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
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.