obviously there's still plenty of mathematics, it's just more about methods than deep structural stuff). Worth remembering that Galileo wrote that at a time when even the most learned "natural philosopher" _maybe_ had modern first year undergrad algebra - as arguably the first "mathematical physicist" it's natural he'd wish he had more. Nowadays any bright high schooler knows basically all the mathematics Galileo did _plus_ calculus and any graduate from a standard "physics major" degree has a _vastly_ bigger mathematical toolbox. In other words "thinking like a physicist" today would look _much_ closer to "thinking like a mathematician" in Galileo's day (so maybe _now_ he'd instead say "I'd concentrate more on physical intuition [given I already have today's undergrad physics level mathematics]").
@@anonymes2884 I agree. Given the scope of applied physics (i.e. nuclear, astro, etc.) where numerous assumptions can be made without proof, having a strong mathematical background is widely overkill. However, like you said, in the countless fields of theoretical physics where absolutely everything must be proven, the case is different and being fluent in higher mathematics is a godsend.
@@TheEmeraldKidRE Where numerous assumptions can be made without proof? If the experiment disproves your idea, it is not physics. You do know that physics is a science and nature is being observed through experiments first?
@@michaelpieters1844 Evidently you haven't a clue of what you're talking about. You can't say that making a hypothesis which turns out to be false via experimentation "isn't physics." Physics is the process of formulating and testing hypotheses -- it's not just the amalgamation of experimentally proven theories. The very fact that you think this immediately shows you have no scientific background whatsoever; and if you do, it's extremely poor and misguided. Quantum mechanics and Einstein's relativity are the pillars of theoretical physics -- the theories of which were devised without prior experimentation/observation. It was only AFTER these theories were mathematically proven that experiments were conducted, ultimately proving the theories correct. You seriously need to read a few books on the history and derivations of modern physics before claiming to know anything about it.
@@TheEmeraldKidRE I actually got 3 masters and the best way to do physics is to observe nature and then create a model to best describe nature. The way it was done in the 20th century was indeed the other way around (also the reason why high energy physics is in such a disarray) but that is not how you normally do science the way giants did it like Newton, Gauss, Weber, Maxwell.
And without math physics is nothing..but without physics math is still there... btw I am a physics enthusiast and I know very little because of having less knowledge of math's..
@@Anuranjana5656 also physics without math is pure physics the contemplation process and curiosity to observe the universe around plus whole mathematics except number theory is based on physics. The holy grail of math is calculus which is based on the physical world.
@@yhistory2688 Calculus is _not_ "the holy grail of math" and mathematics is _not_ "based on physics". Mathematics is clearly more fundamental than physics (where by "physics" I mean the area of study rather than the actual workings of the universe). I say that BTW as someone that studies physics and utterly rejects the idea that "without math physics is nothing" (i.e. i'm not biased towards mathematics, if anything i'm biased towards physics). "[W]ithout math" physics is a much less powerful, less coherent, less predictive version of its modern self BUT physics is "just" the systematic study of the fundamental workings of the universe - you can do that without using the tool of mathematics (not nearly as well but you can still do it).
@@anonymes2884 first I meant calculus was the holy grail obviously now we pretty much understand it but math is discovered not invented okay. So it is based on the universe around thus it’s natural and that’s physics, till you invent math then we will admet it is something else.
Normally I'd settle for used older editions of famous books, but I've read that there are lots of errors in the older editions of the Feynman Lecture books.
I still remember my first lesson of Reactor analysis and design (nuclear engineering) during which the prof. said "in Russia we don't make any difference between math and physics" while filling up the boards with integro-differential equations. God I loved that course...
Pure Mathematics has it's own beauty. However, as an applied mathematics enthusiast, I have an inclination towards physics as well, including astronomy and space science.
whats the difference between mathematics and pure mathematics?
@@shinzo5744it's pure and applied mathematics
@@shinzo5744Pure math is more proof heavy and doesn’t have as many applications to other fields yet. Applied Mathematics is more computation heavy and focuses specifically on math that are immediately applicable to another field of study. A computational mathematician might work on differential equations because they can model a variety of different things. A pure mathematician might try to prove some obscure conjecture in abstract algebra no one outside of math has heard of.
@@shinzo5744pure math = discovering new things that may not have any use, applied math = using these abstract things made by pure math, and try to use them in the real world
Zero. The meaning of Rien
This channel's videos get a decent amount of views, but not enough.
Every Math enjoyer should be watching you in their free time!
Understanding math is one of the most rewarding things ever
Fun fact, Richard Feynman was only 24 when he was part of the Manhattan project. He loved playing bongos and two scenes in Oppenheimer show him playing bongos, even though his character has no role in the arc of the movie. I spotted that immediately and knew whom that must have been a nod to. He was also the guy sitting in the car relying on the windshield for UV protection during the test.
And there are newer editions that have been in print, even recently, although of lesser quality.
