Perelman's proof of the Poincare conjecture was never published in an academic journal, but was merely posted on arXiv. If that's not science, then being correct is more important than being "scientific".
Perelman's proof has been published, e.g. this by the AMS, which has a rigorous refereeing process for books, and this in Asian Journal of Math with a more controversial refereeing process.
Though Perelman's preprints appeared in 2002 and 2003, the Clay prize (which Perelman turned down) was not offered to him until last year, because the rules stipulate that the solutions to the prize problems have to stand unchallenged in published, peer-reviewed form for a certain number of years.
Recently, I gave some reasons for SIAI to begin publishing in mainstream journals, and outlined how it could be done.
I've recently been made aware of some pretty good reasons for SIAI to not publish in mainstream journals, so here they are: