Thanks for the examples. Let's deal with them one by one. What is so special about the decimal representation of pi ? Since most numbers are transcendental, isn't it too natural for pi to be that way ?
The architecture of the universe is mathematical in basis, with the discovery of mathematical matter it suggests me a "universal intelligence" or "organisation" beyond our current understanding. It is what I think the deeper levels of religion were trying to explain, such as the Vedas, and what some might call God- beyond that it is difficult to explain- but it's transcendental.
(BTW I don't believe in big grumpy old men with beards who live in the sky).
That is a very deep question. I know we disagree on many political ideas, but I consider you a respectful member- unlike some others, so I'll answer your question.
Level-1- Because of mathematics, it leads me to believe there is no random causality to the universe.
Level-2- To define belief would be difficult and to give reason would thus defeat faith and therefore defeat the principle of faith- so on the second level it's really impossible to answer without saying crudely "something inside".