I studied chemistry and my son studied physics in college. I loved math and always did well in it. I have to admit that I did not enjoy physics in college because my interest was organic chemistry. I had to take 5 quarters of Physics at UC Berkeley in the late 70s. In those days Calculus series did not include vector Calculus so I taught myself vector Calculus from Div, Grad and all that to do E&M. Then I had to suffer Physical Chemistry for 2 quarters in my senior year which included basic Quantum Mechanics and Statistical Mechanics. I took a separate class in Thermodynamics taught by a Chemical Engineering professor. He stuck to the book so much that I only attended class to take quizzes and exams and got an A. While my son studied Physics, I told him to take engineering classes because most Physics majors ended up as software engineers or electrical engineers or even quants in financial analysis. He ended up working as an engineer at an Amazon subsidiary Lab 126 that made Alexa and has hired a lot of physicists to work for him. I always loved Feynman books, his life, personality and stories about him.
It's great that your son studied physics and did get an engineering position. I took the advice to study engineering instead of physics.
@@sentientartificialintelligence I think that much of it depends on attitude. One naturally gravitates to subjects that they enjoy and want to spend more time on those, but schools define the curriculum and employ professors with different specialties that then need students unless they only engage in research. Some of the better schools become more research focused and therefore are better for graduate students than teaching undergraduates. Since I wanted to graduate, if I had difficulty in a required subject I would work with my friends, go to prof. office hours, ask questions and had to spend more time to succeed in those subjects. Also, in the higher rated schools you will be competing with smarter students so you either sink or swim. Find a school that matches your ability. I hope this helps.
I am a mathematician first and foremost. I think physics is very cool, but I’m actually specializing in biological maths because I also love plants. My fellow botany friend is specializing in biophysics for a similar reason to me. I guess it’s whatever you end up developing an interest in.
That's awesome!
Thank You for your video.
My favorite Feynman video has to be his "Los Alamos from Below" lecture. It really highlights what you said, he seemed like just a goofy, charismatic guy who happened to be really good at physics
Yeah I read that in the book "Surely you're joking, Mr Feynman". Which was really I'd really recommend that book.
A friend of mine who was working on his PhD in Physics back in the 1970s told me some interesting stories about Feynman.
I'm not sure, but one of them may have been repeated in one of Feynman's books. That is the one about teaching his dog to fetch socks laying around the house and dropping them in the laundry room.
The dog would go on sock patrol. When he found a sock that needed to be taken to the laundry room, instead of picking it up and carrying it to the laundry room, the dog was taught to run out the doggie door in the back door, around the house to the front door, through that doggie door, to the sock, pick it up, run back through the doggie door in the front, around the house, in through the doggie door in the back, and to the laundry room where he would drop the sock.
That was absolutely genius.
Inspired by that, I tried to teach a dog something much simpler. In my company, I'm the only one who has never brought my dog to work (when I had one). My dog was very much an outdoors dog and didn't like to be inside. He would have hated to spend an entire day in the office.
One woman here had a little Maltese who was quite smart. In the front of the office, we have doors on the south and north sides of the building to get up to the reception area. I tried repeatedly to get the dog to only use the south door, never the north. I tried everything I could think of, but he was still just as happy to use the north door as the south door.
With all those dogs, the craziest thing was one falling through the ceiling tiles in my office while I was working. Nobody ever expects to find dogs falling through their ceiling. But that's another story.
The physics grad student's second story about Feynman had to do with a topless bar/strip club near Cal Tech. Feynman would go there quite often for a break. Oddly enough, he didn't drink alcohol, just soft drinks or tea or something.
At the time, there was some kind of investigation by the legislature wanting to shut down such businesses. One day the owner came up to quite a few of the regulars to try to get them to testify before the state legislature. According to the Physics student, Feynman was the only regular who did so.
So he went to the hearing and they began their questioning. As surprised as they were when the witness identified himself as a professor at Cal Tech, they were even more surprised when they found out that he was a Nobel Prize Winner. And that he went nearly every day.
The news picked up on this and the next day there were stories in the news about a Nobel Prize winning Physicist who went to topless bars/strip clubs. According to the Physics student, the owner of the bar was so grateful that Feynman got free drinks for life.
I've always understood that in physics, you not only have to understand the necessary math, but you have to be able to identify what math you should apply to specific real world situations, which can be a significant challenge in itself, as this pairing may not be immediately obvious.
Of course Feynman was a math genius as well. He switched from a mathematics major to physics at MIT after asking his math adviser what use all this "fancy" mathematics had, at which point his advisor suggested that if he had to ask that question, perhaps he should switch is major to something more "useful" like physics. Feynman despite being a physics major was recruited to the MIT Putnam team, and won first prize (in the country) by a wide margin. In terms of sheer computing and math power - before the age of people like Witten a Field's medal winner - only Schwinger was his equal (if not his superior).
