Dear Professor Garfinkle,
Enjoyed your essay, learned some things about Galileo's view right off the start, "the image of nature and its laws as a book and asserted that that book was written in the language of mathematics".
Your comment ".. abstraction and generalization generated a great number of new mathematical objects and led to another pursuit of modern mathematicians: classification. For each new type of object (group, vector space, manifold, Lie Algebra, etc.) one would aim to produce a complete classification of all possible objects of that type." and argument that follows was very clear and thought provoking.
I hope you get a chance to have a look at my essay here. I try to build on these classifications and provide visual models of objects that match the proven mathematical models of the particles of the standard model and would be very interested in your comments.
Best of luck in the contest, you deserve a high rating and thank you for the essay.
Regards,
Ed Unverricht