Just when was the wheel invented, and by whom?

Cucuteni-Trypillian cow-on-wheels, 3950-3650 B.C

I was curious, I’ve seen the invention of the wheel down as 3,500 BC in Sumeria. But this funky little ceramic toy from the Ukraine seems to be a bit older. I’ve seen claims that there’s proof the Trypillians used the wheel 6,500 years ago (reports of a copper axle and some museum exhibits) but I can’t substantiate them. There’s also what appears to be wheel tracks for a cart under a barrow grave in Flintbeck Germany about 3,600 years old, which would make a later invention in Sumer seem unlikely.

I’m not sold on a near Eastern origin of the wheel. The Cucuteni-Trypillians predate Sumer. Also, the language surrounding the wheel seems to be PIE, which would weigh against a Semitic origin. From this publication:

The very earliest presently known evidence for wheeled vehicles comes (in the form of wheeled animal-shaped cups and house models) from the Tripolye culture (phases B2 & early C1) (Gusev 1998; Burmeister 2004: 14f.). The slide-car pulled by oxen is widely assumed to have been the predecessor of wheeled vehicles, and it too is documented from the Tripolye culture (C1 and earlier, cf. Burmeister 2004: 21f.). The Tripolye culture is located in the middle of the earliest vehicle finds, in the forest-steppe with big trees needed for solid wheels yet with plains more trafficable than the forested central and NW Europe or the marshy Sumer, where slide-cars remained long in use.

Although the PIE language being forced on the Trypillians by invaders (suggested in paper) now seems unlikely, as it probably spread out with the first Neolithic farmers. At least, the 9k age for the expansion and northern Turkish origin of PIE would seem to suggest that.

There’s a page here about the worlds oldest wooden wheel found in Slovenia, about 5,200 years old.Seen below. The wheel was found in April 2002, together with a squared oak axle, in the remains of a pile-dwelling settlement.