Is Physics Harder Than Math?

[@dopplerdog6817]

I think it's a meaningless question. There are arbitrarily difficult problems in both fields. It's just a question for inexperienced folks to "flex" over which of their preferred fields makes them smarter than others, but ultimately it's a pointless question. What is the standard metric for difficulty anyway, and how would you measure it?

[@odysseas573]

I think by averages. Meaning: what does the average person find harder. To my experience more people find math harder but that is just empirical evidence. In my university more people struggle with Electromagnetism than they do with Calculus, Linear Algebra or Differential Equations.

[@lambda5949]

​@@odysseas573 I'm doing a double major in both (hoping to go into VERY theoretical physics) and I'd say rn the physics classes are overall more approachable-of course, the professor tends to be the real decider for most classes. At least at undergrad level, physics basically comes down to visualizing and modeling very complicated situations with familiar techniques, whereas proof-based pure math classes require you to think abstractly and in unfamiliar ways from the jump. At the grad studies and career level, though, I imagine cutting-edge work in both is equally challenging.

[@7fall]

It would be measured based on progress. We all want better, nicer, cheaper things and better quality of life. Over time, we can see roughly how difficult life was for i.e pioneers vs Medieval peoples and what technology/knowledge they had at their disposal. It’s quite easy to tell how difficult something is, so long as you aren’t speaking of dozens of steps ahead, say in 2150 AD. We can tell present performance by measuring past performance with the lens of the times the people found themselves in.

[@MasoudJohnAzizi]

Well.. it is meaningful for egoic mathematicians seeking to "feel superior" to someone or something to compensate for unresolved past emotional traumas that left them "feeling belittled". Psychology is interesting..

[@MrHaggyy]

In computer science, you can approach intelligence and difficulty from a computational standpoint. How many details or information does your problem contain, and how complex is the relationship between them. In math, you usually have view elements to deal with, but the complexity is vast and remains unknown until you get a grasp of it. In physics, the amount of details gets bigger, but the complexity gets lower as more and more possibilities can be excluded the more and more you understand the subject. Engineering is a huge amount of detail with the least amount of complexity to get the job done. But this approach is also difficult as math and physics always find a way to ad a view infinitely hard into the equation and details or information are also a mess to measure, especially once you leave digital computation.

[@youshaahmed5999]

Being a double major in maths and physics i will definitely say maths gave me the hardest time especially real analysis

[@_454_]

Woah, interesting. Good luck with that man

[@benwhite2226]

@@youshaahmed5999 same as my experience, except I found abstract algebra to be even harder than real analysis. Advanced QM was just a regular hard class compared to those!

[@abi3751]

Maybe because we all compare these two field's on the basis of mathematical difficulty in which case mathematics is hard but physics is not mathematics alone and that brings the point.

[@omicronl2172]

I am beginning my Double Major in maths and Physics in one Month :D (srry for my english)

[@jedediahjehoshaphat]

As a Physics Bachelor who transitioned to a Master's in Mathematics, I'll definitely say in term of pure rigour and abstractions, Math might be harder than Physics, in fact sometimes it seems that pure math has a lot more connections to philosophy than any natural sciences like physics, esp in the scope of Algebra. But aside from that Physics has better real world ( physical reality) problem solving, compared to math which is largely axiomatic based problem solving. So Physics probably has better uses in real life, and better employable skills altogether.

[@GabriTell]

Mathematicians are not even supposed to be dedicated to real world problem solving. A physicist or an engineer may give a solution to a one particular problem faster than a mathematician would. Mathematicians, instead, because of the abstract and rigorous "training" we've been through, can take the problem (giving it a formal structure) and give a general and valid solution from a rigorous abstraction of the problem. Not to mention that all the tools that physics depends on (such as integrals and derivatives) and the fact that we can trust all of their cool properties is only possible thanks to the mathematicians who "programmed" them. Apart from all this, mathematics is an art in itself and not all in it need to have an immediate application.

[@rahulsubramanian6545]

I'm learning Derivatives using Larson Calculus now. I'll learn physics using Giancoli. Both the books are your suggestions.

[@TheMathSorcerer]

awesome!

[@rahulsubramanian6545]

​@@TheMathSorcererI'm actually relearning Calculus after a decade and I'm from a non-STEM background. Your videos actually gave me most of the information that I needed for the right set of books.

[@RONIIAL]

math sorcerer? more like chad thundermath

[@danielfromca]

I personally like Randall Knight physics a bit better than Giancoli. Knight is bit better for self learning in my view.

[@georgemichelakis1202]

@@RONIIAL 😂😂😂

[@sorwerk]

We need a Physics Sorcerer for sure, I don't know of any physics equivalent of this channel

[@Lolleka]

Angela Collier is the one that gets the closest to these vibes. In my opinion.

[@MortalH]

I’ll become the physics sorcerer 😎😎😎

[@corochena]

The Action Lab, SmarterEveryDay, Physics Girl, Up and Atom, Kathy Loves Physics & History are all great channels

[@homamthewise6941]

Bro I did had the same idea just days ago 😅 funny that ,we need one really

[@Gk54493]

It used to be Andrew Dotson or Tibees

[@PanicInSectorFive]

Everything on the cutting edge fringes is equally as hard.

