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Theoretical physics and pure maths careers

  1. Apr 21, 2014 #1
    1. I am puzzled about which to be : theoretical physicist or pure mathematician !! what should i do ?

    2. If i decided to be a theoretical physicist : should i study some pure maths to make new theory in physics ?
    Like general relativity : the maths used on it was before it a pure maths that is useless .

    3. Is learning or reading the proofs of maths theorems useful for theoretical physicist ?

    Note : if i decided to be a theoretical physicist i would specialize in quantum gravity .
  2. jcsd
  3. Apr 22, 2014 #2


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    You seem to have a misunderstanding about the role of theoretical physics. There is theory in *every* branch of physics, not only cosmology/high energy/gravity, etc. In fact, your best shot at becoming an actual theorist is likely to go into condensed matter+related fields, which make up the vast majority of real-world physics.

    If you wonder if you should become a mathematician or a physicist, you should look into the kind of work which is done in the relevant fields. Except for some sub specialities, these have little in common. For example, in most parts of theoretical physics, a *strong* background in programming, numerical methods, differential equations and functional analysis is way more useful than an intricate knowledge of obscure group theory. Additionally, all individual sub-disciplines have established theoretical and numerical techniques which you have to know to make meaningful contributions to the field. So go, pick some leading journals in the fields you are interested in, and read articles. See what suits you more.

    I would also strongly recommend you against fixating on "quantum gravity" from the outset. Especially since you do not yet seem to be aware of what this actually is, and why one might or might not be interested in this. (For a start, despite what "pop-physics" would tell you, this is in fact a tiny sub-field of theory, which few people apart from other quantum gravity specialists care about.) And, in any case: before becoming a theoretical physicist, you first have to become a physicist. If you cannot get yourself to care about the inner workings of, say, a scanning electron microscope or particle accelerator, or the mechanisms behind plastic deformations of metals or cloud formation, this might not be the right field for you.
  4. Apr 22, 2014 #3
    I want to specialize in quantum gravity because i want to make the theory of everything thing

    Answer my 2 & 3 questions .

    How should i study maths as a theoretical physicist going to make the theory of everything ? And which branches of maths ?
  5. Apr 22, 2014 #4
    This is the most ridiculous thing I've read on this forum. If this is from a physicist then its truly sad.
  6. Apr 22, 2014 #5
    Its completely correct as any cursory look at a real physics department's research interests will tell you.
  7. Apr 22, 2014 #6
    Instead of attacking the poster and calling his post ridiculous, can you post a rebuttal instead? Simply calling something ridiculous doesn't exactly make your point.
  8. Apr 22, 2014 #7


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    This doesn't answer your question, but since this was posted in the Career forum, you might want to take a look at this survey I did:


    There is a very strong probability that, at your level right now, what you plan on doing will NOT be what you will end up doing. Keep that in mind as you make your choices.

  9. Apr 22, 2014 #8
    you seem to be interested in TOE research (theory of everything). You have to be a brainy genius to do this (from my perspective) kind of like stephen hawking or albert einstein. Keep in mind that this stuff isn't really practical and there's still a lot of stimulating problems in "practical" physics

    pure math and theoretical physics are kind of different. In physics you have to make a hypothesis on the deeper workings of physical reality based on concepts and intuition. For example can you make a wormhole back in time or something crazy like that. You have to think of what kind of experiment will test that hypothesis and hope someone with the money will do it eventually.

    A mathematician won't care about that. They'll work on stuff that seems like logic and philosophy. There's a series of math problems that if someone solves they'll get a lot of money. http://en.wikipedia.org/wiki/Millennium_Prize_Problems

    They're cool in they're own way but you won't care about physical reality anymore. It depends on which one concerns you more. Personally I like the physics more because I like physical reality. You'll see a lot of math but you won't go into the details of it like in mathematics...

    If you want to study theoretical physics I think you have to know differential equations, linear algebra, and some 3D calculus at the least.
  10. Apr 22, 2014 #9


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    We can't really tell you what you should do. You make this decision as you progress in your undergraduate studies. If you're at the stage in your life where you're deciding what to do after high school, consider a course that leaves both options open and make the decision as you learn more about each field respectively - say a double major in physics and mathematics.

    At the same time make sure you have a solid backup plan. Academic positions are hard to come by these days.

    You'll have to study a lot of math if you want to be a successful theorist. Dive right in.

    I'm not sure I agree with you here. Unfortunately people these days are very quick to jump to the conclusion that something is 'useless' if they don't see an immediate application for something.

    Of course. Why wouldn't it be?
  11. Apr 23, 2014 #10
    Not really. Riemann just had the idea of generalizing what Gauss did for surfaces to higher dimensions. So, if you look at it as an extension of Gauss's work, it deals with pretty concrete physical things: surfaces. It's one step removed from reality. It's necessary to be a little playful and not always be thinking directly of solving some particular practical problem. That's sort of the nature of math, if you have some experience with it.

