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I hold an Electrical Engg degree currently and for the past few months I have been preparing for an entrance test for my Master's degree.Meanwhile my interest in mathematics has grown enormously and I find myself studying mathematics all the time (I have abandoned almost everything else). Although I was not exceptional(or anything close to it) in mathematics earlier it just seems like this is what i love the most. Can I become a mathematician now or is it too late? Please advice and thanks in advance.

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There is no point in doubting. You have to go ahead and see whether you can make yourself into a good mathematician. Offer yourself as the guinea pig to see if it works. I was also an electrical engineer and found myself in the same situation you describe, in a period of doldrums in my life. Then I decided to do a masters and while gearing myself up for the same, I found myself getting much more interested in math. And now I am a somewhat normal grad student in math, though I couldn't do anything exceptional. –  Anweshi Mar 26 '10 at 13:22
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If you have not done the standard "writing proofs" courses for undergraduate math students, then you may need to start there, before you can be admitted to a graduate program in math. –  Gerald Edgar Mar 26 '10 at 15:44
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Community wiki? –  Harry Gindi Mar 26 '10 at 16:46
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I don't think this question is appropriate on mathoverflow, but am presently unwilling to use my binding vote to close. –  Scott Morrison Mar 27 '10 at 5:11
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Talk to a course advisor about this, not to random people on some website. We know only a tiny snippet of your life, not including a description of family and work commitments, or even which country you're from. –  Douglas S. Stones Mar 27 '10 at 5:42
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closed as not a real question by Theo Johnson-Freyd, Harry Gindi, Scott Morrison Mar 27 '10 at 17:10

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Go for it! In any case, if you can't help but study math all the time, you may become a good mathematician whether you want to or not :-)

If you need more encouragement, read the supportive answers to the MathOverflow question "Too old for advanced mathematics?".

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Partly this depends on what you mean by "becoming a mathematician." I'd encourage you to think concretely about what sort of job you'd be happy with and figure out realistically what the odds are that you can get there from where you are.

For example, suppose "mathematician" to you means "tenured professor at a research 1 institution." Realistically this means you'd need to 1) Get a masters at a solid state school (you're unlikely to get into a top PhD program yet given your self-description), 2) Be the best student there within a few years, 3) Use that to get into a top 30 graduate program, 4) Depending on the caliber of the school be the best student, or at least the top handful, 5) Do very good research during your postdoc. That's a tough row to hoe, and although I don't know you personally, it's not something that a lot of people could pull off.

On the other hand, there are lots of other mathematical jobs out there. If you have a more broad set of jobs that you'd be happy with then it'll be easier for you to get there from where you are now. Certainly it'd be a reasonable goal to get a Math PhD somewhere, and end up with a job that involves mathematics.


Update: A good case study that illustrates both the possibility and the difficulty of becoming a very successful research mathematician after switching when not having top notch academic credentials, see William Stein's autobiography. Note the subtext of the discussion of his staying a year at NAU. He must have ended up with him getting basically a perfect score on the GRE and all of his professors must have said in their recommendations that he was by a significant margin the best student ever to have attended their school. A great thing about how few good graduate schools there are, is that even though a school like NAU's very rarely has students of Stein's caliber, nonetheless many of the profs went to good graduate schools (Wisconsin, Washington, Utah, etc.) and so understand what it takes to be successful at a good school. Thus they can credibly compare their once-in-a-blue-moon students to intro level students at a good graduate program.

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This guy also did electrical engineering (all the way to a PhD) before he decided to go into math. The general consensus is that he ended up being a pretty good mathematician.

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Yes. I think Mathematics needs more people like you.

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No, it's certainly not too late. The success is not guaranteed to anyone in mathematics, but from what you describe it looks like your chances to become a mathematician are not fewer than anyone else's. I would encourage you to devote your time to the study of what you find most interesting, having also in mind that a broad education in mathematics is very useful for a (prospective) mathematician.

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Let me just add that your background in EE can, in a way, be an advantage while pursuing career in mathematics, since you have experience in looking at things from a different angle - through practical aspects. Personally I am in a similar situation, but due to some reasons, can't do graduate studies in mathematics, but hoping for a PhD in (Applied?) Mathematics.

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While it can be such the case, I would not take it serious that one part of somebody's education should determine the preffered style when pursuing education in a neighboring field. One person can have many traits of personality, and presuposing that somebody who learned parctical discipline should do applied mathematics and not whatever one eventually gets attracted to is wrong. –  Zoran Skoda Mar 26 '10 at 14:36
    
Zoran, please note that I wasn't implying that it should determine the style - I was just saying that it could - the different angle I mentioned in the comment is not only important in Applied mathematics - it can help in Pure too. Whenever I think of an engineer in mathematics, it's Danilo Blanuša... A perfect example of one. –  Harun Šiljak Mar 26 '10 at 14:45
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Blanuša whom I do appreciate for many personal and mathematical traits, was excessingly pedantic in mathematical exposition and proofs, filling in all up to a trivial detail. Exactly opposite from what I would expect from an engineer :) –  Zoran Skoda Mar 26 '10 at 15:00
    
Well, it is not that surprising, at least not in the circle of engineers I know who turned to mathematics - one of the reasons they have become mathematicians is often the sloppiness of engineers' mathematical claims, lack of rigor, etc. But I do see your point, though - and it does make sense - it's more in the person itself, than in its formal background. –  Harun Šiljak Mar 26 '10 at 15:25
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It sounds like a very nice practical joke: "Meanwhile my interest in mathematics has grown enormously and I find myself studying mathematics all the time (I have abandoned almost everything else). Can I become a mathematician now or is it too late?" I have never heard such questions from people who are in love with maths, even they start later than usual. If you ask whether it's not late to earn money by doing maths, then I would recommend to try something else.

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Money/Job is not what I had on mind. If you could suggest something on the brighter side it would prove more useful. –  user4934 Mar 28 '10 at 15:15
    
In that case you can do whatever you wish, just for fun, and earn money from engineering... Mathematics is strong by its amateurs while professionals are mostly needed for teaching. –  Wadim Zudilin Mar 29 '10 at 7:26
    
Thank you very much –  user4934 Apr 1 '10 at 16:34
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