Someone once asked Murray Gell-Mann why in his quantum field theory course they couldn't use the Feynman approach - and Gell-Mann replied that Feynman's approach was to write a problem down on the blackboard - stare at it intensely for a couple of hours, and then write down the answer - his intuition was astounding. Feynman also in one of his lectures on gravity in the early '60's once started by saying that "now I too will show that I can write down incredibly complicated equations that no one can solve" referring to his work on "ghosts" and non-abelian gauge theory.
Not only did Feynman win the Putnam math competition, he beat the rest of the field by such a wide margin so CONSISTENTLY that he got bored of doing it and stopped. I think he won it three years in a row or something; and I believe he still has the record for widest margin of victory in the competition. Oh and he still has the highest EVER grade recorded on Princeton's notoriously difficult physics graduate exam to enter their doctoral program. I haven't checked if any student has since broken it but as of 7 years ago, the last time I checked, he still had the record.
100% a math genius with, apparently, only a "115" IQ - which means either the IQ test is silly, or it cannot measure genius.
He was 1000% a genius. Period. End of story. His scientific abilities are up there with any scientist that has ever lived - he was at the Manhattan Project at 24!! That's crazy. 24? Yeah. Prodigy.
Apropos "only Schwinger was his equal," I disagree. Dirac, Von Neumann and Weyl were all absolute geniuses of the highest order. Even lesser known names like David Bohm were prodigies with incredible raw ability. Von Neumann was legendary - the last polymath. Weyl knew as much mathematics as virtually any mathematician who has ever lived. Dirac essentially created quantum field theory (or what became QFT).
And Einstein, well, Feynman said it best, "he was giant that the rest of us look up to." De Broglie essentially copied the same equations Einstein had derived for photons and applied them to electrons and called them matter waves, but the underlying physics reasoning was almost copied verbatim from Einstein's 1909 paper on what is now referred to as wave-particle duality.
Feynman was amazing and, had he so chosen to be "pure mathematician" could have won a Fields Medal. He had that kind of imagination and creativity but chose physics instead (because math was easy for him).
@@feynmanschwingere_mc2270 Well I mentioned Schwinger because he was Feynman's contemporary - in fact the exact same age. And by the way, I think both of them are exceeded by Witten (whom Feynman admired) in terms of math ability. Feynman chose physics as I mentioned above because he wanted his math to have meaning and be of use.
Matt Sands was my Senior Project advisor at UC Santa Cruz; he taught me to write physics properly. (He went through a lot of red pens!)
Matt did most the writing and translation from Feynmanese to English for the Feynman Lectures.
Hello Maths Sorcerer, a high schooler here. I had severe math anxiety. Your channel has left no leaf unturned in providing not only helpful math videos but also supportive sensitive content ❤ ❤ thank u , i got this!
A quote from Leon Lederman (Nobel award winner in physics) “the physicists defer only to mathematicians, and the mathematicians defer only to God (though you may be hard pressed to find a mathematician that modest)”
The strength of your interest will determine your best avenue. The gap of knowledge makes one envious or fearful of the other discipline.
Mathematician and physicist are like siblings that want to be right but in the long run depend on each other
Physics is harder than pure mathematics imo.
Look at Einstein v Hilbert and the race for the final field equations of General Relativity. Hilbert was a mathematics god, with as strong an understanding of pretty much every area of mathematics as any human that as ever lived (at least in modern times). And Einstein beat him to the final field equations of General Relativity - even after teaching him the theory in a series of lectures at Gottingen (with Hilbert getting additional help on the physics from Emily Noether).
And according to Ed Witten, the only physicist to ever win a Fields Medal, MANY mathematicians have problems understanding quantum field theory because of the density of the physics (not the mathematics), and that I find fascinating.
If anybody would know about this particular intersection, it would be Witten.
Plus, most physicists are just mathematicians who don't like writing proofs lol.
Love for you , mathematics and physics from Bangladesh
im a first year physics major, my calc professor is amazing and learning epsilon-delta proofs for things ive always taken for granted like limits, and the power rule and the chain rule, was one of the most satisfying things ever. and its absolutely perfect, you pick your axioms and assuming they are true, everything you say about it follows. feynman would be proud - the meaning of any statement is perfectly defined. meanwhile, physics is kicking my ass and I have no idea whats happening.
Mathematics, Physics and Computer Science form a powerful trifecta. Abstract, observe, compute! :D Study all three to the greatest depth time allows until they carry you out feet first. ⚰♾💪
Physics is done in a completely different style. While math, even when it's "hard," is often still vaguely straightforward on a large scale, physics is very much "all over the place," a pretty random collection of math problems that are applied to reality. It is very messy. If you take the time to understand the physics rigorously, like a mathematician and not like a physicist, physics becomes extremely beautiful and clever. Physics students (and often physicists) don't really understand the math they're doing, and just the way it's done can make it an enormous challenge for one used to more mathematical thinking. Sometimes in physics it pays to think *less*, to just take something at face value, warts and approximations and all, and just calculate with it. But I love physics. I continue to study it.
