Mathematics is the discipline of rigorous deduction from appropriately chosen axioms and definitions in order to establish whether a statement which is expressed in defined terms is necessarily true, given the axioms and definitions.
There is no a priori limit to the subject areas that can be covered by mathematics.
As far as we can observe, mathematics and natural law are unchanging, and valid at all times and places.
Mainstream science accepts this as a given, but has no explanation for it.
This may be explained in several ways, assuming QO:
Once there was a time in which Mathematics was an innocent subject. In order to produce a mathematical system, all you had to do was develop some concepts, add some operations on these concepts (a calculus) and top it off with a few self-evident axioms. Euclid was the first to do this systematically.
Mathematics, as Galileo wrote, is the language in which God has written the universe. Whilst we may disagree as to whether there is a God that has anything to do with it, we may expect that anybody who has studied the fundamental laws of the universe will at least agree to the core of Galileo's statement, namely the proposition that natural law is essentially mathematical.
Mathematics develops like anything else, as a resonating set of interrelated quanta, which are entangled with all things that are shaped by it.
A theory of everything has several things about mathematics to account for.
Firstly, it must account for the fact that mathematics appears to be useful for describing natural law.
Secondly, it must account for the fact that the mathematics man has produced until now cannot be guaranteed to be free of contradictions, allows us to choose between contradictory axioms, and is structurally incomplete. In other words, 'mathematics is in a mess'.
QO provides a radically new perspective on mathematics. In QO, mathematics develops like anything else, as a set of interrelated quantum systems. This leads to profound insights, none of which are new, but few of which are generally accepted.