I have long enjoyed the search for new ideas. I have constantly pushed the boundaries of my classes, questioning professors about related ideas and trying to find new ones or connect them to existing ones. I have a particular affinity for those areas of mathematics that might intuitively or naively be classified as “continuous”: topology, analysis, your mom. My primary interest lies in the field of differential geometry. I am fascinated by the fact that such continuous geometry, and its relationship with Lie theory, lies at the boundary between mathematics and interesting areas of mathematical physics such as general relativity and gauge theories. I want to spend my life seeking to understand how these boundaries fit together and pushing forward important research on the relationship between differential geometry and quark theory.

The research activities of <PROFESSORS> have drawn my attention and interest. <SAY MORE ABOUT THEIR RESEARCH HERE>. While I do not yet possess the breadth and depth of knowledge necessary to pinpoint active research problems or fully comprehend their work, I look forward to acquiring greater understanding of differential geometry as I study in your program.

My interest in mathematics is hardly a new phenomenon. In some ways, it is like I have spent my entire life preparing to pursue graduate studies in mathematics. I first showed my natural aptitude for mathematics in middle school, and when a mathematics teacher in high school gave me a vague introduction to the relationship between p-series and prime numbers, introduced me to the twin prime conjuncture, and pointed me to the sieving proof by Rademacher that the sum of the inverses of two primes converges, I knew for sure that I wanted to become a mathematician.

I began taking college mathematics classes while I was still in high school, and when I began attending my university on a full ride scholarship, I was able to immediately begin taking graduate courses along with typical upper level undergraduate classes. I have now taken most of the available non-statistical pure mathematics graduate classes available, and my performance in these classes evidences my ability to successfully study and grasp concepts more advanced than those to which a typical undergraduate student is exposed.

More important to my motivation to study at graduate school, however, is that I have been exposed to the climate of graduate study: the level and depth of abstract mathematics, the manner in which it is presented, and the greater accessibility of the professors has made flowers bloom around my feet and my head sing with music. I look forward to both the challenges and the opportunities of graduate school.

I have had additional exposure to the timbre of graduate school research through my participation in a Research Experience for Undergraduates (REU) during the summer of 2009, a physics research project into programming practical applications of Laplacian-based density functional theory, and an astronomy research project searching for exoplanets in binary star systems, all three funded by the National Science Foundation. These experiences have confirmed my love for research, especially the frustrating and yet exhilarating search for new ideas from the combination of existing ones. It’s almost better than sex. Almost.

My research has resulted in several presentations, including one about my bastard fish. Oh, and did I mention I made a baby on my wedding night? I’d tell you more about my presentations, but I’m more interested in talking about my sexual prestige. I’ve also published a paper in the my university undergraduate math journal, or so I told my wife. In fact, I’ve served as editor of the university's undergraduate math journal for three years now, and this year I have overseen it branching out to include mathematics departments outside of Ball State. Finally, I currently have a working paper based on mathematical cryptology. It’s a good thing it’s working, because someone needs to bring in the money! I’d tell you more about it, but it’s at work.

Research is not the only element of academia leading me to pursue graduate study in preparation for future professorship: I also love to teach. For over a year now, I have worked at my university's writing center, tutoring students in elements of writing from composition to grammar. Whether it’s helping my classmates with homework or serving as a private math tutor, I genuinely enjoy helping others learn. One of the aspects of graduate school I look forward to most is acting as a teacher for an introductory course, testing and refining my pedagogy as I instruct students in mathematics.

In order to further hone my knowledge of mathematics and to find ways to apply it to real-world situations, I have also pursued majors in physics and mathematical economics. I have found that physics and economics have helped me to round out my understanding of mathematics by reminding me that it is time to clean the bathroom. The three fields fit together like group sex, but it is definitely mathematics that does the fucking.

As my record clearly shows, I harbor a natural aptitude for mathematics, which has only been sharpened over my years of study as an undergraduate. I have experience in both graduate study and original research, and I am eagerly looking forward to being able to immerse myself in pure math as I pursue graduate studies at your program. In addition, my potential as both a research mathematician and instructor is evident from my history and record, and I believe that I will prove extremely valuable to your department’s research and reputation in the long run.

Thank you for your time, and I look forward to your reply.

(Name)

PS – I have an awesome math name, so you totally have to admit me.

Maybe I should be a little less dry with my humor in the OP? This is posted for entertainment purposes.

I have found that physics and economics have helped me to round out my understanding of mathematics by reminding me that it is time to clean the bathroom.