Although the Mayan calendar goes deep into the past, the early events it records are legendary. The earliest historical date known is 28 May 585 BCE, the battle between the Medes and the Lydians that was interrupted by an eclipse predicted by Thales of Miletus.

Expanded a bit for E2, 23 June 2003. I have scrappy notes for the above fact, along with other ancient astronomy and mathematics. I believe it came from a reputable book on the history of maths, which I was reading a few years ago, but cannot cite what it was.

Note that this is the first date of a historical event on Earth. Astronomical dates are known earlier. A solar eclipse recorded in Babylonia can be identified with certainty as a certain day in 763 BCE, and another was recorded in China in 720 BCE.

Ancient calendars, however accurate they might be, can't necessarily be calibrated to our own with absolute certainty to the day. Our own Gregorian one succeeded the Julian one. Although this was initiated by Julius Caesar (d. 44 BCE) it quickly fell into confusion, and was not fixed up into precisely the modern form until 8 CE.

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