Think. Transform. Thrive. "The University of Chicago was founded to challenge accepted ideas" said Theodore A. O'Neill, Dean of Admissions. As a person who approaches things-problems, tasks, and ideas- in illogical ways, I was drawn to this sentence.
{I think you could probably omit the first sentence. The University of Chicago probably expects you to be drawn to that, namely because it's coming from their admissions dean and printed on their brochure. Marketing really works, believe me....we live in a society that relies on it as if it were dogma. You could start the essay from the second sentence."I relish the opportunity to approach problems, tasks, and ideas in (abnormal,creative,unconventional.....since illogical ways just tells me that you're most likely to end up with the wrong answer).
I was tempted to challenge the accepted ideas; though, more tempted to challenge the ideas of University of Chicago or perhaps challenged by its ideas.
{Accepted ideas (or conventional wisdom) has always been my arch enemy.......}
This is it, the ideal place for my ideas to come to life.(This is the ideal place for me). With the University's focus on Socratic teaching, I will be more engaged in (to) think with others and share my thoughts (thinking with others and sharing your thoughts seems a bit repetitive, are they not the same thing?), rather than wonder (wander) off in my little world.(note: wandering off in ones own little world can actually be a good thing and may lead to success. One person comes to mind....hint: E=MC squared).....
This along with its core curriculum would provide me with (a) broad academic experiences I never had before. With the rigorous academic works of the university, not only will I be engaged in the life of the mind, but (I will be much:omit,) also better prepared for the future.
Overall, I think you understand what the University of Chicago is about. Be sure to show the reader you are a good fit for Chicago rather than just telling. Perhaps you might want to tell a story of when your propensity for "illogical" thinking came to be a source of inspiration or reward for you, and how the university could help you in harnessing this potential for future application. Hope this helps and best of luck!
Jason J Rhee