Hmm, reading this I would say that to me, to be true? Heh, we once thought the earth was flat, and had all sorts of reasons for it. We thought the universe rotated around us, with us being the crown of creation and some still do. What we can say is that if we create a logic through repeatable experiments and find it to explain new experiments we are getting closer to 'something'. The math we use is seldom thought up without reason as I've seen, although there is always some that somehow seem to create math that won't get their perfect fit until much later, as Boolean mathematics in our digital era. And there are more and better examples of that I guess than what I remember for the moment. But there is also a danger in trusting that results always are 'true' just because it fits ones current mathematics. The more one draw away from direct experimental verification mathematically, while inferring and deducting, the more susceptible that math will be to drawing conclusions that one won't be able to verify experimentally.
The very best math, to me, is the type that draws a new conclusion, and then also suggest some way to test that prediction.