[@7fall]

That assumes all growth in all fields are the same, and have the same support. What if something is easy, at the fringe, and nobody wants to do it? That doesn’t make the difficulty the same for all. It’s simply the low hanging fruit of trees we deem worthy, all being plucked at different rates and this changes over time. These things then feed onto each other, as one field discovers a relevancy in another. Definitely not true that they are all the same difficulty…

[@grugra]

From my perspective math is the hardest of all. I took classes in physics, chemistry, a lot of econ, a lot of statistics and a lot of pure math. In all above mentioned with the exception of math, I was able to always have an intuition about how I should approach an exercise as all of it corresponds directly to stuff in reality. So I never had a physics/chemistry/econ exercise where I was completely clueless about how to solve it, I was always able to at least partly solce it. In comparison, in math, there were hundreds of exercises where Isimply did not know how to atart as I had never seen or learned the proof technique that was necessary. So my conclusion is, that for me, math is by far the hardest of the above mentioned subjects.

[@vrcfncpdci]

Let us learn both, math as the tool and phisics as the goal

[@vegasoverheaven]

I have somewhat of a dilemma that I’d appreciate you weighing in, since you sound like you have a lot of exposure to some of the fields/math I’m interested in: I’ve never thought of statistics as being a separate field rather than under the math umbrella, mainly because I did a stats module for my math A-Level and didn’t really think of it as anything further (only recently did I learn it’s more *applied* math, in the same vein as mechanics.) I enjoyed stats a lot more than the pure math modules I did and am considering switching my major from econ to stats (double majoring is unfortunately not an option for me due to specific circumstances.) But I just don’t know *enough* about statistics to know for certain if I’ll truly enjoy it enough to major in it because my high school stats classes were pretty basic stuff. I’m interested in it from a layman’s perspective if that makes sense - I’ve been told it’s mainly working with and interpreting data for various purposes, and while I like the sound of that, I obviously have no idea what it’s like to be actually doing it. Any suggestions or perspectives you have on this would be appreciated :)

[@vrcfncpdci]

@@vegasoverheaven give a look to theory of probability by B.V.Gnedenko MIR editor 1979 URSS

[@user-qn8vg2zk2j]

I always watch you’re videos and listen to you’re wise words, truly you are my role model in life

[@Nebulous0_o]

I achieved a grade B in British ‘A level’ mathematics (US equivalent is an AP), so at least back then as an 18 year old I had decent math ability (Lol). My father was an engineer in the RAF who also taught physics at a community college in his spare time simply because he found it rewarding to do so. He achieved degree level qualifications in physics, but to my knowledge had no formal education in mathematics anywhere near that level. Despite this, he was at least as good at math as I was, and would often help me with my homework whenever I got into a jam (possibly indicating his superior intrinsic intelligence). I know only fundamental GCSE physics, and I consider myself a physics dunce. Based on this experience, and perhaps I’m taking a limited and parochial view of things, those with an advanced knowledge of physics have a greater knowledge and understanding of mathematics compared to those with only advanced math knowledge have about physics. My conclusion: Solid math skills are required for physics, while knowledge of physics is not required for math.

[@benwhite2226]

I have majors in math and physics and I find the hardest math way harder. But I think that mostly comes from my lack of practice with proofs and the way you need to know every definition and relationship. With physics I can understand a handful of methods and what they're doing to solve a problem and use them on other problems, but math doesn't work the same way. I also found Quantum mechanics to make more sense to me than abstract algebra and everything else in physics makes more sense than QM. Now I also have had much better physics professors than math professors so maybe this is where this comes from too. I think it's mostly a unique experience on which is harder

[@husnainhyder6713]

Physics along with a mathematics Is a one powerful tool by which one can create.

[@dis1ncentivVe]

theoretical physics

[@wickz7119]

I double majored in physics and math and I’m currently doing a PhD in theoretical and mathematical physics. Having taken things like qft, gr, algebraic topology, differential geometry, representation theory, k-theory, algebraic geometry, etc, I have to say math is harder. The level of abstraction and rigor requires a very specific and very advanced skill set. On the other hand, theoretical physics is hard and you have to know a great breath of info (physics, math, programming, etc), but there are many ways to still do research (pencil/paper, simulation, phenomenology, etc). I think this makes making headway in research a bit easier because you can approach problems in many ways, with a range of totally different tools.

[@DavidAKZ]

That is my feeling coming from a physics background. In a lot of physics, you can work things out from 1st principles, units etc.

[@AnakinSkywalker-zq6lm]

That’s awesome

[@uberupense2223]

@wickz7119 As a 1st year Physics undergrad - 2nd year starts in September - I’ve come to be interested in diff geometry and those kind of things you mention from my novel standpoint (obviously this topics are way out of reach for me by now but I’d like to get into GR and all that stuff some day), and it so happens that my university just lacks those “math-related” courses throughout my Physics undergrad program. So seeing your background how would you recommend me to start approaching this topics? I’ve just gone on to become really interested on Math and the theoretical side, as 1st years Physics courses were garbage. Thank you in advance

[@DavidAKZ]

@@uberupense2223 why not email Ed Witten at the Princeton IAS ? I did asking him a question about the Langlands program and he replied in about 5 mins !

[@causalitymastered]

What makes physics hard is the math. If you master the math BEFORE taking physics or chemistry, its gravy. Math is a language that you have to acquire with practice until it becomes an automatic reflex. It's not something you memorize. This is what both teachers and students don't understand and accept.

[@ej2953]

Well said.

[@Mahmood42978]

That's not necessarily true; physics is bridging a conceptual understanding of how to extract information about a physical system and reframe it in terms of equations. In mathematics, you focus on the abstraction in terms of the structure of mathematical objects as a whole. They may be cognate and complement each other, but it's not always as natural a transference of skills as you may think. I definitely know mathematicians that don't thrive in physics, I'm sure there are physicists that aren't apt on the more abstract areas of mathematics.