I like it that TMS is expanding out to these types of topics
My education was in Physics and, if I could go back, I would probably choose math even if my grades were consistently slightly better in physics-related disciplines rather than in math-related ones. My experience is that learning and mastering the mathematical formalism will put a person in a better position when it comes the time to apply that formalism to Physics. The other way around lead to a somewhat more stressful experience in my opinion.
For example, when a Physics student meets the Lagrangian and Hamiltonian formulations of classical mechanics for the first time, he/she usually has no knowledge of differential geometry, and as a consequence the whole theoretical construction is somewhat obscured and feels more like an ad hoc solution rather than a natural application of an elegant mathematical formalism to the description of the trajectories of a physical system.
Same thing with Quantum Mechanics, General Relativity or Quantum Field Theory, where differential geometry, tensor fields algebra and group theory all play a very important role in anchoring the formulation of the theory to a well defined and rigorous mathematical formalism.
As an engineer, I agree. I think if one has a strong aptitude for physics, they should study math instead. It'll make them unstoppable.
I absolutely agree
This is ironic because Ed Witten has been quoted as saying that from his experience he has found that a lot of mathematicians have problems understanding quantum field theory because of the physics not the mathematics.
Fascinating.
I've seen Feynman's own copies of the Lectures books up for sale recently, going for a cool $175,000. 😮
Stop press: I goofed on the asking price, to the tune of $50,000. Apparently, they only want $125K. 😵💫
wow!!!!!!!!!!
Oops! I got a bit carried away there: just checked the price again, and it's actually a snip at $125,000. Much more affordable! My own copy is heavily written over in the margins: I took about a year getting through just the first volume, taking the time to derive his results, and re-reading each chapter many times over until it sank in. One of the best experiences of my life.
I love physics, but everyone told me to study mechanical engineering instead. I'm almost done with my sophomore-level classes, and I'm going to transfer to ASU soon. Mechanical engineering is really cool. I found dynamics and circuits fun! However, I'm also a little sad that I will not be taking any more specific physics classes. Mad respect for physics and math majors!
You can double majors Mechanical Engineering and Physics…I plan to go University of San Diego…they have double majors in 5 years…
I have a degree in ME. In the 2nd year there are basically no engineering classes. Only preparation courses which are just math and physics. So you can change easily if you want. But remember that engineering is just applied real world physics in many ways
@@kevinng1702 I love your confidence in me 😅 I think i'll start with a minor in physics and see how that is. But that's pretty cool in only 5 years.
@@devon9374 Yeah i've been noticing that in classes like circuits and mechanics of materials. Its physics applied to various applications. Yeah i'm only one class away where i could transfer as a physics major. University physics 3. It is tempting. I have also seen physics majors after getting a bachelor's go into a master's program for engineering.
@@tmann986 Ultimately, I don't think your major matters that much as long it's in this math/physics based realm. After years in industry, I became drawn to pure math and CS and that's what brought me to this channel. If I could go back I would have still done engineering (ME or EE) or my first love physics. I know I wouldn't have studied math because I realized I had to learn how to use and apply it first before appreciating it's depth and beauty. Now I'm learning Proofs and Discrete Math alongside low level programming
You have to find your "Knack". Maybe a STEM degree is the right path, maybe learning a trade. Experiment. Do. Be open-minded.
Write down all of the things you'd like to try and sort them by "Job" and "Hobby". Do several iterations. It's the advice I give to my kids & they are doing well building lives for themselves.
After clawing my way through High School Chemistry in my Junior Year, I gave Physics a shot since it was the last science course offered; if that fell apart, "Scientist" would get scratched off my list.
During my Senior Year, Mr. "Nix" helped me *rediscover* Physics: I was all into gizmos and contraptions when I was a little kid. It was revolutionary to discover that a thing called a "Physics Major" existed! Out of all of the other possibilities I was considering, he collapsed my wave function and vectored me into Physics. It has served me well over the years.
That was a while ago: "Against the Wind" by Bob Seger & The Silver Bullet Band was a hit. (We both have held-up pretty well!)
Math > physics,, no hate with full of respect.
From my point of view as a chemist who had to struggle both with physics and math in his education, and very slowly liked to find them more appealing all the time since then, both are hard, but for different reasons. Math is hard because of its rigor and the fact that everything builds on top of each other, so missing out some basics will haunt you for years to come. Physics is hard too, but more because of the opposite, namely its lack of logic, because Nature is, what it is, regular and irregular, logical and illogical, which means that physical truth often has to be taken as is, also the ugly pieces are part of it.
If you know the math, the physics is far easier. The mistake most students make is in trying to learn the math and the physics at the same time.
One semester in grad school back in the 1970s, my schedule was very light and I wanted to take something interesting and so I took their Classical Dynamics course. I had the math already and it was surprisingly not difficult to keep up. Most of the students, though, didn't have the math that they needed and were really struggling.
On our first exam, there was 20 or 25 bonus points. With the bonus points, I made a 118 on the exam. The average in the class was in the 50s. I knew some of the students in the class and I know that several of them were definitely smarter than me. They just didn't have the math background they needed for the course.
