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I am applying for Ph.D. programs in pure mathematics. One of the confusions I have about writing a Statement of Purpose is whether I should concentrate on the things I did (mentioning facts: REUs, Courses, Talks, Putnam exam, Teaching) or whether I should be more poetic and write about why am I a person who wants to do research, why am I capable of doing it, and why do I love mathematics. If I have mentioned some information already in one of the parts of my application, is it bad if I write about it again in my Statement of Purpose?

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