This is trivially true via the pigeonhole principle. SHA-2/512 has $2^{512}$ possible outputs, but $2^{2^{128}} - 1$ possible inputs. Trying $2^{512}+1$ unique inputs is sufficient to produce at least one collision.
That said, SHA-2/512 is designed to be collision resistant, which implies that it should be hard to find two inputs that hash to the same value. Finding a way to quickly create such a collision would be considered a catastrophic break in the algorithm.
Today it is considered unfeasible to even find one SHA-512 collision - none have been found so far. There have been efforts to find a collision for SHA-1 though (notably the IAIK "SHA-1-Collison Search Graz Project"); it is thought that the SHA-1 algorithm is sufficiently broken to find one. These attacks don't translate to SHA-512 because of the increased complexity of the algorithm and the higher output size of the hash.