Mathematics cannot be invented to suit one's convenience. It is often said that i was invented because the equation x^2 + 1 = 0 had no solution; so we gave it a solution and called it i. But I know lots of other equations, simpler ones for that matter, that have no solution (in R, say) for which no corresponding thing can be done, e.g., x+5=x-4. My own view, with this as only a trivial example to show what I mean, is that mathematics is discovered. In a long life spent among mathematicians I have found that most of them take this attitude as well.
Ralph A. Raimi Tel. 716 275 4429 or (home) 716 244 9368 Dept. of Mathematics FAX 716 273 4655 University of Rochester Webpage http://www.math.rochester.edu/u/rarm Rochester, NY 14627 (Webpage contains links to papers)