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David_Gerard comments on Reasons for SIAI to not publish in mainstream journals - Less Wrong
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Indeed. However, you've raised a single remarkable exception to a general heuristic as if a single example is all that is needed to thorougly refute a general heuristic, and of course that's not the case.
The overwhelming majority of papers put on arXiv and nowhere else are:
It's not clear to me what the disagreement is here. Which heuristic are you defending again?
Response: Can we skip the pointless categorizations and evaluate whether material is valid or useful on a case by case basis? Clearly there is some material that has not been published that is useful (see: This website).
Response: Ahh yes, anything not peer-reviewed clearly contains Time Cube-levels of crazy.
Or none of the above? I'm not sure we actually disagree on anything here.
The problem of publication bias is another reason to be wary of the publication heuristic recommended a few comments above. If you follow that heuristic rigorously, you will necessarily expose yourself to the systematic distortions arising from publication bias.
This is not to say that you should therefore believe the first unpublished paper you come across. It's only to point out that the publication heuristic has certain problems, and while not ignored, it should be supplemented. You ignore unpublished research at your peril. In an ideal world, peer review filters the good from the bad and nothing else. We do not live in an ideal world, so caveat lector.
The process of journal publication is also extremely slow, so that refusal to read unpublished research threatens to retard your progress. This link gives time to publication for several journals - the average appears to be well over a year and approaching two years. What's two years in Internet Time? Pretty long.
Most of the math papers are not comparable to Perelman's proof in importance( that should be obvious) but most of them are mathematically correct and interesting to mathematicians. People will often see something on the arXiv and look at it. On the other hand, as I mentioned, people are also more likely to look at a preprint if they know it is actually accepted in a reputable journal.
Let's reword that: the overwhelming majority of papers published in peer-reviewed journals are comparable/not comparable to Perelman's proof?
Probable answer: not remotely comparable. In fact, a lot of them are just plain wrong.