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In recent years there have been major, diverse, sometimes surprising advances in experimental mathematics [1] 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?

[1] Experimental mathematics: examples, methods, and implications. by Bailey & Borwein, Notes of the American Mathematical Society, 2005

[2] Is "Experimental Complexity Theory" being used to solve open problems?, tcs.se

[3] A reading list on experimental algorithmics, tcs.se

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