Determinism is true as far as science can tell. By determinism I mean human actions and thoughts are not above natural laws. Given sufficient knowledge of a person's past, his future is as predictable as the future positions of the planet earth.* If determinism is true, natural law is mere tautology: when you watch a movie, every time when Ali Baba says "open sesame," the mouth of the cave opens; can you conclude that the words "open sesame" causes the cave to open, or the film always arranges these two classes of events in fixed order?
Free will is a relation between one's action and his desire, and is thus independent of determinism. If one's action is the outcome of his own desires, then he is free. In other words, whether one will be free or not in the future is as determined as in the pastwhether one will be free or not in the future is as determined as in the past.
Physics is not governed by mathematics. Mathematics is the art of saying the same thing in different ways. When a mathematical model contradicts a scientific observation, we revise the mathematical model; we do not punish the physical world for defying the law.
*If I'm not mistaken, Bertrand Russell's view is slightly different from materialism. The difference is similar to that between agnosticism and atheism. Russell holds that, although much of materialism is very likely to be true and useful, it may not cover the whole ground. It is true that psychology has become increasingly materialistic in the sense that there are laws that govern mental events, but physics has become less - matter, for example, is no longer considered as permanent substance as it used to be.