Unfortunately, I had a conflict and couldn't take the second semester of the course.
After I graduated and finially had some money, one of my first things I did was to order two sets of books, Feynman's three "Lectures on Physics" books and Spivak's five "Differential Topology" books.
By the way, one year I shared an office with a grad student in Math who had a BS in Physics and intended to earn a PhD in Physics. He felt that he really didn't know the Math he needed to really succeed in Physics. So he decided an MS in Math was the way to go.
That year, he took both semesters of the graduate Real Analysis course using Royden's book on the subject. I always considered that to be the toughest course in the University. He worked hard and made A's in both semesters. Then, to celebrate his second A in the course, he got drunk and that night he threw up in his sleep and choked to death. That was a real tragedy.
Wait, is that story at the end true?
My father was an astrophysicist, and I now have his copy of this textbook (3 volumes).
Physics is mathematics , term mathematics is universal
Physics, algebra, calculus etc this are names of the discipline and action of mathematics
The highest form mathematics is word problems from basic to advanced and complex include mathematical proofs and logic with practical and applied to real world that aid us to be better critical
Thinkers for advancement of the world
Great job ! A intelligent person
"The Feynman Lectures" are available on-line, thanks to Cal Tech, and hard copies are still in-print.
Remember, physics is all word problems which make the subject harder. In solving word problems, the solver must understand the paragraph, understand the physics
concepts to the problem, retrieve the formula from one's memory, come up with an expression, then solve the problem, mathematically at the very end...exhausting.
That's not how physics is above high school level (in my experience at least) - problems aren't usually presented as "word problems", formulae are usually provided and you're taught to frame things mathematically from the outset (not right at the end) - mathematics isn't an afterthought in higher level physics, it's utterly fundamental.
Physics at university is totally different than in high school. I was never interested in physics in high school, yet I did end up studying it at uni and it was goddamn amazing!
That story about him rolling around on the ground to solve problems is interesting. My uncle would do this when he was in school too. He's a family physician.
During my engineering degree I realized how engineering topics are hard without advanced math, and how engineering could be creative with advanced math, that’s why I am starting next year my second bachelor in math major so help me God
Where you starting your second bachelor????
For me, one of the notable features of physics vs math is that in physics, when you work with measuring units, you don't follow the same algebra of numbers. For example, if m is the unit meter, then you have m + m = m and not 2m. In the same way, m - m = m, and not 0. But this allows you to check if your equations are correct, especially with long and complicated expressions.
Indeed. That's called "dimensional analysis" and it's a great way to check your work in physics (and even to derive the general structure of equations from first principles).
The key thing from an "algebra" point of view is, we're only interested in the _type_ of quantity, not the amount. So when you add or subtract, as you note, the units stay the same BUT when you multiply or divide they change (so m x m = m^2 and m/m = 1 i.e. the unit disappears, this is now a _dimensionless_ quantity) because a metre is a different _type_ of quantity to a square metre (one is a length and the other's an area) but one metre is the same _type_ of quantity as two, ten or a million metres (they're all still lengths).
(and I agree it's notable BTW but from a slightly different perspective. Units _make_ quantities _physical_ - a dimensionless number by itself doesn't mean much in physics, it doesn't tell us anything about the universe. Whereas of course numbers by themselves are intrinsically meaningful in mathematics)
Bio is applied chemistry, chemistry is applied physics and Physics is applied math
You know what blows my mind is how light has momentum due to electromagnetic field. It has no mass but yet has momentum.
My physics professor, Dr Dave Olsen, would smell an old book before he lent it to me. I think of him every time you smell one of your old math books!
I'm biased, but math > physics.
In my humble opinion the chance of getting through phisics problems can not be possible with out a strong base on math . here when the buty appear . the buty of transition between them. man that's wonderful. as an example in the topic of Shells. Rays, withdrawal, and also require integrations with an astronomical way . Maybe this is obvious but stunning don't you think
Could a single geometrical process square ψ², t², e², c², v² forming the characteristics of mathematics?
We need to go back to r² and the three dimensional physics of the Inverse Square Law. Even back to the spherical 4πr² geometry of Huygens’ Principle of 1670. The Universe could be based on simple geometry that forms the potential for evermore complexity. Forming not just physical complexity, but also the potential for evermore-abstract mathematics.
Your sniffing of books cracks me up 😂
Hey math sorcerer hope you're doing awesome , so i recently completed my grade 12 and have developed a keen interest in quantitative finance. I’ve decided to embark on a journey of self-study and am seeking your guidance on the best path to follow. Could you please recommend some books that would be beneficial for a beginner like me? Additionally, any advice on the sequence of topics to study, online resources, or practical exercises would be greatly appreciated. I’m eager to learn and am committed to building a career in this field without attending college. Your guidance would be invaluable to me.
I have a book recommendation for you, I came to posses this book by chance when my University decided to give some books away from their library.