[@causalitymastered]

@@Mahmood42978 Still, math is the main obstacle people face while learning physics.

[@Mahmood42978]

@causalitymastered maybe as a whole, but it's not a natural continuum once you get "the math," even how the math is approached can many times be starkly different.

[@causalitymastered]

@@Mahmood42978 True. But the students will benefit greatly if the curriculum focuses on the math first, so, they will be better prepared for physics. Students ask the Math Sorcerer for advice often.

[@astronazli]

I just started studying physics and I thought I needed to hear this video.

[@theoneaboveaall]

I love both the subjects very much, it helps us in understanding the universe. And i love that. To quote richard feynman the truth is so remarkable , so amazing.

[@averege_math-and-physics-major]

im a physics and math major and i think physics is harder by a little beacuse you still learn math and you learned the physical thinking of physics so you need to learn 2 things at the same time so physics is harder

[@Wndnb]

Plus chemistry if you're interested in going into astrophysics/biophysics

[@averege_math-and-physics-major]

@@Wndnb im majoring in general relativity in physics and topology and diffrential geometry in math, so about chemistry i don't know nothing about it

[@LivingBreathingRedFlag]

I have studied math for the past two years or so and am now switching over to mechanical engineering because I'm interested in real world applicability and broadened job opportunities, therefore also broadened monetary opportunities. I would personally say that what makes college math easy and also hard is that it's a choose-your-own-adventure. Undergraduate math is very easy if you spend your highschool years deepening your understanding in your free time and invest some effort into learning the most central material pertaining to it like linear algebra, the various varieties of analysis, basics of mathematical programming, general computer science, probability theory, set theory and logic for proofs, etc.. Undergraduate math though can also be very hard if you go in with only an apt understanding of highschool material and go for courses known to be hard such as number theory, topology, dynamical systems theory, most of discrete math, and so on. Physics on the other hand expects you to grasp some very advanced concepts that are hard for most mathematicians. Undergraduates nowadays are expected to develop a grasp of QFT, statistical mechanics, electrodynamics, and the like. It may not be as hard as what could be considered hard math, but it is definitely harder than the easier undergraduate routes of mathematics, especially since some of the subjects in physics can not be easily self-studied and require a nuanced understanding since both the physical world and abstract worlds are intertwined, it's a marriage of standard scientific method and mathematical modes of logical exposition. Striking a balance between the two latter mentioned cornerstones of physics is very difficult for most people's intuitions, at least if that intuition is not fostered early on in one's education.

[@alexgoldhaber1786]

It depends. As a physicist I know a lot of maths too but I don't necessarily follow each proof rigorously.

[@メガネ男-c1w]

IMO it really depends on the topic but overall they are pretty equal. Jackson's electrodynamics book was just as difficult as Rudin's Functional Analysis book for me.

[@douglasstrother6584]

JACKSON!! I still have, and use, my well-worn, dark, red, (like dried blood) covered 2nd Edition.

[@abhay_cs]

This is the same as a proper course on partial differential equations. So basically it’s a math course

[@douglasstrother6584]

"Modern Electrodynamics" by Andrew Zangwill It's on the level of Jackson without the sharp edges. The selection of examples and problems are very physics-oriented.

[@メガネ男-c1w]

@abhay_cs maybe an applied PDE course. I don't remember proving any existence and uniqueness theorems in that course.

[@2000watts2]

In physics, one need to be able to visually grasp the concepts and fit the proper formula concepts to the subject. In math, you need to be able to use and manipulate abstract certain formal formulas that fits to the problem. I believe, physics demands more imagination which makes it harder at some aspects.

[@hasanozyer6757]

Everytime i see your face you remind me of sid from ice age lol. No hate i love you vids man. It's just so fun to see very genious and smart sid sitting in front of me and explaining things.

[@justin9571]

Fr I thought of sid also in a respectful way of course

[@stefan24georgiev]

He looks like Jeff Bezos

[@johnsnow94]

In college I have a friend who STRUGGLED in math but physics classes he did so well, I was the other way around, physics based courses I struggled but the math courses I enjoyed and found them easy. We always scheduled our physics and math classes together so I could help him in math and he would help me in physics. This is subjective, depends on the individual, his interest and motivation towards that subject, and previous experiences and attitudes towards them too. The more you spend time in either, the easier it gets though.

[@lwmarti]

Having done both for a living, the big difference was that I often had to think long and hard about exactly what things (definitions, theorems, etc) meant in math (algebraic geometry) but NEVER had to do that for physics (solid state/superconductivity).

[@jacobharris5894]

Mathematics has more rigor and is more abstract. But physics is an attempt at modeling some really complicated stuff and requires both experiment and theory. Mathematicians can make up their own theory but physics requires concepts to be grounded in reality. Physics is less precise than math but there is an art to finding good enough approximations, analyzing data and testing theory in the lab. So it’s hard to say. I think for me physics is easier, at least the theoretical side of it, but it depends on the person. I think if you were required to be adept in both theoretical and experimental physics, physics would be harder. But most people primarily do either theory or experiment.

[@rusi6219]

Physics is just applied math just like engineering. Btw if you want to learn useful physics just study electrical engineering. Physics major is really not worth it.

[@psychologienerd7546]

@@rusi6219 engineering is making physics work. so it is applied physics. while physics is not just applied math, its everything concerning reality.

[@rusi6219]

@@psychologienerd7546 haha "everything concerning reality" that's an amazing joke LMAO go read another bogus string theory article kid

[@psychologienerd7546]

@@rusi6219 easy solution for you: string theory = esoteric mathematics.

