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I know my question is opinion-based but I am desperate and do not know a better place to ask it really. I was in love with mathematics since high school and I was always very good at math and physics back then. But due to economic situations, I was forced to go to medical school (after a lot of uninteresting studies) a decision which I regret most to this day. Now I am a 6th-year medical student in Iran (1 more year to go) and I am 25 years old. 3 years ago I started to study mathematics as a hobby, but it got more serious. These are the subjects which I studied since then in chronological order (I always do the exercises):

Calculus I and II - Coursera - Jim Fowler

Calculus Made Easy - S. P. Thompson

Probabilistic Systems Analysis and Applied Probability - MIT-OCW

Mathematical Methods in Physical Sciences - M. L. Boas (first six chapters: infinite series, complex numbers, linear algebra, partial differentiation, multiple integrations, and vector calculus)

How to Prove It - D. J. Velleman

Book of Proof - R. Hammack

Introduction to Graph Theory - R. J. Trudeau

Differential Equations - edX

Differential Equations - Udacity

Linear Algebra and Multivariable Calculus - Youtube - Aviv Censor

Linear Algebra Step by Step - Kuldeep Singh

Introduction to Differential Equations - S. L. Ross

Nonlinear Dynamics and Chaos - Steven H. Strogatz

And now I am studying Lay's Analysis: An Introduction to Proof.

I also learned some machine and deep learning and how to implement neural networks from scratch in Python.

I love mathematics more than anything else. But is there a chance for me to succeed? Given the facts that I am 25 and wasted all these years? I also wanted to know is there a possibility for me to study pure math in a tuition-free university in Germany for example (from the beginning)? To expand my studies further still, I use the resources in http://hbpms.blogspot.com/. Is that OK?

Thank you for your time

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    $\begingroup$ I'd say, go for it. If you have the dedication and drive to do it, you will do well. Of course, you might not become the next Riemann or the next Poincare, but then again, very little mathematicians are. $\endgroup$ – YiFan Feb 18 at 12:33
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    $\begingroup$ If you've worked through all of that, you have a very solid foundation. May I suggest that you try something a bit more abstract now, such as groups and rings, and something more applied such as a first course in quantum mechanics or electrodynamics. Of course there's still geometry, and number theory, and... it never ends. So finish you medical school, and you still have a whole life ahead of you to discover mathematics. $\endgroup$ – Chrystomath Feb 18 at 13:23
  • $\begingroup$ finish medical school first, otherwise you might end up with no degrees $\endgroup$ – Dac0 Feb 23 at 7:10
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If it is actually true that you have gone through all that material by yourself, and that you have a reasonably solid grasp of the material that you've been through, then I see no reason why you couldn't pursue mathematics. You clearly must be a talented/hard-working individual.

If you had started mathematics from the beginning, you would've been finished with the degree some years earlier. While that is true, I don't see this as some impossibly major setback. It is possible to start a degree when you're 25-26 years old and still complete it. I personally know many who have done so.

As a personal advice, and some people might disagree, but I would strongly recommend that you finish your medical degree first (unless having that degree somehow disallows further degrees). Only one year left, and I would say that it is very risky to leave all that aside. If you finish this degree, you would always have this as an option to fall back on.

Whether it is possible for you to pursue a mathematics degree at a tuition-free university in Germany... I don't know, and it's not a mathematics question and is not on-topic. You would have to ask that somewhere else or figure out your academic options in some other manner.

Good luck!

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