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Prompt #6:  Describe a topic, idea, or concept you find so engaging that it makes you lose all track of time. Why does it captivate you? What or who do you turn to when you want to learn more?

Sample Essay:


Every year, roughly 560 of the world’s greatest young mathematicians compete at the International Math Olympiad. 22 of those competitors, a modest 4% of the field, received a perfect score on their proof of the “Windmill Proof.” Intrigued by the legendary problem, I was compelled to compare my mind to the best in the world. Although the abstract question was extremely difficult, after researching the solution, the answer seemed entirely solvable to me. Not only am I confident that I could both recreate this proof and teach the solution to others, I also gained new insights for deciphering future problems. I am always striving to improve my mastery and intuition not only to solve these problems but to one day have an impact on the existing body of mathematics. 

I am never as fully engaged as when searching for solutions to complex math and strategy problems. Each layer presents a new challenge simultaneously requiring logic, creativity, and most importantly lightning-speed insight as I sort through the files in my brain. I felt disappointed with my elementary math classes; unlike other students who found the material boring, I was frustrated that the material was not challenging enough. The concepts were little struggle to master, as I had already studied them independently. My accelerated math teacher noted my desire for challenging problems and encouraged me to take the AMC8 (American Mathematics Competition) and thus introduced me to the world of competitive mathematics. I was drawn in immediately; my math classes were merely repetition of simple skills until the next formula, but the competitive mathematics exams required me to call upon all my knowledge and apply it in entirely new ways. Recently, I was working on an AIME problem that necessitated the strategic use of both algebraic manipulation and Vieta’s Formulas, and though I hadn’t been taught to combine these two concepts, my intuition conceptualized their synergy. The experience left me with a profound sense of accomplishment; I had “outsmarted” the problem.  


It may not shock the reader to learn that I am not an outgoing, social person: the crowded student section at sports games seems like an absolute nightmare. However, through higher-level mathematics I have found a social environment where I feel comfortable. Unlike the average teenager, I prefer to spend my time playing board games or solving puzzles and commonly feel isolated as my classmates’ and siblings’ interests rarely align with mine. Those feelings disappear when I am part of a math competition, working with fellow students in advanced classes, or playing my favorite game, Magic: The Gathering. My interests are not boring and lame to my peers; they share my love of math and strategy. I can talk to them about a tough problem or new concepts without looks of confusion and disinterest coming my way. I feel more at home in these communities than in other circles. During a Sunday class at CMU, my group came across a complex diagram from which we needed to find a specific angle. No one was able to single-handedly solve the problem, so we plotted the image on a whiteboard, and after spirited debate, we discovered a method of isolating the needed value. For these like-minded individuals and I, this experience was a social event; we challenged each other to think outside of the box and joyfully celebrated our eventual success.  


It is a personal goal of mine to dwell amongst the minds of those 22 competitors who received a perfect IMO score on the “Windmill Proof.” Although the IMO questions are just fictional by design, they require the same skill set to solve as do real world problems: both experience and insight. College is where I hope to not only impact the world of mathematics but also join a scholarly community that works collaboratively, is excited about complex problems, and pushes its members to traverse the depths of concepts that intrigue them. 

Prompt 6: Math

  • Paragraph 1: This prompt is different in many ways than the others - typically there is some element of persistence and accomplishment with each other prompt - here you want to discuss a unique and personal interest/passion in a way that only you can 

    • Unlike other essay types, here you reveal your values and personal traits through the passion you have for this subject or concept - whether creating, solving math problems, practicing/performing your art in front of others

    • Introduce us to the passion with an example that demonstrates a desire to continue or master the topic

  • Paragraph 2: Here you ground the audience with your story, chronologically within the paragraph, of how you became passionate or obsessed with subject

    • What were your actions after being introduced to the topic? Take us through the story of your growth - did you start solving new problems, reading about it more widely, playing more difficult pieces, etc. 

  • Paragraph 3: Here get into collaboration and mentorship: Who shares or informs your passion? How do you introduce this subject to others, or do you bring it to the community? You can give an example of growth here or overcoming a challenge within the relevant area

  • Paragraph 4: Personal goals for your passion - what do you want to ultimately accomplish, or is it a lifelong relationship with the subject that will never be mastered? How does it support or fit in with your academic/college and/or professional goals? How will this passion make yours and the lives of others richer and more complete? What are you bringing to your campus?

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