I'm not claiming the Royal Society 'invented' peer-reviewed science. It wasn't a dramatic moment of epiphany, just a gradually growing insight that spread through society. And the Royal Society was at its forefront.
To get an idea of the formation of empirical science in Europe read Quicksilver by Neil Stephenson ~ https://en.wikipedia.org/wiki/Quicksilver_%28novel%29 & a quick synopsis here ~ http://www.wired.com/wired/archive/11.09/history.html
Akademeia was literally the name of the grove where Plato started his Akademeia in 350 BC. Plato took these ideas of an ascetic brotherhood of ideas/mathematics from Pythagoras. No one knows exactly how Pythagoras came up with his ideas, but he did travel widely in his youth, at least as far as Egypt, seeking knowledge.
http://www.etymonline.com/index.php?search=academia
Of course, I wasn't talking about the word, but the idea. That is a little bit older, but it's definitely a post-renaissance creation.
(I also responded at http://news.ycombinator.com/item?id=3615474)