https://www.ancient.eu/zoroaster/

Modern scholars believe that Zoroaster must have lived at some point between c. 1500 and c. 600 BCE.
The 600 BCE limit is based on the fact that the Avesta does not contain a single reference to a ruler of the Achaemenid Empire,
which was the dominant power in Persia beginning in 550 BCE. The Avesta is believed to have been composed in eastern Persia,
which is why one would expect these texts to mention an Achaemenid ruler if its composition was later than 550 BCE. The earlier
date in the range, 1500 BCE, is based on linguistic evidence found in the Avesta. This work is composed of several different texts
and one of these texts, the Yasna, is considered to be the oldest of the Avestan texts. Its language is Old Avestan (sometimes called
Gathic Avestan), which is grammatically comparable to the language of the Indian text known as Rig Veda, since the languages of
Persia and India belong to the same language family (the Indo-European Languages family). It is therefore believed that the Rig Veda
and the Avesta are about the same age, dating to c. 1500 BCE. The range of speculation for Zoroaster’s life is wide. Saying that he
lived in around 1000 BCE, give or take a century or so, is an estimation that would be acceptable to most scholars.

https://www.bbc.co.uk/religion/religions/zoroastrian/history/zoroaster_1.shtml

Zoroastrianism was founded by the Prophet Zoroaster (or Zarathustra) in ancient Iran approximately 3500 years ago.
The precise date of the founding of Zoroastrianism is uncertain. An approximate date of 1200-1500 BCE has been established through
archaeological evidence and linguistic comparisons with the Hindu text, the Rig Veda.


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