It's called Mainstreams of Mathematics by Fraleigh. It's quite old and possibly rare, but if you don't have it in your collection yet it's a really great read, very different than most math books because of the scope of subjects it covers.
(love your videos btw)
Thanks for the book rec! Any other recommendations? I think it would be great to have an exhaustive list. I'd like to learn more physics and mathematics.
I have been wanting to learn more physics as of late. But I barely have enough time to keep up with what my graduate program requires of me. So it will have to be a project for another time
Dear Math Sorcerer,
Firstly, thank you for another excellent video!
When you say, at around 6'19", that you don't think the Feynman Lectures books were meant to be for beginners, but for 'good students who already know some math', I think you might be wrong; I believe the Feynman Lectures WERE meant for BEGINNERS in physics who might also have only quite basic (pre-calc) maths knowledge (at least volume one was)!
If you read the preface in volume I, Feynman states "These are the lectures that I gave last year and the year before to freshmam and sophomore classes at Caltech." Admittedly, the academic calibre of Caltech freshmen probably meant that the material could be pitched at a higher level than might be usual for freshman physics at other universites. Feynman does state that in devising the lectures he was concerned to "maintain the interest of the very enthusiastic and rather smart students coming out of the high schools and into Caltech."
That being said, many of the students taking Feynman's two-year physics course were NOT majoring in physics, as it is the academic tradition of Caltech that ALL students must at least minor in physics, regardless of what they are majoring in! So many of the students in Feynman's classes were actually studying things like Biology, History, English Literature or whatever other undergraduate courses Caltech might offer. Therefore, Feynman's lectures needed to be sufficiently elementary - at least in the freshman year classes - to be accessible for students with hardly any previous background in physics OR maths!
I believe it is partly this fact that marks out the Feynman Lectures as both a unique experiment and a remarkable achievement in physics pedagogy, along with the style of exposition which, as you remark, is very different from a typical textbook because of its somewhat informal, discursive, story-telling format.
On a personal note, I own all three volumes of the Feynman Lectures (they have been treasured possessions for 40 years), having purchased and read through them all prior to commencing my own degree course in theoretical physics in 1982 (and they were an absolute JOY to read!). Unusually, I was also completely self-taught to undergraduate level in most of the branches of mathematics I would need for my physics degree by this point, too. The reason for this is that my path to higher education was somewhat unusual, as was my preceding school career. I learned and/or remembered almost nothing of my school maths (other than perhaps factoring and expanding quadratics) because I made the switch from 'Arts-stream' subjects (e.g. music, English, art, etc.) to the sciences and maths only around the age of 14. And then my school career had ended prematurely due to tragic family events (that I won't go into). But it was at that point that I became fascinated by mathematics to the point of obsession, and set about devouring books on mathematics pretty-much 24/7 (I also used it as a form of therapy, to help me deal with the trauma of the aforementioned tragic events - for which it proved very effective). Some of the books were from my local library (which I made copious notes from before returning them), but most I purchased with my allowance (and later my wage from my first job pre-university). I still have all those books arrayed proudly on my bookshelves, and they are all very precious to me. They are an ever-present reminder of my life-long passion for mathematics and also a link to my past and my exciting early years of mathematical discovery. I still buy yet more books on maths and physics to this day, as my love for both subjects is as strong in my early 60s as it was in my teenage years. But I have run out of bookshelf space and so must now stack them in piles on any horizontal surface... I am also toying with the idea of becoming a maths writer for the popular science market, and also a maths tutor when I finally leave my current career in IT. For these reasons I am also revisiting books that I read many decades ago in order to refresh my memory of the more elementary maths I was learning back then - which is still a very enjoyable exercise.
Of course, now we have the internet as an incredible resource for learning maths (and so much else), and I take full advantage of it. There are many fine mathematicians and lectures on TH-cam (and university outreach websites, such as Stanford and MIT), and I can happily sit through hours of lectures on mathematics, some of it already familiar but also some that is excitingly new and fresh to me. Maths is an endlessly fascinating subject, the most stimulating and absorbing intellectual pastime I can think of (yes, perhaps even moreso than theoretical physics!), and I thank the day that picked up that first maths book and thought 'Hey, this looks cool!'.
Regarding maths channels on TH-cam, your channel is one of my favourites (this is no false flattery). I really like the different approach you take in your videos, which convey a lot of the fascination that I feel for maths, and also put a human face on a subject which many people can find alienating and intimidating. Well done, and please do continue the good work; you are an ambassador for our subject!
Finally, regarding Feynman's Lectures, this is an article I wrote on Quora a few years ago, addressing the question of how best to learn physics from books:
www.quora.com/What-are-some-books-that-a-non-trained-physicist-should-read-in-order-to-get-a-better-understanding-of-science/answer/Steve-Denton
I mention the Feynman Lectures, of course. I also include a link to the online .pdfs of the books, which have been made available free-to-read in the past few years (thank you, Caltech!).