    Never the less, after getting a PhD in topology, I became a little bit skeptical of the value of a lot of the research that is being done in math. Skeptical doesn't mean I dismiss it as useless, it just means, I'm skeptical about its use, in that I don't take it as a given. Historically, there are good reasons to be concerned about this. A lot of research from the 19th century that people thought was so important back then ended up being pretty much forgotten. Apparently, according to Thurston, even work from the 1980s on foliations has been forgotten. It might not be such a bad idea to say, maybe we should only allow X degrees of separation from reality, or at least that we should put more emphasis on things with less separation from reality. You can easily argue that mathematicians should have some freedom to play around with stuff that isn't directly useful, but once you accept that, it is not at all clear HOW MUCH they should do that. I would contend that they ought to do it less than is the case right now.

    It's very frustrating to study pure math sometimes if you have the even the slightest hint of scientific/applied curiosity because you hear these vague hints that so and so is doing research on protein-folding or using topology to determine the chirality of molecules, but it takes a gargantuan effort to actually read about these things and understand them in detail and figure out exactly what role the math is playing and how it important it might be. Learning about such things could could take effort that will make it harder for you to succeed in your absurdly competitive pure math world, unless you change your entire focus to those applications.

    Math is so vast and requires so much effort that it seems strange to devote your whole life to things that are so far from reality and only have an extremely hypothetical potential for application. Some mathematicians might just think of it as fun, rather than work, but after writing a big fat dissertation and finding out what it's like to come up with substantial new ideas and try to write it all down, trying to read ridiculously obscure and formal papers, and attending obscure talks, I can't really see it as fun anymore, at least not the way most mathematicians are doing it these days. It was when I was an undergrad and to some extent earlier on in grad school. I can always understand anything, if I put enough effort into, but increasingly, as I went on, I found it wasn't worth the effort. I found the excessive complexity of it all to be sickening. The usual way to deal with this complexity is to take more theorems on faith and not understand them for yourself, but for me, because the only pleasure I get out of math is in understanding, that defeats the whole purpose. I found out that it wasn't that I wasn't smart enough, it was that I was the one who insisted that I had to understand everything and not build on top of stuff I don't understand. There just isn't enough time for that, so no one does that. Also, people tend to be so specialized, so they are going into these very narrow little pigeon holes. They still have to learn the basics of a lot of different fields, but they tend to dig their holes excessively deep and narrow for my tastes. Math is not the same as it was 100 years ago. It was only through 6 or 7 years of painstaking effort that I was finally able to admit that math, in its current state, was not for me.

    Actually, Ed Witten even gave a talk to a general audience that's somewhere on youtube where he talks about how there's this feeling of understanding that is what would make someone want to be a mathematician in the first, but a lot of mathematicians are not working in a way that allows that to happen.

    It's a very easy trap to fall into because these sorts of issues don't really have their full force until you're almost done with a PhD. I thought it was just unbelievably awful, personally, and I'm far from being alone in that. I still think classical math is great, though.
  12. Apr 23, 2014 #11


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    homeomorphic, I can see your point regarding the frustration you felt regarding pure math, particularly for those who have even a slight interest in applied/scientific interest.

    I'm curious about the experience of those who focus on research in applied mathematics. Since by its very definition, applied mathematics is devoted to the study of mathematics which are tied to applications, I would expect that mathematicians are probably less frustrated with the fact that their specializations are so completely divorced from real-world concerns.
  13. Apr 23, 2014 #12
    I think that would vary from person to person. A lot of applied stuff isn't actually that applied. I have a friend who does PDE who's doing a postdoc, and he's about 10 times more disillusioned than I am. He'd say a lot of the same stuff, only with more force. I suppose he didn't want to bother with the big job search I am facing, since he was able to secure a postdoc. He sounded like he wasn't feeling much better about it, last time I heard from him.

    Part of it is the pressure that is put on newcomers. You enter the big, bad math world, along with the people who have been doing it for 20 years or more, you're expected to start publishing along side them, and you have to sink or swim, so you feel like you're way behind. You're very constrained in what you can do for a long time.

