I'm going to be rather dismissive in my reply, and for that, I apologize, because I'm not quite sure how else to respond.

This is more or less a non-issue. Thanks to mathematicians building on Euclid for the last 2300 years, we have a system of mathematics built on a few basic principles (that you would not disagree with) and deductive reasoning. If you take a theorem that is accepted as proven, you can almost definitely follow an immense chain of logic back to the fundamentals. It will take you a ridiculous amount of time to do so, but it is possible.

If you're referring to specific debates in the math community (e.g. "I feel that the general math community accepting the axiom of choice was a bad idea") then that's worth being specific about in your post.