I'm not sure what you mean by that. Acknowledging the axiomatic structure of logical reasoning is surely valuable.

But if you want to relate this to mathematics, I think you should aim for more rigor.
What definition of god you are even aiming to prove? Or accept as an axiom?

And mathematical axioms are expected to be "self-evident", true! E.g., "if P is true, P is not false".

Discussing these foundations of reasoning is interesting. But your conclusion sounds to me much like "we can't know anything and thinking is futile". The "100% proof" is a strawman — nobody demands one for God, as it is already impossible to perform a "100% proof" of the fact that the Earth revolves around the sun. As far as my feeble mind understands, this is not how science works.

Philosophy of science has moved on from this a long time ago.

Proving that something does not exist ist rarely possible outside of abstract mathematics.

But it is not possible to describe God in purely mathematical terms either, right? At least not without straying far from any concrete monotheistic religion.

At best we can agree that God is one of infinitely many theories which are impossible to prove or disprove. Which makes it something for which "theory" is not even the right word.

But the more serious you take some religions, and the more you go back in time, this is not what religion was all about.

Religion is not only inner peace and positivity.

It has been the foundation of ethics, I guess — which is important to me, again! And I would not argue that ethics can be "logically proven".

But religion also often demands obedience, and used to make very concrete statements about what is true or false in the physical world.

Only the increased possibilities to prove some of that wrong (e.g. praying can defeat physics and cause miracles) led to today's, more fuzzy definitions of Christian faith, step by step, over the course of centuries.

Of course I acknowledge that this is a matter of interpretation and any single religious person can choose to ignore organized religion and such claims — as long as they are allowed to.

> Do we have any true 100% proof for anything (where we don't rely on some assumption that we consider true without a proof)?

I am trying to interpret your comment in a more charitable way, but it just seems to me like a classic logical fallacy that would "prove" anything and basically makes any rational argument futile.

If God is an intangible abstract concept without a measurable, tangible relation to the physical world: fine!
If it is also not a well-defined abstract concept that allows itself to be proven or disproven: also fine!

But then what's left is emotion, ideas, human thought, ethics. Those are powerful and important parts of civilization.

But we have then left any logical argument about "proving god's existence".

And it has been consensus for a long time that these arguments are futile, for the exact reasons discussed here.

Pretending otherwise is what mads high school phiolosophy classes unbearable when there were to many zealousl religious students and a bad teacher. It derails into either woo rhethorics or a shouting match.

And this is why I said that studying these proofs is an interesting intellectual exercise, and sometimes tells a lot about the societal context.

But no, these are not proofs in the sense of a falsifiable scientific methodology.