Mathematics philosophy

I study mathematical models and optimisation and diagnostics methods, and also mathematics appendices (especially methods of optimisation, recognition and neural networks) in some natural and the humanities. In particular, in economy and in medicine. And, probably, it is required to explain, why I have risked to write lectures on mathematics philosophy. First of all Doctor of Philosophy YU.I. Miroshnikov has suggested to write me about these lectures. Besides, as a professional I studied some subjects of logic and methodology of mathematics since 1980, participated in the world mathematical and philosophical congresses, and also in the congresses on the logician and science philosophy. And in general, I have very much interests in this theme. I think that I am moderately subjective. Certainly, I am subjective, but moderately. At a writing of the given work it was found out that for enough full statement of a subject great volume is necessary very much. Therefore the given text is in many respects concise. It will be a question of the metamathematician - about metaphysics and about many other things.