Mathematics

From a philosophers, or more precicely from the most general point of view (in the desire to arrive at something all-encompassing), mathematics is the search for definable structures that emerge from the interactions of a set of axioms and rules of derivation. The important term to note is interaction, and 'action' in particular, because it specifies that a certain action is part of what mathematics is. In other words, mathematics is not static, for otherwise the mere existence of a set of rules of derivation and axioms would be mathematics, which is obviously not the case. The practical observation is that mathematicians enact the process, and study the interactions, which they in turn generate. The backward-forward correlation pattern emenates once again. A further observation is that the type of action can be defined in rather absolute and concise way. This action is the transformation of one set of information into another. Thes existence of these transformation, and particularly their existence as the clockwork of mathematics shines throughout every theorem, or theory at the most elementary and abstract level, converging into nothing and diverging into infinity.