My application to UNC.
read moreComplete each of the following sentences about yourself. Don’t think too long or too hard; just help us get to know you better. Your responses could be as short as one word or as long as about 20 words—no longer, please. Dream job: Mathematician Most overrated superhero: All of them Most underrated superhero: None of them Former kindergarten fear: Heights Favorite movie: "Whatever Works", directed by Woody Allen Favorite place to be or thing to do: Intuitively understand a mathematical principle Advice for adults: Let the generation following you think differently Gadget that needs inventing: Touch screen Apple laptop What's your latest discovery? What do you hope to learn next? I’ve recently discovered that one of the best ways to learn is taking by a risk. I don’t mean this in the conventional way of “learning from your mistakes”. Rather, you can learn from your unconventional successes. That’s what learning from your mistakes is: learning from doing something that’s unconventional. This discovery came from my newfound desire to have a more active role in my intellectual development. I’ve discovered that learning is by no means passive, despite it being treated as so by many students and teachers. One of my Montessori teachers who taught me for ten years would always tell us: “If thinking were easy, there would be more of it”. I challenge myself to think; I make the extra effort to question. I do so without any extrinsic incentive and sometimes I even encounter resistance. It’s this discovery that has taught me to persevere because I know that the effort will be worth what I learn. “It is impossible for a man to learn what he thinks he already knows.” -Epictetus I read articles of opinion and I listen to my friends’ thoughts but I ultimately make sure that I know what it is that I think. I don’t want to be an unoriginal cog, vacuously regurgitating what other people say. I think it’s wrong to close yourself off from other people’s opinions but I don’t think it’s not wrong to question and wonder for yourself before you accept them as your own. Sometimes I’ll even apply the scientific approach of a blind experiment when I’m being exposed to a new concept: I’ll ask them to first tell me the basis of the topic so that I have time to think about it for myself before they tell me the common outlook or their own opinion. Abandoning the fear of being wrong is probably been the most conducive action to my learning. The fulcrum of this abandonment was reading “What do you care what other people think?” by Richard Feynman. The power of that question is formidable. I find myself asking it every day: when I’m considering asking a question in my Calculus class at UNC or when I consider going to talk to the professor after class about solving a problem a different way, or wondering why a solution works in a particular way. Without having done this, I would have missed out on numerous valuable hour-long, enlightening conversations with my professor. It’s because of this discovery that I’ve begun to accentuate my tenacity in the pursuit of knowledge. It’s this tenacity that opens up the entire world for me; it makes it so that there’s nothing that I can’t learn next. What's your latest discovery? What do you hope to learn next? I’ve recently discovered that one of the best ways to learn is by taking a risk. I don’t mean this in the conventional way of “learning from your mistakes”. Rather, you can learn from your unconventional successes. That’s what learning from your mistakes is: learning from doing something that’s unconventional. This discovery came from my newfound desire to have a more active role in my intellectual development. I’ve discovered that learning is by no means passive, despite it being treated as so by many students and teachers. One of my Montessori teachers who taught me for ten years would say to his students: “If thinking were easy, there would be more of it”. I challenge myself to think; I make the extra effort to question. I do so without extrinsic incentive and sometimes even against resistance. It’s this discovery that has helped me to persevere despite the absence of reinforcement because I know that my effort will be worth what I learn. “It is impossible for a man to learn what he thinks he already knows.” -Epictetus I read articles of opinion and I listen to my friends’ thoughts but I ultimately make sure that I know what it is that I think. I don’t want to be an unoriginal cog, vacuously regurgitating what other people say. I think it’s wrong to close yourself off from other people’s opinions but I think it’s proper to question and wonder for yourself before you accept them as your own. In the interest of remaining aware of my untainted perspective, I’ll sometimes apply the scientific approach of a blind experiment when I’m being exposed to a new concept: I’ll ask the introducer to first explain the basis of the topic so that I formulate my thoughts before I’m inevitably exposed to the conventional outlook. Likely the most necessary step in actualizing what I learned from my discovery was abandoning the fear of being wrong. The fulcrum of this abandonment was reading “What do you care what other people think?” by Richard Feynman. The power of the book’s title is formidable; I find myself asking it every day: when I consider asking a question in my Calculus class at UNC or when I contemplate going to talk to a professor after class about an alternate method of approach. Without having done this, I would have missed out on invaluable hour-long enlightening conversations with my professors. It’s because of this discovery that I’ve begun to further reinforce my tenacity in the pursuit of knowledge. It’s this tenacity that opens up the entire world for me; it makes it so that there’s nothing that I can’t learn next.Some additional notes that didn't make it into the essay
