Date: Mon, 1 Sep 1997 13:48:13 -0400
From: Alex Bogomolny
I am just back from a trip to California. In Berkeley, I stopped at the University bookstore and saw a new book by R. Hersh "What is Mathematics, Really?" In the Introduction, Hersh recounts how after reading "What is Mathematics?" by Courant and Robbins he still could not find an answer to the question. I am not sure one gets a clear answer after reading his book either.
Who needs a definition? - this was my first reaction to your letter. Then I thought of "Mathematics is what mathematicians do" which is the only comprehensive one I am aware of. It's also the least informative. Mathematically speaking, one should be able to derive all the properties of Mathematics from its definition if such one existed, right? Now, as I was writing this it occurred to me that (put this way) the task of defining Mathematics is actually impossible. And we both I think have an idea as to why this is so. From here I deduce (conclude?, surmise?, infer? ...) that
|Mathematics is the only science that explains why its definition is impossible.
As usual, deriving all other properties of Mathematics from the above is left as an exercise to the curious reader.