Well, how can one prove that a table is a table? You can only prove your own existence.
I'm not very good at this whole explaining thing, and I'm really sorry for it
t: what I'm trying to get across is that no person can definitely and truly prove anything. That's why scientists call their ideas "theories". Science is pretty much faith, as is religion.
These statements aren't true for many reasons. Obviously, what immediately comes to mind is that mah/geometry/et al. can be proved. That's because "proof" is a mathematical term. Thus the notion, "all you can prove is your own existence" is false. There are, indeed, other things, that is, numbers.
However, I really shouldn't say "there are other things" rather than "there are things" when the notion of proving one's own existence is false in the first place. That is, even Descartes over stepped his bounds when he said, "Cognito Ergo Sum". The more accurate conclusion to his line of reasoning in Discourse and Meditations is the Buddhist's, "I think, therefore there are thoughts." And even that may not be QED. For one, Descartes doesn't prove 100% QED that it is a "I" that thinks or exists. For that, like mathematics, it would have to demonstrate that the opposite of what it states is a contradiction, and that the "I" would have to be necessarily true in all possible worlds. But as an objection to both the Buddhists and Descartes, we can easily imagine a possible world with no "I" or "thoughts". A possible world without numbers is impossible. The number 1 cannot be destroyed or afftected by material destruction or creation. 1ness, 2ness, 3ness, et al stands as a necessary fact no matter what you call it ,or whether you try to think it away.
Another thing to consider in objection to Descartes is Hume's Bundle Theory, which proposes that we could be nothing but the sensation of parts giving illusion to an "I". (Even from a purely physicalist point of view, Roger Sperry's experiments in split-brain research give me reason to pause in shock over exactly what "I" am.) So if a complexity of thoughts can come together and give the illusion of a manifested being, that manifestation would therefore be an illusion. This view is plausible as there's nothing saying it is inherently in contradiction with itself. Thus as this alternate view is plausible contrary to "Cognito Ergo Sum", it stands that "Cognito Ergo Sum" is not proven.
But that aside and to answer your claim, yes, holding science or religion to a mathematical criteria would result in both positions failing to be proven in the sense that an opposing view of their existence could be plausible, and they are not necessarily unaffectable facts. However, this does not follow from your claim that if you don't believe in God then you can't believe science. This would have to assume an all or nothing sense of establishing fact. That if two facts can't reach 100% certainty, then they equally must be dismissed or at least be on even terms. This does not follow. This is like claiming that because many things move slower than the maximum speed limit of the universe, that either nothing moves or at least those slower things move at the same rate. It's a false-dichotomy. Though almost everything is subject to doubt and must be believed, that is not to say that everything is equally doubtful and that somethings aren't less believable than others as you even admit when you say--
I do accept that science has allot more evidence, and is much more plausible than religion. But I still stand by that it is possible that a God could exist, and you cannot prove science.
Which is in stark contrast to the more extreme claim that--
Remember, if you don't believe in God, you can't really "believe" in science.
No matter what you mean by that second "believe", it makes that statement false for the following reasons: If you mean it in the same sense of "belief" as you refer to when talking about believing in God, that statement falls to the errors I just described. If you mean it in a stronger sense of the same definition (e.g. faster is a stronger term for fast), then it also falls again to the same error I described; as I said, just because not all things move the fastest possible speed, does not mean things can't move faster than others, in fact, some things can not move fast at all, making them something we wouldn't call fast. If you mean it in another definitional sense, that statement doesn't follow since you're using a second meaning of "belief" to equivocate with the first creating a non sequitur in your logic; e.g. Nothing is better than getting every thing you want. Having a job you do not want is better than "nothing". Therefore, having a job you do not want is better than getting everything you want.
I certainly don't believe in God in the traditional sense, but I do accept that there may be something out there that created all this.
If you're speaking in possibilities, this is called Agnosticism. Almost all Atheists are Agnostics. The terms don't mutually exclude. But just because something is logically possible does not mean it is true, or that belief in it as true is just as jusified as belief in anything else.