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I'm a first-year mathematics PhD student at an American university.

When I applied to graduate school I thought I would be doing math like I did for the past few years in college. However, after the whole senior year doing a priori estimation for 2-d NS equation(basically frequency analysis stuff in harmonic analysis), I got nothing but fully exhausted and want to try something else where I found the machine learning course on Coursera was really interesting and decided to explore more about that in graduate school.

I passed all qualifying exams before the first year started. I took a graduate statistics course and a computer science course in the first quarter to get a better understanding for machine learning, and found I was thrilled at high-dimensional statistics. Unfortunately there's no one in the department working in that field, so I started working with professors in the statistics department on several different projects which I really, for the first time in my life, found more interesting than I thought mathematics was in college. Now I don't feel like I will ever wish to work in any primary mathematics field, and I'm kind of alienated in the department which makes me feel sick and sometimes lonely (and often enough pure mathematicians tend to degrade statistics or applied math).

I know very clearly from the past year-long research experience with Statisticians that I am now much much more enthusiastic about high-dimensional statistics.

Should I be open to the idea of moving to a Statistics program? The only problem is that I may not be able to get a Master's degree due to departmental coursework requirement. Is it possible to transfer to another graduate program (either within University X or other university) without a master's degree from my current university? (I am pretty sure I can get quite good reference from my research professors, as well as several decent publications.)

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    Why are you not asking this at your university? The department head perhaps or even the department head where the stat guys are. Very simply put; if you are not happy now and would be much more happy doing stat that switch. Otherwise you will have a few miserable years and might even drop out... you should do what makes you happy – Mythio Jun 10 '14 at 7:58
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    i think that if you make this known to the right people at the department(s) it will always be possible to find a solution. Perhaps start from fresh in the stat department. – Mythio Jun 10 '14 at 8:06
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    Oh, just apply. You'll be fine. – JeffE Jun 10 '14 at 12:48
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    If you've been working with profs in the stats department, you should definitely talk to them and make your intentions known. They can help you in many ways. – Suresh Jun 10 '14 at 13:04
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    I think you should switch, even if you think you will loose years. Doing a research that you hate is a very bad idea fro PhD, professionally, personally. Doing two research well parallel is unsustainable. If for whatever reason your Math prof is not content without work (sometimes even if he is content), Stat will be blamed and your transition will be just get more painful. Try to make the switch early, when your Math Prof is still happy and will not feel that X years you spent there was waste of his time. – Greg Oct 8 '14 at 5:27
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Talk to your tutor or professor, they are there to help you and I always found mine very supportive. It sounds like you have thought about this. Find out what your options are they won't bite your head off for changing your mind. I changed direction twice before even getting to my Ph.D. then left that after 9 months when I realised it was not right for me.

Don't spend years of your life doing something you don't care for, you will be far happier and productive doing something you truly love. There is a good chance your profs and tutors will have zig-zagged through their careers as well.

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