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I hope never to study physics. Can I still ace undergraduate and PhD math? Or ought I major in something else?

Background

I finish high school in 2019, and I'm mulling majoring in math/statistics. I'm mostly interested in probability and statistics (not number theory, notwithstanding my user name).

Please presuppose my scorn for physics that can't be changed. I've never been interested in physics, because I'm interested in using probability and statistics to help the poor. I can't grok how physics can instantly help penniless African orphans, as it feels too ivory-tower. I know that many pure math courses are taught with physics applications (like PDEs).

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    $\begingroup$ This is a better question for the math stack exchange but yes, you can be successful. Very little pure math requires any physics knowledge and if you're interest is statistics there are a whole host of applied problems outside of physics. $\endgroup$ – Nate Bade Jun 7 '18 at 4:07
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    $\begingroup$ Some beautiful "pure" mathematics was originally inspired by problems in physics, and in my opinion cannot be fully enjoyed without at least an awareness of the physical origin. You say that the probable reason for your scorn for physics is that you are practical. Isn't physics a practical subject ? Even quantum physics seems to have many practical applications. Not to criticise you, only to suggest that you might be missing out on something very nice, and that you might not yet have enough experience to be certain about something like this. $\endgroup$ – Simon Jun 8 '18 at 17:11
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    $\begingroup$ I find the statement "I've never been interested in physics, probably as I'm practical" so completely incomprehensible that I suspect it's a typo and you actually meant to write "I'm impractical". $\endgroup$ – mweiss Jun 8 '18 at 23:29
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    $\begingroup$ ivory-tower questions, like these --- I don't understand the relevance of your comment directed towards me. The link you gave is to a mathoverflow question, a professional mathematician's site and thus, if anything, the exact opposite of what I was talking about when I mentioned Halliday/Resnick level material and the chapter in Gamow's book, and even more so in view of my follow-up comment about string theory and holographic universes. $\endgroup$ – Dave L Renfro Jun 15 '18 at 20:10
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    $\begingroup$ What an odd notion that science cannot help the poor while a statistical study would. Statistics will only identify problems. Science (including physics) can help solve them. If you want to do social and economic development, the more tools you have at your disposal, the better. See "Science, Technology and Innovation for Poverty Reduction " at iop.org/publications/iop/2009/file_44076.pdf $\endgroup$ – Dan Christensen Jun 22 '18 at 12:59
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I left a comment a while back, but I have been mulling over this (off and on) since then, and feel that I should expand on it. As a first-term master's student, I made some off-hand comment about not liking applied mathematics. My advisor cracked down on me pretty hard at the time, and essentially explained that I lacked the mathematical maturity to have that opinion. You can't dismiss a field until you adequately understand what that field is all about. I could either take some applied mathematics classes and then make up my mind, or I could shut up.

I took a couple of applied classes and learned some nifty stuff. I still don't really dig on applied mathematics, but I have a better appreciation for applied math than I did before. I'm glad that I took those classes, and I now feel pretty confident in my opinion that applied mathematics isn't right for me.


Another anecdote: I have taken a grand total of two physics classes in my life. I took one semester of a combined precalc / physics class in high school, and I took one quarter of quantum mechanics a little over a year ago (I'm a pure math Ph.D. candidate at the moment, so I still take the occasional class). By some measures, I have been relatively successful as a mathematician without a strong background in physics.

However, there are a lot of places where I can see that a physical intuition would be really, really helpful to have. My master's advisor had an uncanny ability to know when my computations were wrong after just a second or two. It turns out that he was doing a lot of quick dimensional analysis in his head, and noticing that the units came out wrong. This struck me as very odd, since we were working in pure fractal geometry, and there were no units anywhere in any of my computations. However, he had a physical intuition about what all of those quantities represented, so it was easy for him to check units.

When I teach multivariable calculus, I can happily explain Stoke's theorem to my students, and even give a pretty convincing proof. What I cannot do is adequately explain to my students how to interpret that theorem physically---I have no intuition for what a flux or curl are (I can parrot back what I've been told, but I don't have a good internal model for these ideas). I don't think that this makes me much less effective as a mathematician (I still work in fractal geometry, after all), but I do think that it makes me somewhat less effective as an instructor in that class.

As a third example, I am currently working with a colleague to study autocorrelation and diffraction measures associated to certain kinds of sets. The project is really my colleague's idea---he is studying quasicrystals---but I am a reasonably good analyst, and there are some tricky questions of functional analysis that come up (how do you take the Fourier transform of the convolution of two measures which may not be finite?). My colleague has a much stronger background in optics, and has an intuitive grasp for what the answers should be based on his knowledge and experience with experimental data. Again, my lack of physics knowledge slows me down a bit (though I am currently learning all about optics and diffraction---yay!).


Long story short: if you have not even completed a bachelor's degree, you are too young and academically immature to have already decided that you abhor physics and don't want to learn it. You simply have not been exposed to enough physics to hold that opinion. It would be good for you to take a few classes, and will make your life easier later.

That being said, it is entirely possible to be successful as a mathematician without a strong background in physics. As I tell my students, I'm a mathematician, not a physician... er... physicalist... uh... physicist.

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I know I'm late to the party, but I'd like to offer a different type of answer:

I would say that, as described, you are not in a good position to do a PhD, in mathematics or otherwise (and may find an undergraduate degree hard too), not because physics is essential, but because learning is. As a teenager you have said that you are not willing to consider changing your views. This sort of mindset will not serve you well in trying to discover new knowledge.

