Monday, September 27, 2004

The Essense of Mathematics

by Asim Jalis

At its core mathematics is a kind of merciless refactoring where we take statements that are true and generalize them as far as we can. We cut out all the specifics, or refactor them out and the see what's left. For example, this dog weighs more than this cat. This is a general statement which might be true. But now if we refactor out the specific animals, and also the concept of "weighs" we are left with the concept of more-ness. We can even refactor this out and be left with a concept of a relationship. We notice that more-ness is transitive, so we can formulate a theory of relations that is transitive. Once we have created this machinery we could apply it to something that is not quantifiable. For example, we could apply it to belongs-to. Or contained-in.