[@abhay_cs]

Except rare cases like Fermi

[@bottlecap6169]

Growing up I feel like I didn't have much interaction with the "real" world or much curiosity in it. Generally, I spent more time inside my head than outside it. I think this lead me to have a greater intuition for abstract things but less of an intuition for concrete things; as such, I find math and philosophy much more intuitive and easy to understand, even when it's difficult, than any more concrete subjects like physics, chemistry, etc. I feel more comfortable in a world of formal abstraction, definitions, theorems, etc. than I do in a world of messy physical objects or phenomena. Much of math and physics is about pattern matching (especially lower level courses) and, even then, I feel like my pattern matching abilities within math are way, way stronger than within physics for some reason. I expect that a lot of people find math more difficult than physics because they're the opposite, with more concrete things to draw intuition from and attach associations to. I felt very stupid in Physics 1 and 2 because every time my professor would mention some example of a real-life solenoid, all the engineering majors would immediately understand and I would have 0 clue what they were talking about or how it related, lol.

[@kummer45]

Math is always a challenge. University courses teaches you 2% of the material in each discipline. The practitioner must do the rest of the work. Physics is equally hard. The practitioner needs books, solved problem books, solution manuals, books about proofs and redaction books for presentation proofs and communication. A math student is always in constant education and with pencil and paper at hand all the time.

[@peterbenoit5886]

I was a double major in mathematics and physics as an undergrad, earning departmental honors in both. I know it seems like a bit of a cop out, but I think it's a moot point: the one you feel is "harder" is really the one that stressed you out more. I found quantum mechanics puzzling, but not hard because of the mathematics therein; instead, it was the deep conceptual problems connected with the "measurement problem" and "entanglement." On the other hand, I found nothing particularly challenging in my undergrad mathematics degree. I graduated with a 4.00 GPA and went directly into a PhD mathematics program. All nearly half a century ago. I wouldn't shy away from either. Rather, I think that for us intrepid should, we pursue these things because they ARE hard. They are a path to self-actualization.

[@professorjogatina]

I have a degree in both, in physics I did better in the mathematics subjects, then when I took mathematics in general I did well. For me, physics caused more confusion, several concepts were difficult to understand, such as entropy. Mathematics for me was more structured, the undergraduate level required less intuition for me than physics, apart from the fact that physics had an experimental part and the experiments didn't always work out. Electromagnetism at the level of Jackson`s book, I think it's more difficult than real analysis. I never got a 10 in any physics course I took, but in mathematics some managed to get 10. I always did better proving things and mathematics gave me the impression of things being more step by step, while physics was more flying. Mathematics is not a tool.

[@jerryeldridge1690]

I think subjects are as difficult as their foundational structure. Philosophy, Mathematics, Computer Science, Physics, Chemistry, Biology, Neuroscience,Linguistics, Language, History, and Politics in that order. So to me, Computer Science is more difficult than Mathematics which as not as difficult as Physics. Chemistry builds on Physics with Quantum Mechanics and Electricity and Magnetism but is yet a different subject. Biology builds upon Chemistry with Organic Chemistry. Biology builds upon Organic Chemistry and Neuroscience upon Biology. Neuroscience explains Linguistics in part, and that builds up Language and Literature and then History and Politics.

[@p0indexter624]

when you get into quantum mechanics and general relativity, someone with a strong math background like yourself would certainly meet the challenge. i would be interested in your views on a few items; - Maxwell's Demon - emergence of life as an example of complexity suddenly appearing 13.7 billion years AFTER the big bang and the implied thermodynamic paradox. - is information conserved as is energy ? - is the second law of thermodynamics an axiom ? - fine tuning as related to cosmology

[@erin-rt6vn]

just graduated with a joint masters in mathematics and physics (50-50) - they are quite different, i think because physics relates to the real world, a lot of the difficulty comes from trying to intuitively understand and conceptualise what is going on, and the actually doing the maths is easier once the techniques have already been established. for example general relativity and quantum field theory i found both really hard to grasp conceptually, but in terms of calculating christoffel symbols or feynman diagrams the maths isn't that hard at all, but that's not where the complexity lies. in contrast, mathematics is always obviously going to be harder mathematically, but generally in pure maths the emphasis isn't on getting results that have to explain anything or need to be understood conceptually, and i think this means maths often feels more like you know what you're getting. in terms of working at the forefront developing new ideas that haven't been done before it very much depends on what you're doing and you can't really compare them.

[@Morris_012]

Sometimes, even a little bit of math can feel like a full-time job, but physics? That's like a full-time job plus overtime. Math might be considered a more delicate task, but when it comes to physics, you literally have to roll up your sleeves

[@KaurSingh-bo6gq]

Absolutely correct

[@childrenofkoris]

true, you need more advance thinking ability to be good at physics.. a lot of theoritical thinking and correlations

[@navid7522]

Not sure if this answers your question but I've recently started learning physics by myself using your suggested book (Halliday) and so far it's been quite straightforward and fun but I'm definitely nowhere to speak from experience whether one is more challenging than the other. However, your videos always help me with both.

[@martingemsa8198]

I would say it really depends on what kind of level you are studying, like for normal folk going through high school and lets say math analysis and linear algebra to finish economics, management or alike degrees, physics seems way harder because it goes through all that plus the physics knowledge but at the very high end of professors of math or physics I would say it is equally hard because then its not really much about time pressure of learning alot of knowledge but more about trying to apply it or get something out of your existing knowledge

[@johnjackson1270]

Man, do I love math (obviously since I am following your channel), but I have to agree with you...I think physics is harder. One example that comes to mind...Ed Witten. We're talking about a theoretical physicist who won the Fields Medal!! The difficulty of the stuff those guys are working on blows my mind.

