Rabbi Aryeh Kaplan has come up with a wonderful argument from which he attempts to derive the current scientific understanding that the Universe is old, billions of years old and that it began with Big Bang from classic Jewish medieval sources. Most people who tout the argument are amazed at it's famous source, but they never really analyze how Rabbi Kaplan composed his argument.
For one, Ramban's view of creation is not the same as is found in modern cosmology. Ramban's idea of creation is that God created a "prime matter" without any characteristics - this a Greek idea - from which all other matter of the universe came from. However, he also asserts the initial creation was actually of two prime matters: one of heaven and one of earth. There is no scientific basis for any of these ideas. This can turn into something close to the Big Bang model, but only if you re-interpret a few things in a different light.
The point where time plays in is that Ramban says that before the first day - time was not set. But he gives no indication for how much time has passed. His disciple R' Yitzchak of Acco is recorded by an Aryeh Kaplan that he goes into some mystical calculations bearing on the 7000 year cycles of the world, with there being 7 such cycles. And with each human day being equal to 1000 years we get a value of around 15 billion years assuming we're in the 7th cycle. BUT, R' Yitzchak does not say we are in the seventh cycle, only the second. And that greatly reduces the amount of time in his prehistory. Kaplan had gone to another source, the Livnat HaSapir, who says that we're in the sixth cycle. But this is already so much mixed sources and contrived conclusions.
"... According to the master Kabbalist, Rabbi Isaac of Acco, when counting the years of these cycles, one must not use an ordinary physical year, but rather, a divine year (Otzar Chaim 86b). The Midrash says that each divine day is a thousand years, basing this on the verse, "A thousand years in Your sight are as but yesterday", Psalm 90:4 (Bereshit Rabbah 8:2, Zohar 2: 145b, Sanhedrin 97a). Since each year contains 365.25 days, a divine year would be 365,250 years long. According to this, each cycle of seven thousand divine years would consist of 2,556,750,000 earthly years. This figure of 2.5 billion years is very close to the scientific estimate as to the length of time that life has existed on earth. If we assume that the seventh cycle began with the Biblical account of creation, then this would have occurred when the universe was 15,340,500,000 years old. This is very close to the scientific estimate that the expansion of the universe began some 15 billion years ago."
-- Taken from Sefer Yetzirah, commentary by Rabbi Aryeh Kaplan, published by Weiser -- 1997, page 186.
Notice how he says "If we assume that the seventh cycle..."
Also, 365.25 days is not the length of a Jewish year. Nor is 2.5 billion years close to the amount of time life is thought to be on Earth - that's closer to 3.5 - 3.8 billion years. Big difference. The numbers are wrong, the math itself is practically arbitrary, and the assumptions are without reason. The 15 billion number wasn't calculated by Yitzchak of Acco, but by Aryeh Kaplan. I'm sure that if scientists had found the Universe to be 100 million years old or 2 billion years or 10 billion years or 12 or 20 - Kaplan would have found that same number amazingly in the texts of Rav Yitzchak ofAcco.
There is no classical Jewish source who gives the age of the universe as even close to what we think today. Rabbi Kaplan messed with math and mixed sources until he found a combination that he liked. Whatever happened to intellectual integrity?