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I know why I want a PhD in Math (I want to study math forever) and I know a little bit about what I like (pure vs. applied, probably something like algebra or algebraic geometry), but I don't feel like I have enough detail for a statement of purpose. I'm not applying to top programs. Is fit a big consideration in math? I feel like it's a lot easier for a history or psychology, etc., student to know what they want to specialize in. Am I expected to know? I'm a math major but my exposure just hasn't been that broad yet.

And how do you turn "I want to study math forever" into a (credible, desirable) statement of purpose?

Posted

I know why I want a PhD in Math (I want to study math forever) and I know a little bit about what I like (pure vs. applied, probably something like algebra or algebraic geometry), but I don't feel like I have enough detail for a statement of purpose. I'm not applying to top programs. Is fit a big consideration in math? I feel like it's a lot easier for a history or psychology, etc., student to know what they want to specialize in. Am I expected to know? I'm a math major but my exposure just hasn't been that broad yet.

And how do you turn "I want to study math forever" into a (credible, desirable) statement of purpose?

What you want to do with your statement of purpose is really qualify why you want to study math forever. You want to appeal to things like advanced classes and research experience which show that you know what graduate school is going to entail, and you enjoy those aspects of it. You should just think of mentioning an interest in something like algebra/algebraic geometry as being an important piece of evidence to indicate you know what "real" math is about and like it, not as much of a commitment to what you're going to study. Most people don't have a very good idea of what they want to do going into math grad school, especially if you're not applying to the top programs, and they're not going to hold you to anything once you get there.

They will probably want to see some kind statement about why you're applying there, and at least an implicit demonstration that you know what they do there. Obviously it's bad if you talk about liking something and the school doesn't have anybody in that area, because then you've demonstrated no potential interest in anything they offer. But you're not limited to statements like "I like algebra and you do algebra". You can even just mention that you like how a department has people in a wide variety of fields, since you're still undecided on what you want to do.

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