[@odysseas573]

Max Born won the Nobel prize in physics in 1954 and he was a mathematician! I think at the highest possible level physics and math have a lot in common.

[@QuantumPhyZ]

@@odysseas573 You don't need to go that far back, Roger Penrose is a mathematician and won the Nobel prize not so much long ago.

[@YTcommentz]

I took an intro math and physics class right when i started college and the physics was impossibly hard for me. The math class felt like it clicked for me but no matter how hard I tried I couldn't grasp the physics concepts. I ended up dropping the class. A large part could've been the professor, but I think a bigger part was some fundamental gaps. Even though this was an intro class, I think I was missing some key basics I should've picked up pre-college. I sometimes think of revisiting physics, but I think my interests will probably end up prioritozing other subjects 🙂

[@Focalope]

I feel like physics becomes more like mathematics when dealing with higher dimensional space, where space in 4 dimensions is a tesseract, and using high dimension vectors (tensor) could explain those in an abstract way. I don't fully understand it but they seem similar to me in a speculative kind of way.

[@saltysnake3774]

I'm a student geophysicist. Personally I think math is a lot more difficult, but that's also coming from a point of view similar to yours (in the sense that a lot of people just know more/different things than me). Pretty much all of the math I use is well established with probably thousands of resources (books, videos, etc...) on not only the concepts, but also applying them in various different circumstances. In a lot of cases, just by plugging in values I can see how/what a formula is actually doing. The concepts are difficult to understand, but the big part here (for me anyway) is I'm not the one who actually figured them out. I'm quite certain I would've never figured out even the most mathematically basic formula I've used. Granted, I'm just a student in one branch of physics. It's probably totally different in another branch.

[@johnpapiewski8232]

I had a math ABD as a study buddy when we both took Physics. I helped him with practical lab stuff and he helped me with the tensors and Hermetians and whatnot.

[@Drganguli]

Developing math models of physical problems is the hard part. So I would say engineering is harder than physics or math. But physics is harder than math as in math you have to deal with disembodied problems which only need a solution. In most cases you can get a numerical solution anyway as closed form solutions are hard to get for most realistic problems involving complex geometries, loadings or boundary conditions.

[@osaomoigui8661]

Hello Sir what are your top 5 picks for math books that cover the majority of the applied maths

[@callummilburn8204]

I did a physics degree ( 30 years ago ) and currently doing a maths degree ,part time. One has to work now.. They can both be very challenging fields to study. I think I if you do either you will be able to have a reasonable attempt at the other. To some degree. If one is harder than the other then comes down to personal preferences, motivations and skills sets you already have.

[@ej2953]

Physics is often harder for students for the simple reason that they often don't know the math they need and so they have to learn the math and the physics together. If you have already had all the math you need for the course and can concentrate on the physics, then you are way ahead. For example, while it wasn't on my degree plan, I had some free time and so I signed up for the Physics courses in Classical Mechanics. All the math required for the course was pretty much ingrained by that point. That made the rest very easy. On the first test, the maximum score with bonus points was, I think, 125. I made a 118, but the average grade on that test was about 55 to 60. There was one thing in the class that was amazing. At one point in a lecture, the prof had an equation with a sin(2x). I don't guess that he knew the formula "sin(2x)=2sin(x)cos(x)". Instead, he expanded sin(2x) into an infinite series. tossed out all but the first three or so terms as being too small to worry about, played around to get them as the product of two and the first three terms of the series for sin(x) times the first three terms of the series for cos(x), waved his hands,, and got 2sin(x)cos(x). I was trying very hard to be respectful and not burst out laughing. It is far easier to use sin(2x)=(e^2ix)-e^-2ix)/2i =(e^ix-e^-ix)(e^ix+e^-ix)/2i =2*((e^ix-e^-ix)/2i)*((e^ix+e^-ix)/2) = 2sin(x)cos(x).

[@imPyroHD]

I think it just depends on the person. Here in France, when you want to go engineering, your first two years post highschool are basically just pure maths and physics (12+ hours a week of each) and some other stuff like comp sci, philosophy (dont ask why) etc, so you really get to have a taste of both worlds. From my experience, some people just seem more naturally inclined to maths while others just seem to have an easier time with physics, so i wouldnt say one is harder than the other, its just a matter of personal preferences.

[@JeffKwak221]

It really depends. this question is way too subjective for it to have an "answer" that isn't personal. so its up to you

[@MasoudJohnAzizi]

Perhaps there is no difference between math and physics, for the latter cannot exist without the former, and the former cannot exist without the latter... "All knowledge is one, its division into subjects is a concession to human weakness." -Halford Mackinder.

[@gadlicht4627]

It depends fully on your own brain and how much you are trying.pushing yourself. Math can be easy as just saying 1+1=2, and thats it or can be one of hardest thing. Physics can be as simple as gravity pulls things down or super complex.

[@nathanmspottswood]

Im a molecular bilogy major. Taking extra math classes beyond calc-1, and taking some extra physics classes beyond the general sequence. In my experience math is harder, but thats just how my brain works. And this is on only the undergraduate level, so still dont have tons of experience.

[@snapman218]

Physics is just one possible subset of all possible multi verses. Mathematics applies to all the multi verses, mathematics is obviously harder.

