PhD Theology, HD, JD.
Any given maths can be most purely considered to be a system of arbitrary starting points, yet we choose our starting points (our axioms) based on our unique, human aesthetic. This is significant. It allows us not to get so proud or sure of ourselves.
Please examine the New Metaphysics that opens up some New Geometry at http://medium.com/@theDoctor/the-new-geometry-8bbec68818d4 for a more rigorous understanding of domains. It's presently in Draft. Perhaps you will help co-author it.
You may also be interested in some applied math I'm working on to hold humanity's knowledge. It's akin to Hermann Hesse's Glass Bead Game (cf. Magister Ludi). It is designed to be a universal knowledge store that provides two independent views into a mathematical space (from a Cartesian coordinate system of Euclidean geometry to a spherical one) which holds a whole epistemology of knowledge (a category of human endeavor I call "epistemics").
Please read my paper "On how to be an Academic", published unconventionally at http://github.com/theProphet/GlassBeadGame/wiki/On-Being-an-Academic.