What's your latest discovery? What do you hope to learn next? I recently had some enhanced insight into the representations of three dimensional objects using transformations of two dimensional shapes. Although the rudimentary insight is taught early that the cross sections of a sphere, for example, are simply circles with varying radii, I expanded the insight to more of a Calculus approach. I came to wonder about this aspect of shapes when I was resizing a circle on my computer’s word processor. I realized that, if we were to stack each of the instantaneously formed circles formed as we resized the figure, we could create a sphere. I realized that the figure we formed was dependent on the rate of resizing (e.g. if the rate of resizing were zero, we would form a cylinder). I had to formalize this resizing to something more mathematical/tangible; I realized that resizing a circle on a computer is changing the intersection of two of four lines tangent to that circle. When resizing the circle to maintain its proportionality (and thus keep it a circle), we move this tangent intersection point along a line that makes a 135 degree angle with the horizontal. The questions that immediately arise from this realization are: What velocities and accelerations of this point lead to the formation of shapes such as a cone or a sphere? We are essentially drawing out the shape through an axis that’s orthogonal to the computer screen. We are defining cross sections along that axis. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Alternate Topic One of the best ways to learn is taking by a risk. I don’t mean this in the conventional way of “learning from your mistakes”. Rather, you can learn from your successes. The successes that are unconventional. That’s what learning from your mistakes is, learning from doing something unconventional. This partly comes from my newfound desire to have a more active role in my intellectual upbringing. Learning is by no means passive, although it is often treated to be by students. “It is impossible for a man to learn what he thinks he already knows.” -Epictetus My middle school teacher who taught me specifically for ten years would always tell us: “If thinking were easy, there would be more of it”. I challenge myself to think; I make the extra effort to question. I do so without any extrinsic incentive and I sometimes even encounter resistance. I read articles of opinion and I listen to my friends’ thoughts but I ultimately make sure that I know what it is that I think. It’s wrong to close yourself off from other people’s opinions but it’s not wrong to question and wonder for yourself before you accept them as your own. Sometimes I apply the scientific approach of a blind study when I’m being exposed to a new concept: I’ll ask them to first tell me the basis of the topic so that I have time to think about it for myself before they tell me more about it. One’s understanding is truly tested when they try to teach. Abandoning the fear of being wrong was likely the best thing I’ve ever done. One of the recent developments was reading “What do you care what other people think?” by R.P. Feynman. The power of that question is overwhelming. I find myself asking it every day. When I’m considering asking a question in my Calculus class at UNC. When I consider going to talk to the professor after class about solving a problem a different way or wondering why this problem works this certain way. Without having done this, I would have missed out on numerous hour long, enlightening conversations with my professor whose value were enormous to me. Tenacity in the pursuit of knowledge is a remarkably profound quality. If I had not abandoned this fear, I would know far fewer things. Being able to stop someone to ask them a question before they continue, is going to allow you to understand better what they say next. When I’m wondering if I should say something that could potentially be embarrassing. I’ve learned not to let social pressures guide my actions. To do so is to die. Developing my own way of thinking has been my most consequential development. The scariest experience I think I’ve had is realizing a thought I’ve had wasn’t my own. Your thoughts really define you; they make you who you are. Self-delusions are an essential part of living happily, but they inhibit progress and improvement. You wanted to know why. Curiosity is more important than intelligence. Sometimes you have to put yourself in the position of feeling like an idiot to learn and really understand. But, doing so makes you better than those who have the illusion of understanding. I’ve learned that The path doesn’t make the traveler successful, it’s the kind of mind that chose the path. Originality is at the heart of my mind.