[@BlackbodyEconomics]

I think they're both equally difficult - but in different ways. One seeks to understand the relationships and dynamics of the world around us - while the other seeks to understand the relationships and dynamics of the world of logic. Both use the same language to describe each world - and ultimately (some might say) the world around us is sort of an extrapolation from the realm of logic. It might be more akin to the difference between studying the brain and biological neural networks and then studying biochemistry and cellular life. They're so similar that they touch in many ways - but the perspectives are a little different and they both ultimately describe the same thing. I think they're about hand-in-hand in difficulty - at least from my perspective.

[@motherboardbroken2305]

Physics seems easier because it got context, pair it with the logics of mathematics - the synergy is there. math is just math and thats how math is done - i don't like that and it just a harder approach to something that could have been easier if it had a base - now just a freshmen so ofc i cant speak in depth nor with actual base to firmly put the argument but ye, the reason for chosing physics is that - oh and over computer scince, the thign i am told i know alot about - you can study physics but CS is something you jsut have to digest till you get it, and alot of rushing and skimming and stuff like, you just need to know this much but I often get distracted and read alot and lose time in the process.

[@himawarigirl1]

No estudio matemáticas pero me encanta escucharte para aprender inglés!

[@UnforsakenXII]

As a theoretical physicist. Eventually physics seems to be effectively mathematics (fight me : p) but the issue with alot of the mathematical structures that a subset of theoretical physicists use is that they're so far beyond what is currently understood as rigorous mathematics. You end up having to use a mix of intuition and rigor so if you were to ask me personally, the questions that I work on in physics are far harder than the questions that I work on in math because they utilize mathematics that will not be properly established for presumably another century or so. If you think otherwise, then I ask you to give me a rigorous mathematical formulation that works for the path integrals of a lorentzian field theory. We don't have any agreed upon notion of path integrals. They're all schematic.

[@corochena]

I teach both math and physics for college students and most of my students fear physics more than math, even when the physics level doesn't require calculus! Physics + Calculus is a killer combination. I have to mention that I live in an under developed country from Latin America and we have very low scores in high school math. I think the fact that you have to know a lot of terms in physics (momentum, impulse, acceleration, force, work, energy, pressure, flux, fields, charge, current, etc), physics laws, units of measurement, then you have to understand a question reading a problem, then you have to use math, charts, diagrams, vectors to solve the problem,... I think that is why most students fear physics more than math, ... well at least in this country.

[@davidcarter8269]

We arbitrarily dump a bunch of different attributes into this vague term called "problem solving ability". However, problem solving ability is a mix of many different things, such as: your tolerance for abstraction, your ability to analyze the components of a system, your ability ability to deduce one property from another, your ability to construct intuitions or visualizations for a problem. From my observations, physics folk tend to be better at breaking a system down into it's components and constructing useful intuitions. Conversely, I would say math folk on average have a higher tolerance for abstraction and greater bare bones deduction ability. So whichever one is harder, in my opinion, comes down to your individual problem solving profile.

[@OrdenJust]

It is one thing to ask which is the harder subject, in terms of problems yet-to-be solved. It is another thing to ask which is the harder to learn. In some ways, math seems more cumulative. Pick a random math article from a current issue of a journal, and do likewise with a current physics article. Which one is more likely to be at least vaguely comprehensible? Personally, the proof of a theorem in math is more likely to overwhelm my short-term working memory. There are too many definitions in math where something is "the this of this of the this of the this....of the that." My brain cannot hold so many levels of nested concepts at once.

[@writer2831]

It really depends on the individual and the context, basically subjective.

[@ruleaus7664]

It depends on an individual's current knowledge, experience, and interests. For example, if you try composing a symphony when you're severely lacking in any of those areas, you'll find it impossible.

[@19thfallenpoet]

Physics II is currently consuming my life. The math isn't terribly difficult but building the intuition for problem solving in physics is a different beast entirely.

[@RickGGb1]

The thing about physics is that it gets pretty much as hard as you want it to be. Working with nuclear physics is pretty different from, say, biophysics. Physics definitely has a 'minimum' difficulty, which I think is easier than pure maths, but it can get hard pretty quickly especially if you are into areas where both intuition and rigor are important like in mathematical physics...

[@jonw4308]

I always found Physics to be more difficult then math but I never took any math classes above Differential Equations. It is possible that certain areas of math -- more of the abstract math -- may be more difficult then Physics.

[@joeldoxtator9804]

Anything you don't enjoy will be hard. The better question is, what do you enjoy more?

[@DiaconescuAlexandru2024]

On the electronics side, 99% of problems I've had to solve (industrial power controllers, LED headlights,

[@surajv1986]

I believe that becoming the best in any field is hard as it requires a unique combination of passion, luck and hard work.

[@TheTrueElohim111]

One is not better than the other, what only matters is what you are more attracted towards / what interests you more

[@Helmutandmoshe]

It's not a meaningless question but there are exceptionally difficult aspects of both fields. I have studied both at research level. One thing mathematics has is a lot of different fields with a huge number of applications to science, economics, computer and data science... etc. The number of journals publishing fairly obvious "low hanging fruit" type mathematics is significant. If someone says they have published research in a math journal, I don't immediately think that it was a hugely difficult or significant piece of work. The entry level papers in journals of physics, especially theoretical and mathematical physics, is much less accessible. That being said, some of the great geniuses walking the earth are the greats of mathematics, sometimes cracking problems that seem to be nothing short of a miracle. AND physics absolutely depends on these deep mathematical insights. Both fields are filled with great unsolved problems, which by definition means they are harder than anyone on earth can currently crack. In that sense, they are equally difficult fields... with a lot of overlap in talent.

