This is how science is meant to work.

No, it's not how math works at all. Math is not experimental science. Results take years to formulate and are generally known to be true by colleagues via correspondence and seminars before a paper is even written. Retraction is very rare.

I don't know why people are talking about something like this that they are clearly not familiar with.

Most good scientists work hard to prove results to themselves before going public.

Peer review is then done _in private_ before publication as a check on quality and significance.

Retracting a paper is pretty embarrassing. And not considered science as usual.

Yes. A researcher who achieves a reputation of making mistakes carries that reputation.

No, scientists check their work before releasing it. Slop is still slop if you wrap it up as an academic result.