Describe an experience that you have had or a concept you have learned about that intellectually excites you. When answering this question, you may want to consider some of the following questions: WHy does this topic excite you? How does it impact the way you or others experience the world? What questtions do you continue to ponder about it? 500 word limit"
Think my essay might be too general...
My main interests have always been associated with mathematics. I naturally have a talent for the field. Complex equations excite me, and there is no better satisfaction than solving a seemly impossible problem. However, as much as I love to apply my mathematical knowledge, my favorite aspect pertaining to the subject is proofs.
Proofs cannot be used to solve an equation. Instead, they serve to explain just why, exactly, those formulas or theorems work, proving that the methods are logically sound. A majority of people find this boring; they rather blindly attempt problems without wondering just why they're able to solve anything. However, wondering is the most exciting part of math. Take, for instance, the simple and well known Pythagorean Theorem. It states that for a right triangle, A squared plus B squared equals C squared, where variables A and B represent the two legs of the triangle and C being the hypotenuse. It seems obvious; of course that works, it is one of the most elementary theorems taught in geometry. But why is this true? When that question is asked, the previously simple theorem is dissected into complicated reasoning. Once this reasoning is understood, it is simply fascinating. It is akin to connecting the dots, in the sense that all of math is related to itself. For the Pythagorean Theorem, there are many ways to prove why it holds true. You can use other areas of geometry, such as trigonometric functions, or combine postulates. Either way, it is an excellent example of how intricately all aspects of math are related.
If the only two purposes of proofs were to prove theorems and demonstrate mathematical relationships, however, I would not find them as intriguing as I do. Mathematics is the backbone of the universe, and is the reason everything exists in the form that it does. Proofs show you in greater detail what that backbone looks like. They transport you into a different type of mathematics, one that is focused on discovering the underpinnings of how the world works. This then transitions into other areas of study, ranging from physics to economics.
The ways proofs are able to connect the world are too numerous to count. They will continue to excite me, because as more are discovered, knowledge will continue to reach new levels of depth, and there is no end to this process.
Think my essay might be too general...
My main interests have always been associated with mathematics. I naturally have a talent for the field. Complex equations excite me, and there is no better satisfaction than solving a seemly impossible problem. However, as much as I love to apply my mathematical knowledge, my favorite aspect pertaining to the subject is proofs.
Proofs cannot be used to solve an equation. Instead, they serve to explain just why, exactly, those formulas or theorems work, proving that the methods are logically sound. A majority of people find this boring; they rather blindly attempt problems without wondering just why they're able to solve anything. However, wondering is the most exciting part of math. Take, for instance, the simple and well known Pythagorean Theorem. It states that for a right triangle, A squared plus B squared equals C squared, where variables A and B represent the two legs of the triangle and C being the hypotenuse. It seems obvious; of course that works, it is one of the most elementary theorems taught in geometry. But why is this true? When that question is asked, the previously simple theorem is dissected into complicated reasoning. Once this reasoning is understood, it is simply fascinating. It is akin to connecting the dots, in the sense that all of math is related to itself. For the Pythagorean Theorem, there are many ways to prove why it holds true. You can use other areas of geometry, such as trigonometric functions, or combine postulates. Either way, it is an excellent example of how intricately all aspects of math are related.
If the only two purposes of proofs were to prove theorems and demonstrate mathematical relationships, however, I would not find them as intriguing as I do. Mathematics is the backbone of the universe, and is the reason everything exists in the form that it does. Proofs show you in greater detail what that backbone looks like. They transport you into a different type of mathematics, one that is focused on discovering the underpinnings of how the world works. This then transitions into other areas of study, ranging from physics to economics.
The ways proofs are able to connect the world are too numerous to count. They will continue to excite me, because as more are discovered, knowledge will continue to reach new levels of depth, and there is no end to this process.
