Sumerian is recorded in quantity from the late fourth millennium BCE and is the earliest written language anywhere, yet no genetic connection to another language or family has ever been demonstrated to the standard the comparative method requires. Proposals linking it to Dravidian, to Uralic, to the Caucasian families, to Sino-Tibetan and to Basque have each been published and none has been taken up. There is no camp to join and no argument in progress, which is what separates this from a contested classification: the absence is of an answer, not of agreement.
What would resolve this A set of regular sound correspondences between Sumerian and another attested language or reconstructed proto-language, covering basic vocabulary and grammatical morphology rather than isolated look-alikes, and surviving the usual controls for borrowing and for chance resemblance. Failing that, a substantial text in a related language recovered from the same region and period would give the comparison something to work from. At present Sumerian's nearest neighbours in the record are Akkadian, which is Semitic and demonstrably unrelated, and Elamite, which is itself an isolate.
OpenHistorical linguistics; Assyriology; comparative philologyMarie-Louise Thomsen, The Sumerian Language: An Introduction to Its History and Grammatical Structure