I did not understand the philosophy to mathematics? Philosophy is the science which teaches us to argue. A philosopher can be any. But mathematics is an exact science of numbers. There will not be able to go different ways. Any mistake leads to collapse.
Klima that is a deep question and one I am not really qualified to answer but I believe you will find the following link helpful.
PHILOSOPHY, MATHEMATICS AND STRUCTURE
http://web.maths.unsw.edu.au/~jim/interview.html