In many areas of math doing something "backwards" is much harder that doing it "forwards", for example - inverting a matrix is harder than multiplying it, taking a derivative is easier that an integral... But why should this be, I mean, there's nothing fundemental in the way that we happened to set things up. Is it possible to "build math backwards" so that all the things that are hard fo us now are easy and vice versa? If not then why not? Thanks.