The greatest proof ever written by man, Andrew Wiles' FLT, was published with a flaw before being retracted and reworked. It's _completely_ normal in mathematics to find flaws in the argument. That's what peer review in mathematics is _for_.

Besides which it's not clear if these papers are considered published or preprint since they appear in no journal, so it's not really a retraction.

It's also very very normal to post preprints on Arxiv before peer review, so it's not the case that mathematics is kept private during review.

Not true. Wiles presented his proof in a series of lectures in 1993. The error was found by a reviewer, and he spent over a year trying to fix it. Once he did fix it, he asked colleagues to review it again, and only once it passed that review did he actually publish it.