User:Pedhuts

Nature of Mathematics
Mathematics may be expressed in many different manifestations. For that simple reason alone, I conclude, any consistent systems found with the postulates it embraces can be paired for use with another system of the same or lesser postulates. However, the conclusion generated from the combined system would require the postulates of both the systems. It may be that some mathematical conjectures and hypothesis claimed to be unprovable may be provable, if we "borrow" another branch of mathematics as the basis for the one we want to solve. That is, when we try to prove something in system A by the methods of system B, we need to make a claim that such objects in system A are corresponding to the respective objects in system B. The drawback is that we're making a claim (of connection) to allow for the proof of another claim. But then one must also realize that this is basically a beneficial and healty element in developement, even awarded as "unification." This means, we must be careful in relating and analyzing different systems.