(This is a Quora article I wrote in a similar vein about learning mathematics from books - a subject about which I consider myself something of an expert... (actually one of my most popular answers):www.quora.com/If-you-had-to-teach-yourself-math-from-basic-algebra-to-high-level-mathematics-what-would-be-your-strategy/answer/Steve-Denton)
I think if someone is good in Mathematics he should have no problem in understanding Physics. The concepts of Physics are not hard to understand but translating them to Mathematics and then working with them is much harder.
Mathematics is a building block, one physics dies you can CREATE another, so it’s applied math. Math you can apply everywhere.
I'm not an expert or even competent in either math or physics but in my experience with both, I think math is harder. I think people perceive difficultly differently depending on their own skill set.
While they are closely related, math for scientists, including physicists, becomes a language that describes physical reality. What does this mean? I think it comes down to, in part, it being used to describe physical events, to suss out physical laws, to make repeatable predictions.
Mathematicians have a different focus. The laws of Mathematics seem to be their own thing, describing its own realm, often unrelated to observable phenomena.
The Ven diagram between the two subjects share an inscribed area, but most of the laws governing each system are to me mostly unrelated.
Have you done any work covering Gödel's incompleteness theorem? I believe it may serve to illustrate my point, somewhat.
You gotta be the kind of guy that would get stumped by a inelastic/elastic collision in physics 1, yet look at something like switching between operater formalism to path integrals in QFT; and have little or no difficulty understanding it.
Generalized thinker. Like Brian from the Breakfast Club, you built the elephant in shop class and the light didn't come.
Applied Math major can be a happy medium ~
The lectures are trivial to get.
Upper division physics and what I’ve seen in my graduate physics texts shows it to be something of an early adopter of pure mathematics: Clifford and Lie algebras, etc. Cryptography of course being another adopter because of number theory.
It’s all good and each has its brain-warping aspects: physics demands we attempt to interpret the math’s implications on the nature and behavior of reality in particular. Beyond recognizing where one’s personal strengths lie, it makes no sense to pick sides about which is “better” or “harder”.
Great review!
Hi, I'm an engineer with a decent BS in Applied Mathematics. I want to teach myself Classical Mechanics. Somehow, I didn't learn either Lagranian or Hamiltonian Mechanics. If I did, it was hidden under the cover of the class. Can you recommend a textbook? Thank you, Baruch
Mat
what do you think is better for training your brain to be better at general problem solving and understanding for any other kind of field? physics or math?
hi, this is a off topic question but why is it important to be able to represent a number as a rational number, And is there any pratical applications of it?
Sir I am 18 year old computer science guy who has no bg in maths as go futher I realised that I lack problem solving skills and that is also because I dont know maths at advance level and one more thing I can do maths but it just mindless remembering of maths tables and formulas, can you recommend me where should I get started
My issue with physics is that every single physics model looks like some kind of crude stick-figure approximation of what's actually happening in an extremely complex natural world. I could never wrap my mind around the 'cut-off point" for this simplification process ... it seems purely subjective and physical science should not be an exercise in subjectivity. It is supposed to be objective. This is still a huge frustration. I really don't like it.
I am sure you can make an introductory course on Newtonian mechanics.
Which one is harder? I guess there a more derailed maths guys while physics guys are still on track. Women don’t take neither except some, and those don’t go full theoretically the respective fields.
this topic reminds me of Albert Einstein who is one of the greatest physicists of all time but mathematician not even close
I study physics but it’s disappointing the lack of mathematical rigor. Physics is absolutely nothing without mathematics, but there’s plenty of mathematics without physics.
If you're worried about mathematical rigour you may prefer studying... mathematics :).
Mathematics is a tremendously important tool in physics but it's not _everything_ - the universe is the sine qua non of physics, so long as you have that and the capacity to examine it you can do physics (a _much_ less powerful, cohesive version compared to the one we've known for the last 400 ish years but still, physics).
(i'm leaving aside the "it from bit"/"mathematics is the foundation of everything" philosophical position which _could_ be true but is currently _highly_ contestable)
I always wonder what people mean when they mention mathematical rigor. Is it the proofs, which I absolutely hate. I just visualize the mathematics and can see the truth in them.
@@michaelpieters1844 Yes, mathematical rigor implies proofs, which are absolutely important and necessary for the development of mathematics. No truths would be uncovered in mathematics if it weren't for the truths
Unfortunately I find the Feynman lectures very outdated. They are taught considering a 1960's (1970's?) audience...I personally don't like his methodology. I suggest you look at the Walter Lewin lectures, they are beyond amazing! Unfortunately, he had to exit MIT because of a sexual misconduct allegation and his lectures were, officially, taken down. You can still find copies around though.
sir I want to ask you a question
Physics is like a "great story", and the words in that makeup that "story" are mathematics.
passed the smell check
Whichever you major in you should also major in philosophy
physics is nothing without mathematics
that is not true.
i have seen very good physics books written without any maths
Actually maths is a language , physics is the subject
They both are different things.
This is such a nonsense debate..