    It's been refreshing for me now that I have quit pure math to get back down to earth and learn more about programming and financial math. When I have time, I still want to learn a little more pure math as a hobby, but right now the priority is to gain job skills. I'd really like to get into the details of the whole Lie Group classification story again, along with Coxeter theory because I have the general picture of how it goes, and I'd like to fill in the gaps, but most of my interests are more applied, now. I still have a bit of an itch to clear a lot of the fog from grad school and try to tie it in more with reality, but no desire at all to publish new results. I'm a afraid I might be too busy with my new work when I get a job, just as I am too busy right now, trying to get one (incidentally, I just got an e-mail informing me I finally have a job interview lined up). I post on physics forums and answer people's math questions to help me keep in touch with it a little bit and very casually studying physics again for a few minutes a day, but other than that, I've left it all behind for the past few months.
  14. Apr 23, 2014 #13


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    Well the more you look at it, a genuine TOE is just a fantasy, based on our current status of knowledge which may change tomorrow in a never ending universe...
  15. Apr 23, 2014 #14
    Alrite. Two things were mentioned. First, that quantum gravity is a tiny sub-field of theory. Second, that few people outside those working on it care about it.

    If by the first was meant that its a tiny field because few people (comparatively) work on it, then I am agreed. I interpreted it as addressing the importance of a prospective theory. A theory that would bridge together seemingly disparate strands of physics and be a major step forward in bringing to fruition a 500 year old dream that started with Copernicus, or farther back even, with the Greeks Democritus and Leucippus. That, to me, is ridiculous. If, regarding this, I interpreted wrongly then I take back the 'ridiculous' comment.

    But the next part is indubitably sad. I refuse to believe that any practitioner of physics would fail to rejoice if a theory of quantum gravity came out tomorrow. But going by the number of responses in favour of our protagonist's assertion and that in favour of mine, I see I might be wrong. Which really and truly is sad. Or perhaps its not a large enough sample to base an appraisal. Yes, I think that's the notion I'll cling to.
  16. Apr 24, 2014 #15

    I think physics can go deeper and deeper forever....
  17. Apr 24, 2014 #16
    Yeah I think math only exists in the mind. It's almost like philosophy. At a mental level it's important but at a practical level not really...even science sometimes is not practical enough which is why we have engineering but i feel like an applied science guy.
  18. Apr 24, 2014 #17
    You have to make a distinction between math and math research. MATH is pretty important in a practical sense. Math research? I'm not so sure about that. But it's not entirely insignificant, either. GPS turns the theory of relativity and, to some degree, all the associated differential geometry into a practical thing. Signal processing does that for Fourier series and transforms. Statistics does that for itself and probability. Things like motors, generators, antennas, or microwaves do that for multi-variable calculus and electromagnetic theory. And there's a lot of stuff like that. The thing is, all that stuff is fairly old math, not current research.

    Cryptography does that for number theory, and perhaps, pretty sophisticated number theory to get it to work right, although, as with a lot of applications, it's hard for me to say too much about it. Of course, it's easy to see something happen as big as someone solving the Riemann hypothesis not having too much effect, so it's hard to say how much relevance the stuff people are publishing in papers has, especially for a non-expert such as myself. However, if someone figures out a way to factor large numbers (as the mathematician, Peter Shor, did in theory, if we could only get our hands on some quantum computers), that would actually have rather large practical implications.

    Another example of more recent math being found useful in some ways might be found in fractal geometry.

    So, I wouldn't make the claim that NONE of the math that was done recently has any practical use. But I would say in my estimation, the vast majority of it has only very hypothetical potential for practical use some time in the future. Often, the contribution might be very indirect, though, which is kind of what you seemed to be getting at. A lot of things seem to have been discovered in a more theoretical way, but then, once the applications have been developed, the practitioners might not necessarily understand all that initial theory. It gets streamlined so that people don't have to learn as much to use it at times.
  19. May 11, 2014 #18
    Thanks for that response. I think your mindset is similar to my own, except that you've traveled a path that I'm looking into (I'm just finishing up my undergrad in physics).

    I'm generally interested in mathematical physics and pretty much live for the 'understanding' part of it. I'm not particularly interested in 'publish or perish', and I'm not so sure that extended academia (like a future university professorship) is right for me. That said, I want to delve deeper into mathematical physics, and I'd like to be able to understand the well-established physical theories of the day. So, with that in mind, I will be getting a PhD in some field of physics.

    The question is, what field do I specialize in? I want to learn theory, but I'd like to develop some career skills outside of academia. I'm trying to brainstorm up some career paths and PhDs that take the best of both worlds (math/physics vs money/job skills). So far I've come up with very little.
  20. May 11, 2014 #19


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    You might want to think about areas that benefit largely from rigorous computational simulation, such as computational astrophysics, comp. condensed matter, materials science, etc. Even numerical relativity is a thing now. There are plenty of interesting areas outside of physics, such as systems biology, that are heavily dependent on numerical analysis. From what I've observed, the main career skills that get theorists work are their modeling/programming skills.

    Personally I enjoy quantum information. If I can focus on the more computer sciency side of things (error correction, algorithms, cryptography) I can study the theoretical computer science structures that I find interesting, as well as quantum mechanics. And I'm kinda banking on this happening:

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