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I LOVE pure math, it sparks joy and excitement for me. At the same time, I want to be a trauma surgeon for a variety of reasons (it interests me, has more job prospects, academia doesn't seem like a great environment for me, I don't love teaching, it pays better). Would it be possible for me to research pure math without getting: 1) A job in academia. 2) A PhD? I would at the very least major in math in college (probably a double major with biology). I am really at a crossroads, and I am hoping it would be possible to at least in some capacity do research-level math so that I don't have to abandon one for the other.

Neptune
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    Look, I'm not one to shut down dreams but, a human can only do so much without getting burnt out. From my friends currently at med school, I hear that they literally have no time to waste at all, other than a minimal amount of free time used to do basic self-care. Maybe pursue math after you are settled in your career if you care about being a surgeon more? Doing research level math and being a surgeon simultaneously seems like a great way to make yourself miserable. – Rushabh Mehta Jan 14 '21 at 02:31
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    I agree. And since you are already talking about doing research in pure math, do not underestimate how hard that is going to be. Doing math on the highest level in research is not performed as a "side project". – David Scholz Jan 14 '21 at 02:33
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    I think it's probably going to be very difficult for anyone on this site to give you a good answer, since it's a very specific scenario in which I doubt many people have experience. That being said, I think the most sensible answer anyone here can give really is basically "look after yourself and don't push yourself too hard", which I think is the message that @DonThousand and David Scholz have tried to convey for the most part – Riemann'sPointyNose Jan 14 '21 at 02:41
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    $$\lim_{\text{Expectations}\to\text{Reality}}\text{Career}=\text{Undefined}$$. – B E I R U T Jan 14 '21 at 03:10

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There are great opportunities for MDs with deep interests and abilities in math. Integrating trauma surgeon with math seems awkward and unrealistic, but if you're a bit more flexible, I'm pretty sure you can find an intellectual home where you'd be happy.

A few examples:

  • Sophisticated mathematical analysis in epidemiology
  • Mathematical and computational modeling of neural functions... everything from perception to memory
  • Mathematical genetics and epi-genetics

There are opportunities where you don't have to teach. Think of NIH, Howard Hughes, and several labs such as Salk Institute.

The best work is always by researchers who understand deeply the problems. As an MD you'll have a great advantage over the "mere" modelers, despite the fact that they might be a bit more mathematically savvy.

An important problem solved well is far more valuable than an unimportant (or misguided problem) solved to perfection.

David G. Stork
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(In my personal Opinion)

( This don´t pretend presure you to take a desition I only pretend tell to you my little experience)

I don´t like broke dreams and in my special case ago a time I had your same situation, but in my case the papers be switch I´m studying Pure Maths in the university and want be a surgeon, but I discover that simply I can´t do both carriers.

My advice here is think and decide which of the two thinks your love more and when you select one think if is possibly apply the other, in my case for example I take Math and since I like medicine I decide make Apply maths and do all my researches in Pharmacology .

If you can apply one over the other nice, but in otherwase you should take one of them and think of what form your apply your love to your carrier.