ABSTRACT
What is “Mathematics”? Is it the science of patterns that is motivated through observations of nature, or is it the body of knowledge derived from pure axiomatic logic, aspects of which have applications in nature? Is it manmade or are individuals simply uncovering the work of a higher deity? Is mathematics intuitively driven or is it logically driven? Is abstraction an inherent part of it or is it simply the medium of its communication? Are proofs of theorems time dependent or do they stand as absolute truths? Does it stand on a base of Aristotelian logic or can mathematical statements have a variety of meanings and degrees of truth? Are the demarcation lines as to what is mathematics as opposed to physics, economics, linguistics, or even astronomy defined clearly enough so that one could classify selected pages of textbooks from those disciplines as belonging to those disciplines? Questions like these soon lead us to the unsettling conclusion that there is no definitive answer as to “what is mathematics and what is not.” When asking “what is mathematical thought,” however, the situation gets a little better, and a little worse.
