raprap wrote:Oh and in the strictest definition math is not a science as it has no connection with the physical.
Whose "strictest" definition? Carl Friedrich Gauss, a person for whose achievements I have the very greatest respect, said that mathematics was the queen of sciences. The Latin and German words Scientiarum and Wissenschaft respectively mean "(field of) knowledge. Indeed, this is also the original meaning in English, and there is no doubt that mathematics is in this sense a science. The specialization restricting the meaning to natural science is of later date. If one considers science to be strictly about the physical world, then, yes, mathematics, or at least pure mathematics, is not a science.
You may take the position that mathematics is not experimentally falsifiable, and thus not a science according to the definition of Karl Popper. However, in the 1930s important work in mathematical logic showed that mathematics cannot be reduced to logic, and Karl Popper concluded that "most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently."