Dear fellow posters and readers, I want to thank you ahead for your help.
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 questions do you continue to ponder about it?
I woke up to the fresh, misty northwest weather. A week before, my math teacher, Dr. Gorman, recommended that I attend a math seminar at Reed College on abstract math. I, a novice in abstract math, decided to go because I wanted to explore math beyond the conventional computational work and redundant formulating.
When I arrived, some other high school students and I went to a classroom where we met Thomas Wieting, our professor for the day. When we sat down, in front of us were giant parchments of drawing paper and some basic drawing tools. Mr. Wieting asked us to go away from the geometry of two dimensions and of three dimensions. He was going to guide us on a journey "to capture infinity" with hyperbolic geometry. We started out by drawing a large circle, and then we drew smaller, congruent circles and lines. We ended up with large patterns near the center of the circle and smaller, identical patterns near the edge of it. We drew in the second dimension what would be a top view of a paraboloid, a three dimensional parabola. The idea behind this drawing is that the figures near the middle of the paraboloid, although they look bigger, are exactly as big as the smaller sized figures near the edge.
I think to myself, how can two objects that I definitively drew as different be the same? That is what the hyperbolic plane does. Because the paraboloid continually goes up at an extremely rapid pace, thus what we cannot see is the paraboloid going to infinity. M.C. Escher experimented with this math and made masterpieces with it. Now we have the ability to experience it. This topic intellectually excites me because I get to learn and reproduce legendary mathematical work. Not only do we get to explore a new dimensional outlook on figures, but we get to explore a whole new dimension in mathematics, one that is warped and atypical. This topic was a great first exposure to abstract math, and this ultimately sparked my interest in learning more about the unknown. I had felt uncomfortable about learning what I did not understand, or comprehend, but I loved it.
Now I ponder what other great mysteries in math have yet to be discovered? What other dimensional outlooks are there, and how can they be used? But my questions span beyond math and into life, the soul, history. Maybe one day I will solve one.