Mathematics; Invented or Discovered

Mathematics: Invented or Discovered?
I J G

Mathematics is, by most scholars, divided into two sections; arithmetic and geometry. The former involves the computation and manipulation of numbers and identities under addition, subtraction, multiplication and division while the latter constitutes the study of figures represented in space. Mathematics is an interpretive language of reality which is inherently advantageous over conventional speak when one is seeking to understand and manipulate the physical world. In this paper I seek to investigate and to give a heuristic analysis of the question ' Mathematics : Invented or discovered'.
One way of analysing the ontological nature of mathematics, in our search for answering the titled question, is in the understanding of its relationship with nature. However, there exists a problem in defining its relation to nature due to the sometimes abstract concepts described by mathematical thought i.e the ideas which don't directly 'map' onto nature. When mathematics describes reality we are not exclusively concerned about the model's inability to reflect nature perfectly; most, if not all models, are approximations. This is not the abstraction we are concerned with; the abstraction of consideration is the 'higher thought' which seemingly transcends our phenomenological experience which can on first sight enter the realm of metaphysics. If this 'higher thought' was non-existent, we would then say that mathematics is just a language for describing nature and physical processes therein, and would then infer that mathematics is just a descriptive tool for representing nature that was invented by the mind.   How do we account for mathematics' ability to obtain insight, and, in retrospective analysis, accurately describe ideas that are on the border of the phenomenological/metaphysical realm. Herein, I wish to separate ideas that just 'appear' as non experienceable due to our intellects inability to 'think' about such. In addition, I wish to reflect on these unexperienecable events and how logical steps resulting from the firm setting of mathematics based on the experiencable world result in ideas and concepts so far removed from its base.