muki muki
"What’s infinity times infinity?" my mom asked.
"Infinity!" I chirped.
I paused, and my three-year-old brain exploded when she nodded. One times infinity is infinity, but how could infinity times infinity still just be infinity? Inspired by this "magic," I participated in all sorts of math competitions in the years that followed. Yet, somewhere along the line, I traded my mathematical passion for the formulaic memorization needed to win. The limits of math became finite.
One day, I noticed a book tucked away in the top corner of my bookshelf: Contemporary Abstract Algebra. The multicolored optical illusion on its cover intrigued me. I opened it. The foreign symbols inside left me baffled. Though I thought I’d explored all math had to offer, here was blatant proof of the limited scope of my mindset.
In an attempt to satisfy my curiosity, I enrolled in a mathematics program focused on symmetry. At first, the daily lessons and problem sets seemed impossible, but after pouring over notes and online papers, things began to make sense. As I delved deeper into the equations and formulas, I discovered a transcendental elegance in the intricate simplicity of proofs and the innate symmetries in the world. When I returned from the program, mathematics once again extended beyond the finite—the piano compositions I’d been practicing corresponded to group theory, and my M.C. Escher Circle Limit III poster held hidden gems of mathematical genius.
Mathematics is, once again, infinite.
Overall Feedback
Summary
The essay explores the student's rekindled passion for mathematics, moving from a child's confusion to an adult's deeper understanding. Enhance the clarity by detailing the symmetry program and elaborating on how it reignited your enthusiasm. Reflect on specific moments that shifted your perception of mathematics as infinite, using concrete examples for abstract ideas. Ensure smooth transitions between ideas and employ a reflective, engaging tone, avoiding clichés, and refining grammar. Phrases like this resonate but lack specificity. Provide an example of a proof or inquiry that demonstrated this elegance, making it relatable and clear how it influenced your perception of math.
Brief essay summary and detailed feedback, including suggestions for improvement.
Organization
Organize your essay by weaving a coherent thread from childhood wonder to mature understanding. Reorder thoughts to elaborate on your rediscovery of math before discussing its relation to music and art. Start with a captivating introduction and move logically through your experiences, development, and insights. Refine transitions between paragraphs to maintain a smooth and engaging narrative.
Analysis on the essay's logical flow of ideas and paragraph breaks.
Clarity and Style
Focus on simplifying complex phrases like "The limits of math became finite" for clarity. Replace clichés like "my three-year-old brain exploded" with language reflecting genuine wonder. Use vibrant language to convey discovery moments, maintaining a reflective tone. Ensure grammatical precision, correcting phrases such as "pouring over notes" to "poring over notes."
Edit suggestions regarding jargon, conciseness, varied sentence structure, and tone.
While it's interesting that you engaged in competitions, specify one or two significant events or achievements. This will make your experience more vivid and illustrative of your passion. Consider providing an anecdote that highlights your involvement.
Yellow highlights indicate that there is potential in this part of the essay, but it needs some work. Expect 5-8 yellow comments per 250-words.
This is a strong metaphor, but explore it more deeply. Discuss specific limits you encountered or how this perspective affected your motivation. Adding a short example can clarify and enrich the metaphor's impact.
This sentence is weak because it lacks connection to the essay's main narrative. Clarifying its significance to your mathematical journey could strengthen the transition to your exploration of abstract algebra.
Red highlights identify the weakest parts of the essay. Thorough analysis on how to improve it. The top 2-3 weakest parts of the essay will be commented on.
"Pouring" should be corrected to "poring". "Poring over" means to study or read something carefully, which is the correct expression in this context.
Orange highlights pinpoint specific instances of grammar issues or typos accompanied by correction suggestions. There will be an unlimited number of orange comments for grammatical errors.
This sentence effectively conveys your engagement and enthusiasm for complex mathematics. It's impactful because it shows your committed effort to understand challenging subjects, highlighting personal growth and depth in your academic interests.
Blue highlights showcase the strongest points in your essay! Comments on what you’re excelling at. You can expect to see the best 1-2 lines in the essay annotated.
This conclusion nicely references the essay's beginning, but it could be more impactful. Expand briefly on how this renewed view of mathematics will guide your future endeavors or studies, adding a personal touch to your closure.
This interdisciplinary connection is intriguing. Explain a bit more about the relationship between music and group theory in one sentence. Doing so will help admissions officers understand your unique analytical perspective and passion for both subjects.
This concluding line poignantly ties back to the opening and represents the regained wonder in your exploration of mathematics. It leaves a resonant image of your renewed passion with the reader, making it memorable.