[@brianchoi4542]

I studied both and their emphases are slightly different. As you said, math requires a deep understanding of proofs and connections of concepts. Physics is about...in my opinion, somehow getting the right answer even with hand-wavy logic and assumptions.

[@thenightking7167]

Mathematics is a tool or language. Physics, a scientific process. But for the sake of discussion, if we take a look at College Board AP scores, a clear picture emerges: Significantly more students score a 5 on Calculus than they do on Physics ((1, 2, C: Mechanics, and C: Electricity & Magnetism).

[@MortalH]

There’s a field in physics called mathematical physics where you use the tools of mathematicians (proofs) in physics

[@theotoniomendes]

Most of comments go on the direction that compares theoretical physics x math. The point is IMHO that physics is essentially an experimental science BUT most of famous physicists are theoretical physics! It creates a BIAS in the general public perception of what physics actually is. In physics you cannot simply start from a set of axioms and derive reality. In fact, when a new problem appears to the community, a bunch of VERY REASONABLE theories come out. Moat important: All of these theories make sense from the mathematical perspective. Examples are the rise of relativity after years of the ether hypothesis (which did not survive to the Michelson Morley Experiment), and the black body radiation. It's just after the scrutiny of an experiment that things move on. See for example String Theory, which is beautiful from the mathematical perspective but without ANY chance of an experimental test in the upcoming decades. It makes string theory a luxury speculative theory IMHO than anything else.

[@morganasplund7929]

it depends on what levels of math and physics that gets compered => they are close.

[@kubetail12]

My lowest grades for my physics major courses were two A-minuses. I barely got departmental honors for my math major because I have a few Bs and a C in my proof-based math courses. Physics is much easier for me. But physics was still tough; I still had to study my butt off.

[@shootstars256]

Depends on the subject. I usually find physics harder than math, but some subjects in math - such as combinatorics - are harder than anything of physics which I have studied.

[@childrenofkoris]

i love math, but physics just makes it feel applicable in real life.. same goes like programming.. but between these two i prefer math compared to physics because to be good at physics u need a different set of skills compared to maths.. math is really straight forward if you know the suitable/correct way to solve a problem but in physics , there can be a problem inside a problem and it can go neverending.. until you put a limit to what you are looking for

[@zeronicel4455]

great question!

[@scottthornton4220]

It's a meaningless question as described before. I think that the answer is very dependent on the individual. As a physicist, I have very good intuition which helps me get an intuitive feel about a concep or a problem. As the field gets more abstract, my intuition helps me less and less. Math is more axiomatic ... writing proofs seems hard to me (because I've never done it).

[@tamasburik9971]

Physics is very interdisciplinary and can require you to learn as much math, programming, and/or engineering as a professional in either of those fields depending upon your work/concentration, beyond the strictly "physics" requirements. For that reason, I'd call it harder than just math.

[@marcosluz3354]

Well, I am a physicist by training with a minor in math. I have already seen world class mathematicians saying nonsense about physics, but I never saw a world class physicist saying very wrong things about math. This has nothing to do with the question which one is harder. Nonetheless tells us how nowadays a mathematician and a physicist are formed. Physicists tend to have many math courses, but the other way around often is not true.

[@yash32745]

For sure physics is amazing in itself but the fact is physics is nothing without maths and we can't even imagine the world withouth maths and "applied mathematics is known as physics".physics is based on Mathematics but maths is independent.

[@dylanrees2966]

I think the division between physics and maths is less significant than the division between differnt branches of mathmathics and physics to each other. For example Im doing a PhD in topological design applied to nuclear materal science. I can tell you that theoretical physics is a damn sight more conseptually challanging than nuclear physics. But theoretical physics is probaly close to pure matmetics while applied statistics is probably simiar in difficultiy to nuclear physics. With such broard disciplins its the sub specialty that determins dificulty

[@bestopinion9257]

Physics uses math. It doesn't need to prove theorems, just use them. Also, as physics evolved as a science, you have to get rid of intuition and common sense and just use math (and then of course, sustain all with experiments). For that reason physics can be at most as hard as math.

[@KaurSingh-bo6gq]

It depends on your situation but I enjoy doing physics and learning about math.

[@IntuitivelyCurious]

My view aligns quite closely with yours. If someone asks me "Is something hard?", my answer is dependent on what I already know. If I've been studying physics for years I will say math is harder and vice versa.

[@colinfjelsted6970]

I majored in physics and math in my undergraduate. I have to say math is harder, especially the upper level stuff. Physics classes may take more work, but the math concepts and some problems are simply much harder. That being said, you can’t really compare the two

[@LorenzoAvanzini]

I think that the question has not a well defined answer: it depends on the field you are studying. Moreover both math and physics are extremely hard, more or less they are hard the same. Nonetheless, when it comes to "college-studies" I think physics is a bit harder because you have to face off math, physics of course, computer science, statistics, chemistry, laboratories and so on. But I think that "in real life" math and physics are hard the same

[@NithishBsc]

My college physics students say maths is harder and maths students say physics is harder. But great mathematicians don't differentiate maths and physics.

[@ValidatingUsername]

Yes and no. PDEs basically solve problems geometrically for the axial component of the problem. Proofing that a PDE is a valid mathematical tool is pretty hairy.

