The statement of purpose isn't really intended to be a philosophical statement - instead, it's a statement of academic purpose. Your main goal should be to talk about what you intend to research, and that should be supported by your previous experience. It needs to be specific about what types of issues you want to research (and unless you're a math genius I'd suggest not placing yourself in the running for solving Poincaré conjecture-class problems!) It also needs to be aligned to the departments you're applying to, because they'll need to find you an advisor. As for the anecdote that takes up most of your current statement, I'm not as down on anecdotes as some people. I do feel they can be useful, but to do so they need to be both highly unusual and directly related to the problem of study. This anecdote doesn't meet those criteria, so I'd cut it out entirely.
I think you need to start over. A good structure, IMO, is: one short paragraph introduction (what you're applying for specifically and what your general area of research will be); one medium paragraph previous work that applies to this (research, etc); one much longer paragraph outlining what you intend to study and how it fits with the program; and a conclusion paragraph targeted to fit each program you apply to.
I think you need to start over. A good structure, IMO, is: one short paragraph introduction (what you're applying for specifically and what your general area of research will be); one medium paragraph previous work that applies to this (research, etc); one much longer paragraph outlining what you intend to study and how it fits with the program; and a conclusion paragraph targeted to fit each program you apply to.
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