Long and fascinating history
In ancient Greece, before mechanical odometers, distances were measured by “bematists” — specialists trained to measure distances by counting their steps.
Although they may have existed earlier, the first descriptions of odometers found so far are from the first century AD.
During the Han Dynasty in China, independent of what was happening in Greece and the Roman Empire, odometers were invented in China.
Much more of the history can be found here: https://en.wikipedia.org/wiki/Odometer
Nartnional Odometer Day is May 12. It was the day in 1847 William Clayton, a Morman pioneer, invented his “Roadmometer” that was attached to a wagon heading west to Utah.