Know math, know physics,
no math, no physics
@@tmann986 nonsense. there are lots of people who know maths but know nothing about physics, and vice versa
@@einstein6285 Agreed. It's the equivalent of "PC vs Mac". No serious person cares about (or even believes in) some made-up "mathematics vs physics" competition. Just pick whichever you like best and study that, both are interesting, valuable fields.
(does anyone "brag" that "without French there'd be no French literature" or make spurious claims like "if you know French you know French literature" ??)
Ooof doing physics without knowing the basic math is tough
Good evening everyone, I have a very simple question, what is Fortex Mathematics. Have you heard about him?
Physics cannot exist without mathematics
~Henri Poincaré
Wow
are you Issac Newton :D ?
Is really funny when you pick a book and smell it out of nothing and say: "yeah". You're literately a book addict.
I preferred Chemistry except my experiments blew up mod of the time! 😆.
Physics is more esoteric and abstract than math in physics 1-3.
To me, Physics is harder.
“If I were again beginning my studies, I would follow the advice of Plato and start with mathematics.” - Galileo Galilei
This quote resonates with me, as I wish to get my PhD in a field of theoretical physics - however I found that having a solid foundation in math is essential. It is because of this realization that I switched my undergraduate major to Math from Physics.
Sure, likely true for theoretical physics (which is more abstract) and its resonance for yourself is what matters. Not so true for e.g. astrophysics though IMO (where obviously there's still plenty of mathematics, it's just more about methods than deep structural stuff).
Worth remembering that Galileo wrote that at a time when even the most learned "natural philosopher" _maybe_ had modern first year undergrad algebra - as arguably the first "mathematical physicist" it's natural he'd wish he had more. Nowadays any bright high schooler knows basically all the mathematics Galileo did _plus_ calculus and any graduate from a standard "physics major" degree has a _vastly_ bigger mathematical toolbox.
In other words "thinking like a physicist" today would look _much_ closer to "thinking like a mathematician" in Galileo's day (so maybe _now_ he'd instead say "I'd concentrate more on physical intuition [given I already have today's undergrad physics level mathematics]").
@@anonymes2884 I agree. Given the scope of applied physics (i.e. nuclear, astro, etc.) where numerous assumptions can be made without proof, having a strong mathematical background is widely overkill. However, like you said, in the countless fields of theoretical physics where absolutely everything must be proven, the case is different and being fluent in higher mathematics is a godsend.
@@TheEmeraldKidRE Where numerous assumptions can be made without proof? If the experiment disproves your idea, it is not physics. You do know that physics is a science and nature is being observed through experiments first?
@@michaelpieters1844 Evidently you haven't a clue of what you're talking about. You can't say that making a hypothesis which turns out to be false via experimentation "isn't physics."
Physics is the process of formulating and testing hypotheses -- it's not just the amalgamation of experimentally proven theories. The very fact that you think this immediately shows you have no scientific background whatsoever; and if you do, it's extremely poor and misguided.
Quantum mechanics and Einstein's relativity are the pillars of theoretical physics -- the theories of which were devised without prior experimentation/observation. It was only AFTER these theories were mathematically proven that experiments were conducted, ultimately proving the theories correct.
You seriously need to read a few books on the history and derivations of modern physics before claiming to know anything about it.
@@TheEmeraldKidRE I actually got 3 masters and the best way to do physics is to observe nature and then create a model to best describe nature. The way it was done in the 20th century was indeed the other way around (also the reason why high energy physics is in such a disarray) but that is not how you normally do science the way giants did it like Newton, Gauss, Weber, Maxwell.
Math is only math while physics is both
And without math physics is nothing..but without physics math is still there... btw I am a physics enthusiast and I know very little because of having less knowledge of math's..
@@Anuranjana5656 also physics without math is pure physics the contemplation process and curiosity to observe the universe around plus whole mathematics except number theory is based on physics. The holy grail of math is calculus which is based on the physical world.
@@yhistory2688 Calculus is _not_ "the holy grail of math" and mathematics is _not_ "based on physics". Mathematics is clearly more fundamental than physics (where by "physics" I mean the area of study rather than the actual workings of the universe).
I say that BTW as someone that studies physics and utterly rejects the idea that "without math physics is nothing" (i.e. i'm not biased towards mathematics, if anything i'm biased towards physics). "[W]ithout math" physics is a much less powerful, less coherent, less predictive version of its modern self BUT physics is "just" the systematic study of the fundamental workings of the universe - you can do that without using the tool of mathematics (not nearly as well but you can still do it).
@@anonymes2884 first I meant calculus was the holy grail obviously now we pretty much understand it but math is discovered not invented okay. So it is based on the universe around thus it’s natural and that’s physics, till you invent math then we will admet it is something else.
Normally I'd settle for used older editions of famous books, but I've read that there are lots of errors in the older editions of the Feynman Lecture books.
I still remember my first lesson of Reactor analysis and design (nuclear engineering) during which the prof. said "in Russia we don't make any difference between math and physics" while filling up the boards with integro-differential equations. God I loved that course...