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Rabbi Harav Yaakov Medan (etzion.org.il/en/chapter-12b-daniels-prayer-continued) states: 'According to historical scholarship, the second year of the Persian Darius, when the rebuilding of the Second Temple commenced, was the year 521 B.C.E., and the Second Temple was destroyed in 70 C.E. Thus, according to this system, the Temple stood for 591 years. However, according to a beraita in Seder Olam [which places Creation at 3760 BCE] and the gemara in Bava Batra 4a, the Second Temple stood for only 420 years. Its construction began in the year 3408 and it was destroyed in 3828.' How is this year discrepancy to be explained--an important question for the elucidation of the seventy weeks prophecy of Daniel 9:24-27?*

*'The accepted interpretation in the Talmud (Nazir 32b) and all the commentators is that the "seventy weeks" allude to the 490 years between the destruction of the First Temple and the destruction of the Second Temple. This period includes within it the seventy years of desolation from the destruction of the First Temple until the second year of the reign of Darius (the Persian), when the building of the Second Temple commenced, and the 420 years that the Second Temple stood.' (Medan) In a footnote to this, he says, 'The discrepancy between these two calculations [that of historical scholarship and Seder Olam] is discussed at length in our article and that of C. Chefetz in Megadim 14 on the period of the kings of Persia and Media.' This journal is not accessible to me.

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    Related questions: 1 2 3 4 – Joel K May 29 '18 at 6:32
  • Also related: judaism.stackexchange.com/questions/91632/… – Joel K May 29 '18 at 12:28
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    @Yaacov I’m pretty comfortable that this falls under “general knowledge (science, etc.) as it relates directly to Judaism”. – Joel K May 29 '18 at 18:43
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    @yaacov if you have an answer for what the explanation is ("secular historians are stupid and promoting nonsense") then just post that as an answer with whatever supporting evidence you have. No need to continue yelling in the comments. – Double AA May 29 '18 at 20:00
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    @joelk I agree completely that this is on topic. Just like asking how to understand any other discrepancy between a Jewish teaching and realia (eg. Big Bang vs. literal reading of Genesis). This one just happens to be more esoteric than most. – Double AA May 29 '18 at 20:40
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This excellent source sheet produced by R. Anthony Manning, lists a number of different approaches to resolving the discrepancy:

1. Seder Olam is correct and the conventional chronology is incorrect.

Conventional chronology is incorrect due to Christian manipulation (R. Sa'adia Gaon) or Greek manipulation (R. Alexander Hool).

2. Conventional chronology is correct and Seder Olam is incorrect.

To quote directly from footnote 1 in R. Manning's source sheet:

Mitchel First’s book gives a comprehensive account of over 100 different Jewish responses on this issue! He lists a number of respected orthodox thinkers who take different positions. These include: (i) some who follow the C.C. [conventional chronology] without even mentioning S.O. [Seder Olam], such as R. Hertz in his Chumash, R. Shlomo Riskin, and R. Emmanuel Rackman; (ii) some who quote both systems, without deciding in either direction, such as R. Aryeh Kaplan and R. Ya’akov Meidan; (iii) some who consider that S.O. is not to be taken literally, such as R. Mordechai Breuer ... It is interesting to note that the Da’at Mikrah Tanach published by Mossad HaRav adopts C.C.

Mitchell First's book mentioned above is the one listed here on amazon.com.

3. Conventional chronology is correct and Seder Olam was intentionally adjusted.

Seder Olam was adjusted in order to obscure the date of the Messiah's arrival (R. Shimon Schwab), to line up the '2000 years of Torah' with the production of the Mishnah (Epstein / Dickman / Wilamowsky), to connect the Jewish year count with the 'minyan shtarot' system (R. Menachem Leibtag), or to hide the failures of the Jews to return to Zion at the start of the Second Temple period (R. Menachem Leibtag).

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    Rabbi Manning is awesome. I was zocheh to hear shiur from him for over a year, even though he usually only teaches in women's seminaries. Here's a link to an audio shiur he gave on this topic (based on the above source sheet). – robev May 31 '18 at 13:56
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A full discussion of this complex historical problem is found in the article 'Missing Years' in Religion-wiki: religion.wikia.com/wiki/Missing_years. It mentions that the following sources have been taken into consideration to support the traditional dating of Seder Olam:

The internal chronology of the Hebrew Bible.

Transmitted tradition regarding the dates of annually commemorated events.

The Tannaitic chronicle Seder Olam Rabba and later chronicles such as the Seder Olam Zuta, Seder_Ha-Dorot and Toldot Am Olam.

Comments on historical events in other Jewish writings such as the Talmud and the commentaries of Rashi.

The secular Greek writings of the Jewish historian Josephus and the national traditions preserved by the Persian historian Firdausi.

The Greek, Babylonian and Persian sources cited by those supporting the secular dating, but interpreted in a manner consistent with the traditional dating.

And it concludes by saying: 'This approach to the discrepancy is the most problematic. The reinterpretation of the Greek, Babylonian and Persian sources that is required to support the traditional dating has been achieved only in parts and has not yet been achieved in its entirety.'

Jewish Encyclopedia in the article 'Seder Olam' has a brief discussion, asserting that Seder Olam's handling of the Persian period is 'contrary to historical facts':

The 420 years of the Second Temple are divided into the following periods: the domination of the Persians, 34 years; of the Greeks, 180 years; of the Maccabees, 103 years; of the Herods, 103 years. It will be seen that the allowance, contrary to historical facts, of only thirty-four years for the Persian domination is necessary if agreement with the Biblical text is to be insisted upon; for it is stated (Dan. ix. 24) that the second exile was to take place after seventy Sabbaths of years (= 490 years). If from this number the seventy years of the first Captivity be deducted, and the beginning of Alexander's domination over Palestine be placed, in accordance with Talmudical evidence, at 386 years before the destruction of the Second Temple, there remain only thirty-four for the Persian rule.

Suggested Further Reading: Seder Olam: The Rabbinic View of Biblical Chronology, Heinrich Guggenheimer, editor. (Lanham: Rowman and Littlefield, 2005).

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