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I'm an undergraduate student following a physics degree outside USA or Europe. My college is rather unknown, but it has a solid physics curriculum. The following are some facts about my degree and the mathematics involved in it.

  1. Rigorous mathematics up to real analysis, linear algebra and group theory.
  2. Rich in applied mathematical techniques related to physics (ODEs, Greens' functions etc)

Right now I'm in senior year, and have studied few undergraduate mathematics topics (topology, complex analysis) independently. But I haven't taken any graduate courses in physics or maths.

How can I become a mathematician with this background? My interest is in mathematical physics.

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    You would probably be eligible for admission to a doctoral program in math in the US. Other places will differ.
    – Buffy
    Dec 24 '21 at 21:33
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    It might be helpful if you could provide more information about the location of your undergraduate degree, beyond "outside USA or Europe."
    – Buzz
    Dec 24 '21 at 22:10
  • I'm from Sri Lanka, in Southern Asia. Can I still apply for a doctoral program (for example in the US), without recommendation from the maths faculty? My thesis project is also a bit inclined to the experimental side of physics, so it's not close to mathematics.
    – chan
    Dec 25 '21 at 4:46
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    Why not ask the admissions section of the department or university that interests you? They are the people who know; all we can give you is general advice. As you well know from your physics and maths, the general solution is not the special solution.
    – Anton
    Dec 25 '21 at 8:35
  • You can apply to Masters and PhD programs. Many schools in the US may still be willing to admit you. See also: academia.stackexchange.com/q/7927/19607
    – Kimball
    Dec 28 '21 at 20:31
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How can I become a mathematician with this background? My interest is in mathematical physics.

The only way is to complete a PhD in math (or a field close enough) if you really want to be a mathematician. (There are extremely rare exceptions such as S.Ramanujan.)

From your post, maybe you are not sure if your academic background is enough to pursue a PhD in math. Without more information, I don't think anyone in this forum can really give you a definitive answer on whether you have what it takes to become a mathematician. Your math instructors might have a better answer for you. The truth is, even if you have a "strong" undergraduate math degree, it is still impossible for anyone to give you the probability of success in getting a PhD in math because the road to a PhD depends on way too many variables.

However, not to be too pessimistic, I encourage you to apply to a couple of math doctoral programs in the USA and see how things go. You should google "usnews mathematics ranking". With only the information you have given, maybe you do not want to apply to the top 10. Maybe pick one that is ranked 11-15, one from 16-20, etc. This is only a suggestion. You definitely want to talk to your instructors and get input from them. You will need three very strong letters of recommendation from them anyway.

Kudos to you for studying some math topics on your own. Keep at it. Talk to your math instructors for guidance.

Good luck.

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    The only way is to complete a PhD in math. That’s factually incorrect. My department (math) has multiple faculty members with a physics PhD.
    – Dan Romik
    Dec 28 '21 at 20:58
  • Ahh yes. I've edited.
    – spoock7824
    Dec 28 '21 at 21:48
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    why can’t you call (rightly) yourself if you “just” have an MSc in math? Dec 28 '21 at 22:39
  • Mathematics, like economics, statistics, etc, is not a licensed profession. Anyone who wants to can call themselves a mathematician. Only people who are licensed can call themselves a doctor or a lawyer. Dec 30 '21 at 22:48

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