TITLE: Mathematical predictions of AdS/CFT
QUESTION [21 upvotes]: What sorts of mathematical statements are predicted by the AdS/CFT correspondence?
My "understanding" (term used very loosely) is that this correspondence isn't a mathematically rigorous statement, but I can still imagine that certain baby cases might spit out interesting well-defined identities or relationships. I'm very happy for this question to be broadly interpreted.

REPLY [4 votes]: New exact solutions in classical general relativity have been found using AdS/CFT methods. It may sound trivial since there are already encyclopedias of exact solutions, but those new ones have quite unexpected properties. Some references to those works are found e.g. in sec. 4.2 of Hubeny's notes (in the same document you encounter an extensive catalog of applications of AdS/CFT to problems in mathematical physics).