Here is the answer given by GPT-4: If the FullSimplify function in Mathematica simplifies the right-hand side of an equation to look exactly like the left-hand side, it suggests that the identity is mathematically valid. However, whether or not it is “new” would depend on if it has been previously discovered and documented. In this context, “discovered” means that the identity has been found or recognized by someone in the past and has been documented or recorded in some way. If the identity has not been previously discovered and documented, then it could be considered “new”. Mathematical identities are often studied and documented extensively, and many well-established techniques exist for simplifying and manipulating expressions. Therefore, it is rare to come across entirely new mathematical identities. However, novel variations or alternative formulations of existing identities can still have value and contribute to mathematical research.