Using the quotation below as a jumping off point, tell us about an event or experience that helped you define one of your values or changed how you approach the world.
"Some questions cannot be answered./ They become familiar weights in the hand,/ Round stones pulled from the pocket, unyielding and cool."
Jane Hirshfield, poet, Princeton Class of 1973
I hate proofs, I concluded.
The words were neat and tiny, and took up about half of the chalkboard. There were no familiar plus/minus signs, fractions, exponents, or even a hint of an equal sign anywhere. The structure of symbols and numbers that I was used to seeing was no longer there. It was replaced with convoluted words, therefore signs, and Q.E.D's. The writing on the board made absolutely no sense to my naive, ninth-grader mind, and all I could do was helplessly copy it down, word for word as I drown into more confusion as my math teacher began to explain it.
Worst of all, it was a proof on about how two points can make a line.
By the end of middle school, I was riding on a 98 average in math, bogged down only by careless mistakes that occurred because I didn't bother going over my tests after I finished them. I understood the concept of bases and powers, had the quadratic equation down to a T, and knew how to multiply binomials in my head.
I thought I was ready. I thought high school math was going to be the same plug-and-chug deal they handed out in middle school. Stick the numbers into the appropriate equation, get your numbers, and circle the correct answer choice. I thought the most difficult part of math was going to be memorizing extra-complicated equations and performing multi-step problems.
Then, math honors happened.
I had to prove things existed. I had to prove the facts that I once thought were common sense and were kindly given to me in math workbooks. Every fact and equation, every line, polynomial, and shape came from somewhere. They were all derived from something, and those somethings were derived from something else, and everything was derived from Postulates.
Postulates are the Ten Commandments of math. It is the set of inescapable truths that is universally observed and lays the foundation of mathematics. Some of them are painfully obvious, but from simple axioms come forth copious amounts of theorems waiting to be proved in this way or maybe that way, like trying to find eight different creative paths to go from point A to point B.
I left math class, dazed. Everything that I once believed was math was destroyed in the short span of 42 minutes. All that I knew before was nothing more than the skeleton of math - the basic operations, simple algebra - and that day I began to see its flesh, its organs, and the blood that makes the system run.
Frankly, I rejected the notion of a proof at first. The concept of a proof still eluded me. It was common sense. Of course two points made a line. You can clearly draw two points and connect them, just like a three-year-old can on a connect-the-dot picture. Why did anyone need to prove something that was just so fundamentally obvious?
Eventually, I stopped questioning that. Forget the greater benefits of applied geometry and calculus. Proving theorems and equations was fun. To start from the very beginning and reconstruct the world in math is art. It is the pursuit of knowledge simply for the sake of knowing the proof of an existence.
As second term freshman year began, I found myself launching into circle geometry. There were more theorems to prove than ever, but the esoteric terminology and signs were no longer strangers. I found myself using therefore signs and Q.E.D's. My thoughts were no longer constrained to the rigid structure of basic arithmetic symbols, but found freedom in prose and the Greek alphabet. I poured hours struggling to figure out how sin (a - b) = sinacosb - cosasinb, or why Ptolemy's theorem worked.
If some questions cannot be answered, I'll prove it.
I feel like that this essay is sort of all over the place. I think it's strong at certain points, but is weak at other times. Should anything be expanded/ cut out? Is the ending too abrupt? Do I sound incredibly pompous for including a number grade? Did I even address the prompt correctly?! I'm not even sure if I'm supposed to make a reference to the poem or something. Also, if there are any grammatical errors, please let me know. Thank you. (:
"Some questions cannot be answered./ They become familiar weights in the hand,/ Round stones pulled from the pocket, unyielding and cool."
Jane Hirshfield, poet, Princeton Class of 1973
I hate proofs, I concluded.
The words were neat and tiny, and took up about half of the chalkboard. There were no familiar plus/minus signs, fractions, exponents, or even a hint of an equal sign anywhere. The structure of symbols and numbers that I was used to seeing was no longer there. It was replaced with convoluted words, therefore signs, and Q.E.D's. The writing on the board made absolutely no sense to my naive, ninth-grader mind, and all I could do was helplessly copy it down, word for word as I drown into more confusion as my math teacher began to explain it.
Worst of all, it was a proof on about how two points can make a line.
By the end of middle school, I was riding on a 98 average in math, bogged down only by careless mistakes that occurred because I didn't bother going over my tests after I finished them. I understood the concept of bases and powers, had the quadratic equation down to a T, and knew how to multiply binomials in my head.
I thought I was ready. I thought high school math was going to be the same plug-and-chug deal they handed out in middle school. Stick the numbers into the appropriate equation, get your numbers, and circle the correct answer choice. I thought the most difficult part of math was going to be memorizing extra-complicated equations and performing multi-step problems.
Then, math honors happened.
I had to prove things existed. I had to prove the facts that I once thought were common sense and were kindly given to me in math workbooks. Every fact and equation, every line, polynomial, and shape came from somewhere. They were all derived from something, and those somethings were derived from something else, and everything was derived from Postulates.
Postulates are the Ten Commandments of math. It is the set of inescapable truths that is universally observed and lays the foundation of mathematics. Some of them are painfully obvious, but from simple axioms come forth copious amounts of theorems waiting to be proved in this way or maybe that way, like trying to find eight different creative paths to go from point A to point B.
I left math class, dazed. Everything that I once believed was math was destroyed in the short span of 42 minutes. All that I knew before was nothing more than the skeleton of math - the basic operations, simple algebra - and that day I began to see its flesh, its organs, and the blood that makes the system run.
Frankly, I rejected the notion of a proof at first. The concept of a proof still eluded me. It was common sense. Of course two points made a line. You can clearly draw two points and connect them, just like a three-year-old can on a connect-the-dot picture. Why did anyone need to prove something that was just so fundamentally obvious?
Eventually, I stopped questioning that. Forget the greater benefits of applied geometry and calculus. Proving theorems and equations was fun. To start from the very beginning and reconstruct the world in math is art. It is the pursuit of knowledge simply for the sake of knowing the proof of an existence.
As second term freshman year began, I found myself launching into circle geometry. There were more theorems to prove than ever, but the esoteric terminology and signs were no longer strangers. I found myself using therefore signs and Q.E.D's. My thoughts were no longer constrained to the rigid structure of basic arithmetic symbols, but found freedom in prose and the Greek alphabet. I poured hours struggling to figure out how sin (a - b) = sinacosb - cosasinb, or why Ptolemy's theorem worked.
If some questions cannot be answered, I'll prove it.
I feel like that this essay is sort of all over the place. I think it's strong at certain points, but is weak at other times. Should anything be expanded/ cut out? Is the ending too abrupt? Do I sound incredibly pompous for including a number grade? Did I even address the prompt correctly?! I'm not even sure if I'm supposed to make a reference to the poem or something. Also, if there are any grammatical errors, please let me know. Thank you. (:
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