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I am a math major in my early years of undergrad, and I'm wondering if math majors can or should consider pursuing graduate school in (theoretical) physics. I don't think there's a barrier in terms of logistics, since there's quite a bit of overlap between pure math and theoretical physics — but I'm not sure if math majors fulfill the prerequisites (if any) to pursuing graduate school in physics.

Would a typical math major be required to take some more physics classes than usual, or have some research experience in theoretical physics before trying for grad school in related areas? Or are schools (and advisors) happy to accept pure math majors with minimal physics background whatsoever (maybe to start certain things from scratch in grad school)?

My question is specific to PhD programs right after undergrad, and schools in the U.S. or U.K.

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  • So do you want to know how many more physics classes a math major should take?
    – Promaster1
    Oct 17, 2020 at 17:01
  • To answer the "should" part: In general, only enroll in a PhD if you are really sure you want to, and you are informed of the career outcomes. Oct 18, 2020 at 0:36
  • @Promaster1 How many and which? Oct 18, 2020 at 3:38

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A pure math major with no physics classes beyond those required for an undergraduate degree is going to be woefully unprepared for graduate school in physics. There is, in fact, relatively little overlap between pure math and theoretical physics; vector calculus, linear algebra, and group theory are about it. (I double majored in pure math and in physics as an undergraduate, and there was very little useful overlap between the two, although some more subtle connections do become apparent at the advanced graduate level.) I would be very surprised if graduate program in physics would admit somebody with no physics beyond two introductory semesters of mechanics and electromagnetism.

Many (although not all) graduate programs in physics will let their less-prepared graduate students take (or retake) senior-level classes in classical mechanics, quantum mechanics, statistical mechanics, and electrodynamics. However, if you have little to no familiarity with the intermediate level physics topics, like waves, special relativity, thermodynamics, statistics (even people doing research in purely theoretical physics generally need to have to have a very firm understanding of statistical methods), etc., you are simply not going to be prepared for physics graduate school. An undergraduate major in applied mathematics is much more likely to cover material relevant to graduate study in physics.

Many of the strongest physics students double major in math, since a physics major already typically requires a certain number of advanced math classes (selected from things like vector analysis, linear algebra, group theory, probability theory, etc.). And there are also people who major only in math, but take enough intermediate- and advanced-level physics classes as well to make them plausible candidates for graduate school in physics. Some physics departments (such as mine) would seriously consider math majors with this level of preparation, but others will not even look at applicants without a full program of quantum mechanics, statistical mechanics, etc. classes. So if you are hoping to go to graduate school in physics, you will probably need to take a significant number of intermediate physics courses, at a minimum. (Sometimes, these courses may not actually need to be taught by a physics department though. There are often applied math classes covering wave behavior, for example, that could be suitable substitutes.)

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    The first paragraph is exaggerated. Vector calculus is absolutely essential for physics students and is more than a "little" overlap. Oct 18, 2020 at 0:34
  • I would agree with the first paragraph as written, vector calculus is essential but just knowing vector calculus would leave you woefully unprepared for a masters or PhD in physics. I would probably say the key point is that physicists tend to see maths as a tool rather than something to study in its own right (something the current answer is missing). for that reason if you want to go into a physics PhD you should try to take undergrad physics courses, it will help you prepare/learn the language while letting you try physics, even if you are mainly a mathematician. Oct 18, 2020 at 15:55
  • Secondly I'll also support the comment about a maths degree supporting a physics degree. I have taught myself a lot of maths by myself and attended schools (along with a few traditional courses beyond the standard maths courses for physics). During my physics post-doc I have found a deeper understanding of the maths useful because I can pick up theoretical topics easier and approach problems from more technical angles (even if I eventually use a traditional approach). But don't expect to always be able to solve your problem with some new and fancy piece of maths. Oct 18, 2020 at 15:56

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