I think you're talking about the axioms which form the modern foundation of mathematics, but mathematics isn't a science, at least not in the sense I'm referring to. Mathematics is a tool; it does not aim to describe the world, but rather provides a toolbox useful for doing so. It doesn't work the same way science based on observation does. There is no faith involved, but rather just arbitrary choices that result in a useful end result. That's good enough. It's like a protocol standard we all use because it makes our life easier. You don't need faith in HTTP to use it.

If you mean the foundations of the scientific method, e.g. things like trusting your perception of the world (to some extent), that indeed crosses over from science into philosophy. But that does not invalidate the scientific method, not does it mean all of science is faith-based; it just means we had to make some assumptions to be able to accomplish anything at all. Those assumptions are still something we can and should question, we just don't have any good way of testing them.