I know this question is very harsh to the mathematics community and so it is to me.
I have just started learning formal rigorous mathematics. I also heard of Godel's incompleteness theorem. I also know as of today, there are no mathematical contradictions even with millions of different mathematical theorems.
Nobody can tell if there is a contradiction or not. But if mathematics has contradictions, will the entire mathematics be destroyed?
$1+1=2$ can be proved using Peano axioms. Will its validity be also under question?
Every self evident axioms would turn out to be unreliable. Should we give them all up?
Feel free to downvote if it hurts anyone. But please also explain the reason for downvote.
We have on occasion had to address contradictions. Erroneous assumptions about which properties of real numbers also applied to complex ones caused problems, but they were fixed by reframing these as proofs by contradiction that those properties didn't carry over. Later, Russell's paradox (as well as earlier but more advanced arguments) required more precise efforts to axiomatize set theory. So if something else goes wrong, we'll probably just delete or weaken an axiom somewhere. It would require starting from scratch on the proofs of some theorems, but it's such a rare event we can live with that.