It’s hardly naive either considering so much has been learned about the limitations of mathematics only in the last century.
Highly recommend this short video
The title mentions Gödel, but it’s a broad treatment that really discusses a lot of the context of the subject.
Keep in mind there are multiple reasons why proofs can become problematic.
Gödel deals with some of them, other problems go unproven for centuries until our techniques catch up. Some proofs are impractical being nearly infinitely complex, etc.