Beautifully said alexander....
I believe that the universe is just one almighty "if-then statement"; If such n such is true then it follows that such n such is true....And if that is true then this must be true....because were it not true, these are the paradoxical consequences.
Mathematics in the grand scheme of things is not just a bunch of arcane symbols that only braniacs can manipulate. Mathematics is a language that once established, will fixate its own grammatic structure. The symbols are simply invented as conveniant mechanisms for conveying the message, they are the letters that make words that can be read by mathematicaly litterate individuals. Humans didn't invent mathematics, the structure of logic is independant of human tamperring. Any invention can be innovated upon; logic can not be made better. All we can do is explore its implications with tactics (that can be innovated upon). Our mathematical formalism is the invention, not the logic it stands for. And our formalism must represent the logic it stands for and not vice versa. Logic is simply a series of assertions that must follow if the previous is taken to be true. Logic must be explored, not be created (by man anyways).
This leads me to my conclusion; logic is such that it doesn't contradict itself. Any implication may follow but the structure of all such implications is rigid and unchanging. In other words whatever is a rule today is a rule the next and the rules can never be broken. Mathematics is a vessel to explore all such implications. The universe itself must adhere to logic in order to not contradict itself, and hence a tool to describe the structure of logic must somehow explain all consequences of what is logicaly possible. The universe is one such possibility and therefore the language of logic (mathematics) must encompass this possibility. So the universe can be explained in a mathematical fashion. Whatever is possible mathematicaly is possible logicaly. The hard part is that we have to work backwards.
Ironicly we weren't given the math and told to figure out a possible universe. We were given a possible universe and told to figure out math.