Indeed, math isn't science. ;)
I wonder - if Perelman was just "some guy" with no reputation as a mathematician, would anyone have noticed when he uploaded his proof?
Essentially yes, though he might have had to individually contact a few mathematicians to make his existence known. Consider the example of Ramanujan. Wpedia:
In 1912–1913, he sent samples of his theorems to three academics at the University of Cambridge. Only Hardy recognized the brilliance of his work, subsequently inviting Ramanujan to visit and work with him at Cambridge.
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: