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I am a Physics undergraduate, but over the past year, I have developed more attachment to Mathematics than to Physics. How common is it for a Physics major to go into research in Mathematics and what should be the steps that I should take. Would studying the specific area of maths I am interested in by myself suffice, or would I need a formal degree in Mathematics? Also, would I have to be well-versed and knowledgeable of all areas of Mathematics, or studying only the area that interest me suffice?

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For some precedent, see the case of Raoul Bott, en.wikipedia.org/wiki/Raoul_Bott. He did an undergraduate degree in electrical engineering. –  Gerry Myerson Jun 8 '12 at 4:38
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I'm only a graduate student so I shouldn't give career advice about what to do, but I can say that it is not even uncommon to meet professional mathematicians whose undergraduate degrees were in physics or engineering. In fact it's not even terribly uncommon for someone who only has degrees in physics to end up working in a mathematics department. I know of at least one such case at Wisconsin (where I am a graduate student). –  Chris Janjigian Jun 8 '12 at 4:57
    
One of my favorite professors did his undergrad in physics and then switched to mathematics. –  Asaf Karagila Jun 8 '12 at 6:07
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This is getting too long for a comment.

The transition physics->mathematics is of course nothing unheard of (apart from the examples already given, see also Dan Shanks). I have met plenty of professional physicists with extremely strong background in mathematics, and I believe that they could change their field from physics to a suitable area of mathematics and become productive within a year or less if they so chose.

You certainly do not need a formal degree in Mathematics. Whether or not a degree is the most efficient way for you to acquire the necessary knowledge and skills, depends on how good you are at self-study versus guided study.

As for the last question, it all depends on what you mean by "well-versed", as well as on your own aspirations. It does not hurt to have a good overview of the different branches of mathematics, but that is something that comes over time. An undergraduate degree helps, but personally, I still don't feel that have a good overview of all of mathematics. Most mathematicians nowadays know two or three areas really well. Then they have a few other areas in which they would know how to phrase a question when approaching an expert, and might understand enough of the answer, when they need a specific result. Strictly speaking, if you want to work in combinatorics only, say, and do nothing else, then you would be able to find suitable problems. But firstly, it would limit your choice of problems, and secondly, you would find it unsatisfactory yourself. After all, I assume that the reason you want to go into mathematics is because you like mathematics, so a minimalist approach might not be the way to go.

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I think what turns off most people who consider switching into mathematics for graduate school is the required surgery. –  Will Jagy Jun 8 '12 at 6:03
    
@WillJagy: what exactly do you mean by that? I am not too knowledgeable about the admission process to graduate schools. –  ramanujan_dirac Jun 8 '12 at 6:14
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@ramanujan_dirac: I thought Will Jagy was making a joke about Milnor's surgery on a manifold technique, which I imagine most physicists involved in geometrization notions would know something about but aren't connoisseurs. But perhaps I'm over reading his comment. –  Dave L. Renfro Jun 8 '12 at 15:02
    
@ramanujan_dirac, I was indeed making a joke, but I was pretending that it would be required to, say, have one's tonsils out or have the appendix removed. So Dave gives me too much credit. I placed this here for Alex B. and did not give adequate thought to the fact that you might also look at this and be confused. My apologies. –  Will Jagy Jun 8 '12 at 15:45
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