## Cannot tell exactly what research I want to do

### Cannot tell exactly what research I want to do

Hello everyone!

So, I want to apply for PhD in pure math. I have an excellent GPA (4.0), a research experience (bachelor thesis and master thesis, both in operator theory, the second one in more advanced, both are unpublished) and I expect to receive pretty high scores on GRE math subject, GRE general scores are V153/Q168. However, I have one gap which I cannot fulfil - I cannot say in details what I want to study.

The situation is simple: my university specialize mostly in analytical areas - mathematical analysis, complex analysis, operator theory, PDE, mathematical physics, you name it. However, algebraic disciplines are presented as supplements for information security theory (signal coding theory, cryptography, etc). It turned out that I enjoy group theory, ring theory and things like that way more than operator theory. I took every course in algebra which I could but due to the family issues I cannot change a school for master degree and, as a consequence, cannot have a research in algebraic fields. Now I want to apply for a PhD program, but I cannot state directly "I want to study object X to prove the properties Y and Z, and contribute to theory A" because I have never done a research in algebra and I don't know open and perspective problems in it as well as modern techniques or results. I can only say general words that I want to study group theory\algebraic geometry\group representation theory\ect. I feel it is just not enough to be accepted to any school, and I don't know what to do.

Should I just write general phrases like "I am interested in X, because I took courses in it in which I performed excellent, and I read books Y and Z in it and now I am reading book A and book B in it, and I love all of it" in my personal statement? Are there anyone with the same problem to consult with?

Thank you for all responses in advance.

So, I want to apply for PhD in pure math. I have an excellent GPA (4.0), a research experience (bachelor thesis and master thesis, both in operator theory, the second one in more advanced, both are unpublished) and I expect to receive pretty high scores on GRE math subject, GRE general scores are V153/Q168. However, I have one gap which I cannot fulfil - I cannot say in details what I want to study.

The situation is simple: my university specialize mostly in analytical areas - mathematical analysis, complex analysis, operator theory, PDE, mathematical physics, you name it. However, algebraic disciplines are presented as supplements for information security theory (signal coding theory, cryptography, etc). It turned out that I enjoy group theory, ring theory and things like that way more than operator theory. I took every course in algebra which I could but due to the family issues I cannot change a school for master degree and, as a consequence, cannot have a research in algebraic fields. Now I want to apply for a PhD program, but I cannot state directly "I want to study object X to prove the properties Y and Z, and contribute to theory A" because I have never done a research in algebra and I don't know open and perspective problems in it as well as modern techniques or results. I can only say general words that I want to study group theory\algebraic geometry\group representation theory\ect. I feel it is just not enough to be accepted to any school, and I don't know what to do.

Should I just write general phrases like "I am interested in X, because I took courses in it in which I performed excellent, and I read books Y and Z in it and now I am reading book A and book B in it, and I love all of it" in my personal statement? Are there anyone with the same problem to consult with?

Thank you for all responses in advance.

### Re: Cannot tell exactly what research I want to do

A lot of my friends who went on to graduate school in Mathematics didn't know exactly what they wanted to research in. I don't think graduate schools expect you to know exactly what you want to research in.

### Re: Cannot tell exactly what research I want to do

AMGMScrub wrote:A lot of my friends who went on to graduate school in Mathematics didn't know exactly what they wanted to research in. I don't think graduate schools expect you to know exactly what you want to research in.

AMGMScrub, did any of your friends not know what they wanted to research after Masters? If yes, it would be very helpful if you could share some schools they went for PhDs.

### Re: Cannot tell exactly what research I want to do

They went straight from undergraduate to graduate school. No masters. I know several that went to UCLA. One that went to MIT. I knew some that went to Berkeley. The research experiences they had were REUs.

I don't know whether the OP is international or not. But these people I knew were domestic. Not sure that says much.

I don't know whether the OP is international or not. But these people I knew were domestic. Not sure that says much.

### Re: Cannot tell exactly what research I want to do

The problem is that I want to change the area of my research. If I wanted to apply for research in operator theory, I would be able to describe the area and figure out what I want to do. Still not sure that I will be accepted...

### Re: Cannot tell exactly what research I want to do

I was pretty vague about my interests (I said the general area of things I like, and what intrigued me about it, so that maybe they could gauge what type of thing I liked if not the exact field), and got into 6/8 of the schools I applied to. The ones I didn't get into are ranked in the top 10 - I don't really think it was my vagueness alone that kept me out of those.

Math isn't like other fields. Especially in the US, they don't expect you to really know what you want to study. Most people applying haven't seen much "real" math at all, so how could they possibly know?

Math isn't like other fields. Especially in the US, they don't expect you to really know what you want to study. Most people applying haven't seen much "real" math at all, so how could they possibly know?

### Re: Cannot tell exactly what research I want to do

Yeah, I had such thought in my head that in math it is much more difficult to explain your research goals than in other areas. Thank you, guys, you give me additional support. By the way, MathCat, in what schools did you apply?

### Re: Cannot tell exactly what research I want to do

I applied to 5 schools in the US - all were ranked in the top 30ish. I also applied to a few schools in my own country. If you want to know specifically where I applied, I can PM you.