i think the main reason i got into the cornell reu was that my background was very well suited for the project i applied for, which was in logic. i had done the penn state reu/mass program the year before, and one of the courses i took in the mass program was in computability theory, which was taught by one of the more famous logicians; i did well in that class and had that professor write me a recommendation letter. otherwise my stats were good but not necessarily phenomenal: i come from a very good small liberal arts school, my math gpa at the time was probably about 3.8, and beyond the introductory math classes i had taken 2 terms of combinatorics, 2 terms of abstract algebra, and 1 term each of number theory, odes, complex analysis, computability theory, geometric topology, and analytic probability theory, in addition to 3 terms of cs. my only real research experience at the time was the penn state reu i had done the year before, and i did not have anything published. i think i wrote a pretty good personal statement more geared toward why i was qualified to participate in the reu rather than why i really wanted to participate in the reu, though i did at least mention the latter.