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    $\begingroup$ +1 Maybe late, but I think you've zeroed-in on what is probably a first-order issue (a linear correction term), with interest and desire in physics being higher-order issues (quadratic or cubic correction terms). (Maybe I'm trying to push the physics-lingo analogy too hard, however.) $\endgroup$ – Dave L Renfro Jul 11 at 18:05
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    $\begingroup$ For what it's worth, I also decided upon leaving high school that I wasn't really interested in physics, or science in general, and managed to complete my math degree just fine. You can still maintain a healthy eagerness to learn even if there are some things you don't care to learn about. I mean, you have to make choices at some point. I did not gather from the question that s/he is resistant to learning per se. And I agree with others here that the subject of math is big enough that you can be fruitfully engaged in it without having much to do with physics. $\endgroup$ – Richard Sullivan Jul 11 at 23:38
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    $\begingroup$ @RichardSullivan I'm not really responding to the 'I don't like physics' but the 'assume there is no way I can possibly change my mind'. $\endgroup$ – Jessica B Jul 12 at 9:11
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    $\begingroup$ @Edge 'I'm interested in using probability and statistics to help the poor. I can't grok how physics can instantly help penniless African orphans': as has already been pointed out, physics is significantly more useful to penniless African orphans than statistics is. Knowing they are penniless doesn't help. Knowing how to move the water from the bottom of the hill to the top can do. $\endgroup$ – Jessica B Jul 17 at 6:37
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    $\begingroup$ Or some efficient solar panels. Or GPS. Or satellite images that can't be blocked by a corrupt government. Or any form of air transport. $\endgroup$ – Jessica B Jul 17 at 7:07
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I don't see why you would need any physics knowledge to get a math degree. I have a masters and took one physics class that I took purely out of personal interest. There was no physics involved in any of my mathematics classes.

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    $\begingroup$ Because a general education is HELPFUL to teaching math. The major applications of calculus are science and engineering. Therefore "what you did to get your degree" is not the end of the discussion. Capisce? Oh...and there are probably a lot of things you don't "get". $\endgroup$ – guest Jun 24 '18 at 17:57
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    $\begingroup$ @guest First, the original poster never mentioned teaching. Second, I teach math and we never touch on physics related content at the undergraduate level. This is going to be even more the case at the graduate level. Why would you discuss physics in a course on number theory or abstract algebra? With respect to your last comment, I'm going to assume English isn't your first language. Get, in the context of my post, means to achieve or earn something not to understand. Capisce? $\endgroup$ – G. Allen Jun 24 '18 at 17:59
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    $\begingroup$ The number one use of calculus that MOST of your students will be using the calculus for is calculus based physics. Calculus is a pre/coreq for that course. That all the scientists and engineers take. Like 90% of your students. If you know what they use it for, you are a better prepared teacher. this is regardless if you have specific examples that are physics based (although that is not uncommon either in many calculus texts). $\endgroup$ – guest Jun 24 '18 at 23:44
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    $\begingroup$ @guest I teach mostly business calculus so I can safely say that not a single one of my students is going to be using it for physics. $\endgroup$ – G. Allen Jun 27 '18 at 4:19
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    $\begingroup$ Great response (I mean it). I think there are a lot of calculus classes for engineers and scientists who do take physics. So part of the consideration/analysis needs to be overall population, not just your situation. (P.s. why even have business calculus? Think they would get more out of a course on how to use Excel better, do DCF modeling, etc. I am a business consultant and never use calculus, but Excel, DCF, compounding, etc. are useful.) $\endgroup$ – guest Jun 28 '18 at 16:33
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You definitely can do well in mathematics, without knowing (almost) any physics. Some first year mathematics subject, most notably calculus, will have some physical application (spring/circuit) when teaching differential equations for example, but even here not having the 'real' understanding of the pysical concepts will not hinder your progress in any significant way. These are two very different fields, in the sense that they employ different types of thinking. A lot of theory from mathematics is applied or is useful in physics, some was developed for that purpose. But again, in a maths department, it is mathematics that is taught. Some mathematicians will have a very good grasp of the field and may be working with physicists or on developing theory for physicists. You obvioysly don't need to be working with these: There are many branches of mathematics, and plenty with no obvious link to real world (at least for now).

Note: I am not aware of any pure mathematical course being taught with applications in physics. It is mathematics that is taught that is likely 'useful' in physics and that is all you are likely to here (rather than have physics taught - unlikely to happen even in an applied maths class).

Rather than believe the above, check it yourself. Universities will have subject lists with brief descriptions of topics covered, together with prerequisits and corequisites.

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Some math courses will have: simple applications in physics, simple applications in economics, simple applications in biology, simple applications in engineering, and so on. Beginning calculus, or differential equations, for example. So you perhaps will not ace those courses, but still you could do OK.

Now in most cases, when you work on a Ph.D. in mathematics, you will want to (or even be required to) work as a teaching assistant on low-level undergraduate courses. And it may not be possible to avoid beginning calculus courses. So in the end you will, indeed, have to know a small amount of physics.

Back when I was a student taking basic calculus, I had a TA who explained that she could get by with just a few basic notions from physics, and that she never intended to learn any more physics than that.

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