Your math analogy is nowhere near as convincing or on point as you think it is. I put two stones in a pile. I add two more; there are four. it is proven that two plus two equals four
Not at all comparable to the existence of a being/entity/force defined in such a way that does not lend itself to that kind of proof.
If one can't see the flaws in his analogies, one is not even ready to have this conversation.
Defined as an intelligence or conscious or force or energy or however the hell smug people who say "I dont believe in a white man in a beard in the sky" define their god. Something like that could theoretically exist without being measurable or testable with any current technology we have or will have any time soon. I don't at all believe that it does.
Thiest- One who believes in God.
Athiest- One who does not believe in God. I actually prefer 'one who knows there is no God'.
Theology- The study of the nature of God and religious truth (it's hard to even write).
Atheological- Well, you get the point.
In what universe does the impossible have even a small chance to exist?
Atheism is a statement about belief.
Agnosticism is a statement about knowledge.
They are related to each in much the same way as knowledge and belief are but knowledge is not belief, nor is vice versa.