Answering "Why do you want to become a research mathematician?"-type questions in a statement of purpose

Question

How should one address the classic "Why do you want to become a research mathematician?"-type question that is normally asked in the statement of purpose when applying to Masters (and also) programs?

I've read (and I bet so has any admission board) lots of statements beginning with

(*) "I've always loved numbers and solving problems, which is the most rewarding thing of my life"

(or variations thereof), which seems like a rather lame way to start off.

I do have an enthusiastic love for mathematics and the challenges of research work, and have some "philosophical" reasons to dedicate myself to it (I've been mostly inspired by Prof. Thurston's answer to this question which was asked on MathOverflow), and a somewhat defined (although broad) area that deeply arise my interest (which I surely should mention). However, I'd really like to avoid seeming unprofessional (or outright creepy) as in passage (*), and trying to convince anyone that I've always been in love with my field "ever since I could take my first trembling steps". So my question is:

What points should you keep in mind to address the question "Why do you want to become a research mathematician?" in a statement of purpose without seeming unprofessional but communicating your genuine and deep passion? And what is actually expected?

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A related question is Choosing research ideas to include in a statement of purpose.

Answer 1

I can't speak for all mathematics graduate admissions everywhere, but when I was on the admissions committee for my department (UGA) we generally did not take the statements of purpose all that seriously. Most statements of purpose are indeed a bit dull and similar to each other. The particular question "Why do you want to become a research mathematician?" is certainly not explicitly asked across the board (somewhat crankily I could ask "Why are you asking that for a master's program? The degree needed to become a research mathematician is a PhD. Depending upon your local academic culture, getting a master's degree could either prepare you to enter a PhD program or it could be totally unnecessary for that.").

It's not a bad question, but to me a very acceptable answer -- really the best answer -- is because I really enjoy mathematics, I am good at it, and I am eager to learn and do more of it. Not to brag too much, but I am in fact a research mathematician. Why did I become one? Please see the above bold-faced text: even with the benefit of many years of retrospective, I don't really see a better answer than that. In fact, honestly I think the bold-faced answer is probably better than the wordier answers I gave in my early 20's: how mathematics is the best field because it has an amazing internal consistency and a level of rigor and certainty unmatched by any other intellectual endeavor, how mathematical theorems are eternal so proving them is a form of immortality, and so forth. Yikes. It's not so much that I don't believe these things anymore but rather that I don't find these beliefs very interesting or distinctive: I think they fall nicely under "because I really enjoy mathematics".

The problem with taking the personal statement too seriously is that the ability to write an excellent personal statement -- especially an unusually interesting or insightful one -- is only weakly correlated to success in a math PhD program. I looked at personal statements to see whether they were adequate, e.g.:

• Do they use flawlessly correct grammar, syntax and punctuation? Do they express their (not so complicated) ideas clearly? Do they convince me that this student has strong enough writing skills not to be dragged down by this in the future? (Many STEM-types have alarmingly weak writing skills, and for sure it drags them down. I take the GRE Verbal score very seriously.)

• Do they avoid gross misconceptions about what a math PhD program and a math research career will be like? I don't expect an incoming math PhD student to really understand either one: most don't, but they learn eventually and adapt accordingly. However some students are clueless so far beyond the norm that it becomes a risk that as soon as they arrive they'll think "Wait, what is all this??" and drop out in their first semester.

• Do they seem like a responsible person and not a snowflake who thinks that graduate school is a summer camp that they get paid to attend? (It happens...)

• Do they avoid sounding too weird? Yes, mathematicians can be weird, like many people, and the amount of allowable weirdness in the mathematical profession is probably greater than most. But it is still only a finite amount, and I know people who have the intellectual skills to be a mathematician but not the requisite level of socialization. It's not pretty but it's true.

If you avoid these and similar negatives in a personal statement and mostly just evince a sincere, not terribly pretentious or twee "I really like math", then I suspect you'll do fine with this part of your application. You would in my department, certainly.

Answer 2

Of course it would be unreasonable to expect/demand a sophisticated (either technically or psychologically) answer to this question, from a relatively young and inexperienced person, so that cannot be the use of this question.

My own reading of "personal statements" is as a sort of Rorschach test... allowing a gauge of the writer's maturity, sensibilities, and accurate anticipation of what grad school will be like, sharply different from letters of recommendation, transcripts, and such. Fluidity (or not) of writing is also evident. If/when I can hear the writer's "voice" in the letter, I find this very helpful in trying to visualize their future.

Some letters are, or seem, obviously duplicates of things-on-the-internet, or so ill-thought out as to be worthless except as evidence of disinclination to think things through (!). Some seem deliberately uncommunicative, which gives a strange impression. Some are childish.

Probably "sincerity" and/or "honesty" are best... although, yes, it is hard to be entirely honest when one knows that one is being appraised, and that manipulation-of-self can have an impact on one's future. I guess a point is that unless one is very adroit at "faking sincerity", it's better to not try. :) An inadvertently clumsy attempt at faking something is not a pretty thing. :)

After all, admissions committees know that most applicants are in the usual age bracket, so a certain immaturity or inexperience is expected. It's in the subtler, secondary features that admissions committees may find reason to make distinctions, and it's probably somewhat harder to "arrange" these, even in good faith.

Answer 3

We can't answer what amounts to a personal question here.

As @BorisBukh's comments, you have to answer with the kind of questions that interest you, and why you believe you will be able to provide (at least partial) answers to them.

You will obviously have better chances to be accepted if your questions are in line with the interests and expertise of the faculty where you are applying.

After question edit: What a commitee wants to know is if you already have some knowledge of the area, are really interested, and know what you are stepping into. They don't want people who find out halfway that they don't like research after all and drop out.

Answer 4

What points should you keep in mind to address the question "Why do you want to become a research mathematician?" in a statement of purpose without seeming unprofessional but communicating your genuine and deep passion? And what is actually expected?

What is expected is that you answer the question (honestly, as JeffE helpfully recommended). Nothing more, nothing less. We are not you and we do not know the answer. If the supposedly "creepy" (really? What makes it so?) passage (*) seems most correct to you, that's what you should write.

And if I may add a personal note, to me the fact that you are asking on Academia SE about how to address this question carries an unpleasant whiff of someone trying to game the system, i.e., trying to come up with some kind of "correct" answer to the question that would ostensibly be most pleasing to the admissions committee. Probably I am being a bit harsh on you in saying this -- I have no doubt you are sincere in your passion for math and just want to maximize your chances of acceptance -- but that's my gut reaction. If you ask me, I would much prefer an "unprofessional" answer from someone who actually gave the question proper consideration and wrote about their own feelings on the subject, to a polished and slick answer that feels "professional" because the writer received help from a committee of senior mathematicians on Academia SE.