Admitted: Princeton Early Action
I look around, surrounded by the universal darkness which has no bounds. All I have is a freshly made and unused piece of white chalk. For the next unimaginable length of time, my head reverberates with only one statement: Show that if a manifold Mg × Mh is homotopic to another manifold Mg’ × Mh’ then gh = g’h’. In this darkness I cannot see, but my guiding light, the piece of chalk, is with me. I convince myself to draw a path following solely based on my previous knowledge and instinct. As I walk around, I notice an inconsistency. The path I am walking stays the same and only brings me back to where I originally was, but I want to explore this place and find what this phrase in my consciousness means, not walk in circles. With my mind still sharp and charged, I draw myself a new path. This time when I proceed forward, I encounter a bifurcation. Do I go left or right? Who cares. I take the leap of faith and blindly choose one side as either path seems equally as good as the other. Along this path, I see different geometric shapes, some which look like eggs, some which look like teacups, and others that are entirely within their own category. These objects seemed abandoned by others, so I decide to take a few, for I never know when it will be useful.
Continuing, I proceed forthwith for the next few hours. The walking only makes me enervated, exasperated at the lack of progress. For not only is the darkness still present, but it looks even murkier now. I want to give up and submit to whatever holds me. After a bit of self-pitying, I remind myself that if I can escape the darkness now, I will not have to deal with this later on. Spurred by this thought, I keep walking and trip over some mysterious tools, including a chisel. Again, I truly have no clue what these are for, but I take them anyways for nothing bad can come out of gathering help and information. Diligence pays off when I finally I meet another person searching for the same answers I seek. He suggests that I use the “useless” items that I have garnered to perhaps find a way out. I look at the tools and the funny-looking shapes and a stroke of revelation has stuck me. I realize that I need to use the chisel to carve myself a few lemmas and theorems. These beacons of light illuminate a portion of my surroundings that I would have never seen before. As I look around, I immediately see certain words that are tinged with a slight hue, and refusing to give up on my intuition (which has brought me this far already), I run with deliberate purpose to gather words like integers, homology, matrix, and form. I bring these words to these beacons of light to get closer inspection. Combining these words in the context of the statement that reverberated in my head immediately causes the dark’s presence around me to melt away. I tear a hole in the darkness and can finally see my path ending with Q.E.D., quod erat demonstrandum, which is to say that I have shown what was to be demonstrated. I have found my way back.
As I slowly look up, the smell of freshly brewed tea wafts around, and I realize that I am standing in front of one of the multitudes of chalkboards mounted on the third floor of the University’s math department. I hold splintered pieces of chalk, realizing that the scribbled writing contains oddly looking diagrams which look exactly like the funny shapes I had picked up earlier.