Ok a couple of things:
Atheism - This is a label of the theists, used by theists to label people who don’t play with the theist’s toys. Just as I don’t need a special word for not believing in goblins since I don’t play with goblins, only the people who play with goblins need a word to describe me as an A-Goblinist. Atheist is a descriptor for a single question about a single topic. That is all that it can encompass. “Do you believe in the supernatural?” - “No, no I do not.” That response is neither a positive claim or negative claim about the actual existence of a deity in reality. Just as not believing someone’s bad evidence and arguments for meeting Bob yesterday has no bearing on whether or not Bob and this person actually met or that Bob actually exists. Atheism is not a belief structure, political structure, world view, etc. It has no leaders, texts of rules and methodology, or anything else that structures around how and what it is to be an atheistic person. You do not have to be scientific and be an atheist. There is no necessary link between the two.
Science is, necessarily, practiced by methodological naturalism. That means that since, we cannot investigate the supernatural in anyway, we are not allowed to use it as a causal link to events observed and studied in reality. First you have to demonstrated that realm is there, then demonstrate how that realm can interact with this reality, then study an event in this reality to see if there are markers left behind from the supernatural interacting with that event. Until we can do this, the supernatural and any other imagined idea are not allowed to be part of the explanation of observed and studied reality. IE: We have to be able to tell the difference between an unknown natural cause and the supernatural being the cause. At this point, there is zero evidence of any event having a supernatural cause for it. Every event that we’ve studied for what caused it was always a natural cause. AKA: God of the Gaps.
I do disagree that mathematics has nothing to do with the natural reality. Reality is the reference point of logic and mathematics is the most fundamental language for explaining the predictability of that reality that we observed first. Math is just the adjectives to describe reality. two rocks, 10 lbs of force, etc.