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I'm currently studying for a PhD in pure mathematics (the topic is the cohomology of differential graded categories, just to give you an idea of how pure I mean), although the first year of my undergraduate degree was in mathematical physics before I transferred to mathematics, so I have a little (but unfortunately not that much) background in physics as well.

I'm seriously thinking about whether I want to pursue pure mathematics as a career, and since astronomy and astrophysics were, one could say, my first love when it comes to science-y type things, I've been wondering if it would be possible for me to switch fields, and what would be necessary to do so. Although I'm aware that astronomy/astrophysics is a wide area and could mean lots of different things in terms of a profession.

To give you a little more background, my current level of astrophysics knowledge is propped up mostly by my short time studying physics at university and a continuing interest and reading various non-technical books and low level textbooks of various topics. The topics I've found most interesting are things like supernovae, and the formations of stars and star systems, although I haven't studied the mathematics or technical details of these things in any serious depth. I should say that I split off from applied mathematics some time ago, so topics such as PDEs and statistical analysis are not areas I'm adept in (although I have no doubt that I would have relatively little trouble learning them at this stage). I've also spent a short amount of time (~ 1 year) working as a software developer, so I have some proficiency with programming. And actually I thoroughly enjoyed my time as a developer, and I know that software development/programming is an important aspect of work and research in this field for analysing images, data sets, creating simulations and that sort of thing. So something of that sort is of great interest to me, especially if it could directly involve mathematics. So perhaps working with simulations would be a good option for me?

Is a change of this kind possible for me? And if so what would you recommend I do to make it happen?

Apologies if this question is off-topic by the way. Please do let me know if there are more appropriate places to find this information.

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    $\begingroup$ Have you tried googling "cohomology" (or other terms in your specialty) with "cosmology", "physics", "gravitation", etc.? $\endgroup$
    – Keith McClary
    Commented Aug 29, 2020 at 23:49
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    $\begingroup$ @KeithMcClary I've often tried to see how my specialty might apply to physics, and it mostly seems to be with gauge theories and other weird stuff to do with string theory, which I have to say is not an interest of mine. Although I haven't really made much effort with searching specifically within astrophysics so maybe there will be something there. Thanks for the suggestion! $\endgroup$
    – SeraPhim
    Commented Aug 30, 2020 at 10:23

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There exists an area of astronomy where mathematical (and computational) skills are of supreme value. This is celestial mechanics. One of my colleagues got his PhD in dynamical systems (an area that is, arguably, closer to pure than to applied math), and is now modeling orbits at NASA.

Get in touch with me if you wish to chat on this. You will find my e-mail address on my website.

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    $\begingroup$ OP asked this 2 years ago. They probably have sorted out their life by now.. $\endgroup$
    – AtmosphericPrisonEscape
    Commented Mar 31, 2023 at 17:44
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    $\begingroup$ @AtmosphericPrisonEscape you'd be surprised at how little my life is sorted out with regards to my phd :') I've actually continued to struggle with this and I just the other day actually had a meeting with my supervisor to inform him of my intention to leave my course entirely. So this answer actually comes at a weirdly prescient moment. $\endgroup$
    – SeraPhim
    Commented Apr 1, 2023 at 10:53
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    $\begingroup$ The respond directly to you Michael_1812 I appreciate the answer very much and I think I will take you up on your offer to chat. Celestial mechanics certainly seems like a very interesting topic! $\endgroup$
    – SeraPhim
    Commented Apr 1, 2023 at 11:04
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There are fewer placements than qualified applicants so competition is strong. Moreover, suppose this was the other way round: A person doing a PhD in (say) planetary nebulae comes to the maths department saying that they are really interested in maths, they're good at equations and calculus and really like all that topology stuff (you know, rubber sheets and so on) so can they start doing cohomology of differential graded categories?

It's not impossible, and a strong foundation in maths is a prerequisite for progress in Astronomy but the question you should ask is why should a university hire you, when there are 5 others with PhDs in astrophysics?

Talk to your supervisor and careers advisor before burning any bridges.

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    $\begingroup$ Indeed, I realise my position is not strong to begin with and I would not in a million years expect a department to accept me on my current qualifications alone. Which is why I've come here to ask a soft question about what steps someone in my position should take before I could seriously expect to compete with other applicants to a job. $\endgroup$
    – SeraPhim
    Commented Aug 28, 2020 at 23:06
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    $\begingroup$ I should also say that at the moment this is simply a thought experiment about what I would do if I really decided to sack off my PhD to pursue something else. It's generally going fine and I'm mostly happy with it, I'm just at something of a crossroads and casually thinking about other options. So talking to my supervisor and careers advisor would be serious overkill at this point. $\endgroup$
    – SeraPhim
    Commented Aug 28, 2020 at 23:35
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Perhaps try to get a masters degree in astrophysics, or at least consider taking some graduate-level astrophysics classes. This will be helpful on several levels

  • give you a feel for what is being done in the different sub-fields of astrophysics. Maybe give you some ideas of what part of astrophysics (e.g. magnetic fields of the interstellar medium, asteroseismology,...) you would most like to work in.
  • If you do simulations, for instance, it will help you understand the physical phenomena involved and give you "physical intuition" to interpret the results you get.
  • give you the opportunity to meet some astrophysics researchers (your profs!) and discuss options directly with them.
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Having a strong mathematical background may be a strength in astrophysics and cosmology. Not so much in astronomy and observational types of sciences. Although you would not have the physics background you still seem like a very smart person and I'm sure that you do have some adequate general science knowledge.

What I would advise is that perhaps you take some remedial classes to catch up and start slow within the area. This is to see if it's really meant for you. I did my masters degree in astrophysics and most of it was programming Mathematica in order to solve equations. The physics then came in when I had to apply the results to real-world applications.

Your tutor may then help fill in the gaps in that case.

Wish you the best

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