And that brings to mind http://www.conwaylife.com/w/index.php?title=HashLife, an example (of many) of an algorithmic improvement that gives a way higher speed up than parallellizing and throwing hardware at a problem.
Hashlife is a brilliant algorithm. For anyone not familiar (and vaguely interested in Conway's GOL), highly recommend reading up about it. I found it mildly mindblowing :)