It is very hackneyed. The adcom wants to hear about what subfields of mathematics interest you and what type of research you want to do. Do you want to explore number theory? Topology? Algebra? Partial differential equations? Pick a subfield and write about what you want to explore in that subfield.
Additionally, you shouldn't be mentioning anything from high school. It's better to say a few things about a math class you took in college or a research project you did that left a strong impression on you.
In other words, I think you need to discard this draft and start completely from scratch. I would write a little bit about a math class/subject area/past research project that left a strong impression on you. Then you can use this to segue into your research interests and what you'd like to explore about that subfield. It doesn't need to be super-sophisticated (many adcoms won't expect you to propose a startling revelation or new theorem or whatever in your SoP)... but you do need to give a good idea about the research you'd like to do in that subfield. Finally, you can tag on a fit paragraph where you mention some professors you'd like to work with, the strengths of the program, etc.
IA, especially that not every MS program in mathematics is going to specialize in the same type of mathematics. You really need to show the adcom how you fit within their program.
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
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Additionally, you shouldn't be mentioning anything from high school. It's better to say a few things about a math class you took in college or a research project you did that left a strong impression on you.
- Ray
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