Mathematics is a

"formal" discipline formed around a

human cognitive mechanism which accounts for

perception of

discrete entities (and by extension,

quantitative relationships). It should be noted that discrete entities and quantitative relationships do not actually

exist in

nature per se; rather, we accept the

notion that they do as part of the natural

reductive process of our

consciousness (a sometimes-convenient

compromise). In this context, Mathematics is a (characteristically

exhaustive and

rigorous)

compendium of

metaphors based exclusively on discrete and quantifiable subject matter (i.e.

numbers), where that

description is itself, as much as possible, discrete and quantifiable.

Kurt Godel's Incompleteness Theorems (published 1931) correctly identify that any formal system (i.e. Mathematics) is inherently flawed, specifically "in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system." To restate, Mathematics is effectively a study of the consequences of the particular compromises inherent in human cognition. Caveat emptor.