GABRIEL KOCH Ph.D. Candidate Teaching Assistant Department of Mathematics University of Minnesota, Twin Cities (as of Spring, 2006)   I am currently an "L.E. Dickson Instructor" postdoc at the University of Chicago; you can access my current website HERE.

"...[There is a] most remarkable relationship between mathematics and physics. (Mathematics is not a science from our point of view, in the sense that it is not a natural science. The test of its validity is not experiment.) We must, incidentally, make it clear from the beginning that

if a thing is not a science, it is not necessarily bad. For example, love is not a science. So, if something is said not to be a science, it does not mean that there is something wrong with it; it just means that it is not a science."

-Richard P. Feynman, from his "Lectures on Physics", on the topic of "The Relation of Physics to Other Sciences"

"One fact should surprise us, or rather would surprise us if we were not so used to it. How does it happen there are people who do not understand mathematics? Is there not something paradoxical in this? Here is a science which appeals only to the fundamental principles of logic, and yet, to think there are people who find it obscure, and actually are in the majority."

-Henry Poincaré (1854-1912, French mathematician, physicist, and author)