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