The (currently) top rated answer to this other question says that:
R' Aryeh Kaplan z'l teaches as follows:
R' Nehunia ben Hakana brings in Sefer Temuna that there are larger shmita cycles of 7000 years each, of which we are now in the 6th, putting the age of the earth at 42,000 years old.
I am interested in these 7000-year shmita cycles and would like to ask a couple of questions about them:
Is any information available on how old this concept is? For example, if it was perhaps proposed relatively recently such as in 19th century, or if it is older than that.
Does additional information exist (sorry, it would have to be in English) where I can read more about it? I am interested on what reasoning or sources this concept is based on.
Update: The answer by Menachem brought me to the Wikipedia article about Sefer HaTemunah. This article refers to a document called "Babylonian Talmud: Tractate Sanhedrin" which says in Folio 97a (3rd paragraph from the end)
R. Kattina said: Six thousand years shall the world exist, and one [thousand, the seventh], it shall be desolate
and in Folio 97b (3rd paragraph from the beginning)
and the remaining [period] will be the Messianic era, whilst the Holy One, blessed be He, will renew his world only after seven thousand years
So it looks like this concept itself predates the book Sefer HaTemunah?