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Can I have a PhD in mathematics or physics after having a bachelor degree in medicine provided that I score high in GRE physics or math?

I have had zero coursework in math or physics but I am not sure if I could greatly increase my chances into grad school by taking GRE and scoring highly in the test.

I'm not trying to show that I'm smart or anything but I think that mathematics is my cup of tea for I'm very passionate about it and I have studied analysis and algebra and quantum mechanics other things from standard textbooks getting help from resources such as MIT OCW.

  • Zero coursework? That'll be a problem. A Math or Physics minor, at the very least, is 5 courses. At my school of those were 300-level courses. As someone who's gone through the Bioinformatics/Pre-Med track, I feel like that jump is pretty big. I switched to CS, but I had 8 CS courses as supporting interest. – Compass Oct 9 '14 at 12:46
  • It's not impossible. Some very successful mathematicians have done it, look up Chris Godsil, who graduated with a biochem bachelor's and is now a leading combinatoricist. But you do need mathematical maturity, you have to spend some time to catch up on math. – user10033 Jan 9 '15 at 22:01
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The hard answer is a straight no.

Doing research level Mathematics or Physics requires a broad set of knowledge and maturity that takes years to achieve. GRE exams are quite crappy, they just ask a lot of questions on basic knowledge and arithmetic; but you won't see an integration by parts (first year maths).

But not everything is lost. There are fields where medicine and maths overlap, and definitely your expertise on one field and interest in learning the other can definitely help. Look at Biomathematics, Bioinformatics, and perhaps, Biophysics. I myself am a Physicist working in Bioinformatics. I do pure analysis of the data, but in the group we also have a wet lab, where my colleagues are trying (among other things) to come up with new creative ways to gather data more suited for our purposes.

  • Another hybrid field you forgot to mention is Biostatistics, and to a point, Computational Biology. Bioinformatics, at least as our U interpreted it, was micro-level work (genome processing) vs macro-level (population analysis). Biostatistics I am not wholly familiar with. – Compass Oct 9 '14 at 12:50
  • +1. As to GREs: calculations and computations are not what you will be doing as a math Ph.D. - you will be doing proofs. So whether or not you find an integration by parts on the GRE is not really important. However, the OP mentions he studied analysis and algebra - if he means analysis and algebra as understood at the university level (not high school, even AP), then his aptitude at the proofs required there might be more informative. – Stephan Kolassa Oct 9 '14 at 14:27
  • @StephanKolassa well put. I mentioned integration by parts as a very low lower bound, needed both for Physics and Maths. But yes, from there, all the way up. – Davidmh Oct 9 '14 at 16:28
  • @Compass Bioinformatics does include CB, as well as things like Statistical Biotechnology (v.g. accurate statistical analysis of proteomics mass spec, nothing to do with Biostatistics). Biostatistics usually deals with "how many subjects I need for this study?" and "my patients seemingly got better, but was really because of my treatment?". They are much lighter on the maths, but possibly a good fit for a MD. – Davidmh Oct 9 '14 at 16:36
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In the U.S., this idea is fraught with difficulties, but is not impossible, in part because the usual undergraduate math curriculum in the U.S. is pretty thin and slow in any case, so that the typical first year or two (or more) of graduate work in mathematics is still coursework, getting-up-to-speed. Despite rumors of "undergrad research" in the U.S., genuine such is quite unusual, although "research experiences for undergrads" do give a positive experience showing that "classroom math" is not what mathematics is eventually about.

But there are intangibles acquired by doing that undergrad coursework, including "being on the same wavelength" as one's potential cohort, and having practice understanding what the instructors expect. While it is true that some of this is not particularly constructive pure convention, it does affect communication in both directions. If you're missing this experience, this will be an added catch-up project.

Beyond conventions and standards for communication, there is also the potential issue of accidental self-deceit about the degree or depth of one's understanding, if one has not interacted with other people. It's not that the typical U.S. undergrad curriculum is terribly substantial, but in a way this makes it all the worse, insofar as the truly important points can be lost or misinterpreted in a context of vast ocean of seemingly uniform technical details. Or, from another side, a too-physics-y attitude about mathematics may generate lots of trouble for you in a "strict" mathematics context.

After these cautions, I guess the point is that it is nevertheless possible, if one really wants it, to pursue mathematics (e.g, in the U.S.) despite not having the corresponding undergrad degree. Your issues would be primarily two: (1) getting letters of recommendation from mathematicians with PhD's, (2) demonstrating some self-study knowledge/awareness despite lack of transcripts showing such. Prepping for the GRE subject test in math might be feasible, and getting a good number is plausible without the undergrad degree, but this wouldn't be sufficient.

Probably taking at least one, probably two or more, upper-division or intro grad level math classes at a serious university would help you generate letters and also demonstrate that you can do the work at that level. At many places in the U.S., it is possible to register for such courses as "non-degree student", paying a lower tuition.

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