In recent years there have been major, diverse, sometimes surprising advances in experimental mathematics  for a variety of sophisticated uses such as developing/deriving exact formulas, theorem proving, resolving previously unresolved conjectures (some deep), etc., ie basically core areas of mathematical research activity.
Are there applications of this "experimental mathematics" in TCS/complexity theory?
 Experimental mathematics: examples, methods, and implications. by Bailey & Borwein, Notes of the American Mathematical Society, 2005
 A reading list on experimental algorithmics, tcs.se