Putting conventions aside (i.e. base 10 versus another number, 24 hours a day and so on), and underlying philosophical explanation for why mathematics itself (i.e. ideas not conventions if that makes sense) reflects the reality we find ourselves has a long and rich history. Plato's Theory of Forms
, with its land of pure forms and when we 'do' mathematics we perceive a shadow cast into our world, In fact, I take the same viewpoint with the study of risk which I see as some higher dimensional form, where us as parties in quantitative finance perceive merely shadows of this ideal. No one model or method can encapsulate this form yet each reflects a shadow of this form cast into the reality we exist in. A risk manager capture one aspect, a stat arb trader another and so on.... That is, maths fits the reality we find ourselves in because our understanding of and the world itself are shadows of these ideal forms.
This aside the work of Réné Descartes I would also cite, in particular his Method and Meditations
. In particular, the Methods describe the scientific method which is in words of Plato, would be the means by which we can perceive the shadows cast by the ideal forms.....