[@rome8726]

As a undergrad physicist who also love math ( can't be prominent in both, i had to choose ) I consider math to be very, very, very hard. But the thing is, if you're smart enough you can be very successful as a mathematician without much resistance from the outside world since math is so much grounded in logical ideas and is only concerned with logical thoughts. If you're smart enough you can build the tools you need to write your proofs or come up with the concepts you imagine. In Physics, what's considered hard is almost or literally impossible for the time being because you need experiments to refute or acknowledge your ideas no matter how smart, beautiful or coherent it might be. Imagining and building experiment devices is not an easy task and it becomes harder and harder as we ask more fundamental questions. Look at our situation today, with the research for quantum gravity, dark matter and dark energy, superconductors, and many more... where we need experiments literally on the cosmic or quantum scale ! There sure is a certain logic or some intuitions behind it all, but it's still very hard to find the right postulates, figure out the maths that suit your ideas and derive conclusions that do not conflicts with all established ideas from your predecessors. I believe It's a common fear among all physicist that your idea, even if right, might outlive you. There's more i'd like to say about it, but this is only a comment on KZbin. In my opinion, Physics is harder nowadays because Maths, though harder than Physics when it comes to producing valid ideas, gives a certain freedom of thought to Mathematician, that we physicist (or at least I) are quite jealous of. There's a reason the greatest mathematician have pages long of achievements to their names while the greatest physicist only have a few lines.

[@carlobenedetti2407]

Mathematics and Physics require two different way of thinking, that's why it is so difficult to find someone who can master both of them. So for a person with a more Math oriented mind Physics would be more difficult and vice versa.

[@ej2953]

In grad school, I shared an office with a Math graduate student who had received his BS in Physics. He decided he needed to understand Math better and so he intended to receive his MS in Math and then go back to Physics for his PhD. So that first year, he took the Real Analysis course (two semesters) with Royden for the textbook and worked very hard at it and received an 'A' both semesters. (In the 1970s, you had to work hard for an 'A'). I always considered that to be the toughest two courses in the entire university. Then on Friday night after talking to the prof and learning that he made an 'A'', he got drunk. That night, he threw up in his sleep and choked to death. The world lost a very talented and hard working physicist that day.

[@farzamimran3960]

All the more reason why Edward Witten is so insane .

[@jyothikodali9778]

It’s a fascinating subject ❤

[@1eV]

I am a physics student so I don't know a lot about math, so I think math is harder. I think it is harder to deal with abstract concepts that physical ones.

[@douglasstrother6584]

Physics is more difficult because the first principles (Newton's Laws of Motion, for example) are counter-intuitive in many ways, especially rotational motion. From Classical Mechanics, Electrodynamics, Quantum Mechanics and Thermodynamics/Statistical Mechanics, one has to formulate well-posed problems based on physical principles which generally results in an intractable problem; the next hurdle to clear is formulating the intractible problem into a tractible problem + perturbations. Developing the "knack" for good approximations is non-trivial. The "AHA" moments consist of seeing more of the problem as tractible, and fewer terms as perturbations. Mathematics is easier because it is based on the more intuitive concepts of Arithmetic and Geometry, which are much more tangible and visual. Elementary Algebra, Trigonometry and Calculus built upon these ideas. Linear Algebra and Differential Equations continue to elaborate on new mathematical structure in a very applied theme. All of them are very computational that has "an answer" as the final result. Higher Mathematics (in whatever subfield) presents the logical structure as the problems now to be solved as the final result; the new tools are logical rather than computational. The "AHA" moments consist of formulating theorems which connect the concepts ("These two things should be related."), and *then* proving them.

[@一本のうんち]

your talking about applied maths, not pure. applied maths is what every engineer/cs and other stem majors learn. pure math and modern algebra is none of that 'computational' stuff you're talking about.

[@douglasstrother6584]

@@一本のうんち We all start as Applied Mathematicians.

[@AB-zv6dz]

Maths almost always makes sense and if you understand the pure logic, most things make sense because they are pure logic. On the other hand, physics is a physical science explained by maths and maths, obviously, is not a map of reality. So physics is often illogical and unexpected because physicists have had to hotwire maths to explain what is observed in reality. So I would say physics is harder, because its less intuitive. A really great mathematician probably doesn't struggle with any maths at all and could probably figure most stuff out just because they have a really deep grasp on mathematical logic. Physics on the other hand, theres often no logic except the existence of a physical phenomenon which isnt understood well if at all anyway.

[@jerryeldridge1690]

What is the hardest math topic? Topos theory? What is the hardest Physics topic? QFT?

[@elendor3428]

I'm starting my MSc next year and for me, physics is harder. I aced all my pure maths modules but struggled on some of the physics ones. My difficulty lay in taking a real world problem and transforming it into a maths problem.

[@Andrumen01]

Physics is no different than math, or any other discipline for that matter, in the sense that you train your brain to think in a certain way. I struggled with math and proofs and it's what deterred me from going into math. However I find computer science quite easy, even the mathematical component of it. Put me to argue like an attorney, I fail miserably; same goes for philosophy! So it's the way you train your brain.

[@abhinavshourya]

I once went through lot of gibberish physics book & I lost my interest and thought one proper handbook can give me information about lot of thing but now I need info on physics book to restore my interest like irodov book but that's too cryptic on simple concept I want something in middle

[@markborz7000]

As a physicist, I would say, yes, physics is the pinnacle of natural sciences. A physicist must know at least that much math as a mathematician. He/she has to deeply and thoroughly understand two disciplines, while mathematicians only one. In fact a good physicist also knows a lot of chemistry, engineering and programming. And even more, like philosophy, sociology, medicine, biology, genetics, ...

[@bigm383]

Both part of a continuum.

[@JohnConway-dg6lc]

Isn't the delineation between the two more a matter of degree than kind? I always considered Physics to be applied mathematics anyway.