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-This paragraph is mostly unnecessary. Saying that you have the intensity, persistence, knowledge etc. means very little. Showing it is what an SOP is all about. The last sentence should absolutely be removed: their program is obviously designed to produce mathematical scholars and saying that you "hope" it will do so it a little strange. -It seems to me that this paragraph would be much more forceful if you elaborated on this paper you wrote and explained, in depth (for that is the major thing this SOP lacks), what you loved about it. What, specifically, interested you? Can you pursue the same (or similar) lines of inquiry in other instances? You give no specifics which compromises your ability to demonstrate depth of knowledge and careful consideration of your interests. -You do not have to pursue the area of interest you adopt in your SOP, but this sort of generalizing could easily portray you an uninformed and superficial in your pursuit of graduate studies. -If you love your job so much, why make this sort of career change? What's missing from your career that would be fulfilled by grad school? I'm not sure what your goal is with this paragraph. Again, you are saying how prepared you are without showing it. Why should they just accept everything that you claim here? -This paragraph is not a good idea. It basically shows that you are not serious about academics. Change this to say something about the determination necessary for completing your degree, its importance, how it didn't complete your education but motivated you to continue it. - So, you end this SOP by claiming that you've made this decision carefully. You need to demonstrate this - explain how your current situation is insufficient, what you would like to do that you are currently unable to (and "doing research" is not specific enough). -Also, they know that they have a strong mathematics program that enables graduates to do research, so why are you telling them this? -I think you've gotten off on the wrong foot here. My suggestion would be to concentrate on developing a specific set of questions which you would like to pursue. A good way to do this is to expand on the paper you mentioned and reveal what it was that interested you so much. Also, use your work and educational experience to explain why what you've done isn't sufficient. What, specifically, makes you want to trade your current life for an academic one? Your statement is so general it makes it difficult to believe that a) you really are interested b ) you know what you're talking about and c) that you've considered this choice carefully. -I don't want to be so critical but you hint at a few things that could be very productive for you in this essay (your work experience and drawn-out education) but you don't use them effectively. All that said, I'm not at all familiar with mathematics, but you need to focus on including more specifics, and showing what a great candidate you are, not just saying it. Good luck! and don't be discouraged. These things are very hard to write!

- This is sort of strange. First you undermine your own work, and then you call it "useless." Perhaps it was insufficient, or a beginning, but calling it useless is probably not the best idea. If you're trying to contrast your feelings at that moment with later realizations then you need to follow the "initially" with another sentence that explains your revised understanding. - The sentence beginning "Human Trafficking" can be deleted, it doesn't provide any information that connects it to the sentence before. If you're trying to explain why it made you feel like your work was useless (or compromised) then you need to make a strong connection (that connection being, perhaps, that there wasn't a strong connection) between your own volunteer work and the human trafficking problem. - I think you should also delete the sentence about you feeling "naive." Explaining what you felt isn't as compelling as explaining what it make you realize. I think this is a distinction you need to consider carefully. You speak about how you felt but not in terms of how it altered your understanding. Rather, you tie this experience to a desire to overcome your own feelings of powerlessness. I don't think you really want to do this. It's a better idea to explain what it made you realize about the world around you and how continuing your education will provide you with the necessary resources to provide more substantial aid in the future. - Is this actually true? Is Super Awesome University X the only place where you can study these things? If it TRULY is then fine, otherwise you will sound ill-informed. - Instead of just name dropping, it would be better if you gave a sentence or two about how their research, in particular, interests you. - This paragraph needs work. I don't know much about international relations but it seems to me that you basically just said you're interested in everything. You named transnational crimes, weapons proliferation, terrorism, negotiation and coercion. Isn't this a little bit too diverse? maybe not, but just a thought. I think you should try to refocus this paragraph. Try to state your interests and demonstrate some depth of knowledge about those interests, not just explain the categories of IR that interest you, but the particularities as well. The part about the internships should be moved to the preceding "fit" paragraph. You need to do a copy-edit as well. -Don't undermine your degree! I like the sentence about how your English degree provides you with the tools necessary to succeed, but you don't need to act as if it puts you at a disadvantage. -Highlight your work experience!! But you need to do this differently. Instead of explaining what skills it gave you focus on what it taught you about the world. This paints you as someone committed to learning about the world and what work needs to be done in the future, rather than someone who has work experience. Those are just some suggestions. But I think overall you need to focus more on explaining how your experiences have alerted you to certain problems which you are interested in fixing - and continuing your education will put you in a better position to do this. It should not be about overcoming your own feelings or demonstrating what you've already learned, but rather what you have left to learn.