All proof is based on assumptions—ultimately, axioms. Non mathematical, everyday arguments for the reasonableness of some position tacitly assume a world view.
One world view takes as an axiom: "There are no miracles." This world view maintains either atheism, or if there be some god, that god either could not or would not do anything out of the ordinary from our human perspective.
My own world view is theistic. More on this below.
John Polkinghorne in his The Way the World Is  states, “Again and again in physical science we find that it is the abstract structures of pure mathematics which provide the clue to understanding the world. It is a recognized technique in fundamental physics to seek theories which have an elegant and economical (you can say beautiful) mathematical form, in the expectation that they will prove the ones realized in nature. General relativity, the modern theory of gravitation, was invented by Einstein in just such a way. Now mathematics is the free creation of the human mind, and it is surely a surprising and significant thing that a discipline apparently so unearthed should provide the key with which to turn the lock of the world.”
The ability of mathematics to "provide the key with which to turn the lock of the world" is popularly known as "the unreasonable effectiveness of mathematics".
Now whether this capacity of mathematics seems reasonable or unreasonable depends entirely on one's world view. An eminent mathematician in the area of abstract algebra wrote an article on the philosophy of mathematics—which he concluded with the admission that he had no idea why mathematics was so effective in describing the real world.
On the other hand, John Polkinghorne has said:
The reason within [leading to abstract mathematical structures] and the reason without [the path and order of the physical world] fit together because they have a common origin in the rational mind of the Creator, whose will is the ground both of our mental experience and the physical world of which we are a part. ... I, in fact, believe that science is possible, that the world is deeply intelligible, precisely because it is a creation. To use ancient and powerful language, we human beings are creatures made in the image of our Creator. The power to do theoretical physics is a small part—a small part, no doubt—of the imago Dei [image of God]. 
My own world view is presented in my personal philosophy.
1. B. Eerdmans, Grand Rapids, MI, 1984, page 9. (return to text)
2. So named by the physicist Eugene Wigner (return to text)
3. Socrates in the City, Eric Metaxas, Ed., page 13. The book is a collection of talks given at a Manhattan speakers' series also entitled "Socrates in the City". Dr. Polkinghorne's talk was given on Oct. 29, 2003. (return to text)