I was recently on a tour of Chichen Itza in Mexico, and our tour guide informed us that, despite using round-shaped stones & logs frequently, the Mayans never developed the use of the wheel. Are there any reasons that a civilization that could map the stars & planets, could not invent the wheel? Or was the tour guide giving us false and/or exaggerated information?
There's some previous discussion here on the topic. I'll add a few notes:
/u/SerLaron has it spot on when they say that it's hard to answer "Why not?" It presupposes a default way history progresses and requires us to find a reason why a society deviated from it.
He is correct that we have no evidence for major use of the wheel.
A bit about the "why." The functionality of the wheel skyrockets given a few factors, like pack animals like horses or oxen (which don't live in the Maya region) and navigable terrain (which is hard to find in the mountains and jungles of the Maya world). While there were plenty of raised/paved roads to easy transportation, there wasn't a single unified state that could create a regional infrastructure, as the Roman or Inca empires are rightly famous for.
Something that's frequently left out of discussions of the Maya and the wheel is the extant maritime/coastal trade routes. Long distance trade frequently occurred along the coast or inland waterways, so the need for land based routes wasn't overwhelming.