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After giving Jesus's genealogy in the first chapter, Matthew goes on to point out the number of generations between significant events:

Thus there were fourteen generations in all from Abraham to David, fourteen from David to the exile to Babylon, and fourteen from the exile to the Messiah. —Matthew 1:17

What is the significance of '14 generations'? Does this fulfill a specific prophecy? Does the number 14 itself hold any special meaning? How would a 1st century Jewish reader interpret this fact?

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Welcome to BH.SE. Thank you so much for including the final question, which really gets at the heart of what we are about here. Matthew makes a big deal about the number of generations, which is strange to us modern readers. Hopefully we can dig down to the way this was understood by the gospel's earliest audience. –  Jon Ericson Jan 30 '12 at 21:15
    
Just read a really good thesis on the subject. rtforum.org/lt/lt13.html –  user567 May 5 '12 at 4:11
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6 Answers

Numerology

A recent question linked to a reference of meaning of various numbers in the Bible and this passage seem to be the primary source of meaning for the number 14. None of the other references seem particularly compelling and seem to be included for data-mining purposes. I would say that the number 14 has no particular meaning in the Bible outside of this passage.

Prophesy

While there are many Old Testament prophesies that are said to apply to Jesus, I don't know of any that involve 14 generations. It is clear that the Messiah must come from the line of David, but nothing in the Jewish texts require him to be any particular generation away from David.

Interpretation

So why did Matthew make a point of specifying the number of generations? Simply put, genealogy and numerology were important to 1st century Jews as they are to most people throughout history. It's vital that the Messiah descend from Abraham and David. So Matthew recorded the lineage from Abraham to David and from David to Jesus. When he did so, he must have noticed that there were roughly the same number of men from the start of the Jewish people to its height, as from the start of the Jewish kingdom to its end, as from the captivity to Jesus. There weren't 14 generations exactly, however. So Matthew edited the list by jumping from grand- or great-grandfathers to their later decedent ("son of" can mean any male decedent).

The image that Matthew seems to invoke that of a deep plan in human history managed by God and culminating in the person of Jesus. It is the story of the rise and fall of a people and the redemption of that story when a new "King of the Jews" was born. We are meant to be reminded of the very familiar names that take up the bulk of Jesus' genealogy and remember their triumphs and failures.

For a fairly exhaustive interpretation of this passage, I highly recommend Bob Deffinbaugh's article on bible.org.

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In Hebrew, the values of the letters of David's name add up to 14. –  Bruce Alderman Jan 31 '12 at 5:57
    
Good article; thanks for the link. +1 –  Kazark Jul 15 '12 at 19:13
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I see Bruce stated this in a comment, but I'll give more detail. In Hebrew, David's name adds up to 14 when each letter is treated as a number (called gematria).

You skip the vowel points (nikkud) and just add up the values of the consonants dalet waw daleth (the same character is used for V and W). Dalet counts as 4, Waw counts as 6, and another Dalet adds 4 more. Thus, 14.

The name David means "beloved."

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Nice. I was going to look that up, but I see I won't have to. –  Jon Ericson Jan 31 '12 at 17:19
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If we are to think like the first-century hearers, we must recognize that the importance of the number fourteen is that it is a multiple of (that ever-so-important number) seven. Matthew is implying that the entire flow of God's history of creating a people for himself shows that Jesus the Christ is our Sabbath rest.

Forty-two, not Fourteen

Three sets of fourteen is six sets of seven. The operative number here is not really fourteen but forty-two. And no, forty-two is not the answer to life, the universe, and everything; actually it is the precursor to the one who is the meaning of everything. Jesus Christ is the seventh week of history; he is the completion and the culmination; he inaugurates the last days.

In the Lord Jesus, God's redemptive work comes to a rest. This does not mean that God becomes inert, but that that the finality and totality are invested in him, and history never moves beyond him, as he lives on in his indestructible life, ruling from on high.

Old Testament Prophecies

I am not aware of prophecies that reference the number fourteen. However, when this is seen as a matter of the seventh seven, all the significance of seven and its square come into play. There are a handful of references to forty-two in the Old Testament, but none of them shed a lot of light on this situation. The most relevant prophecy may be Daniel's reference to the week of weeks:

Now listen and understand! Seven sets of seven plus sixty-two sets of seven will pass from the time the command is given to rebuild Jerusalem until a ruler—the Anointed One—comes. Jerusalem will be rebuilt with streets and strong defenses, despite the perilous times. —Daniel 9:25 (NLT)

Admittedly, Daniel is giving a different perspective on the narrative than Matthew, but the same theological meaning of the seventh seven: the Messiah will be the fulfillment of all things.

New Testament Prophecies

The meaning of forty-two is further clarified by the last book of prophecy as the time of the dominion of the nations over God's people:

But do not measure the outer courtyard, for it has been turned over to the nations. They will trample the holy city for 42 months. —Revelation 11:2 (NLT)

And:

Then the beast was allowed to speak great blasphemies against God. And he was given authority to do whatever he wanted for forty-two months. —Revelation 13:5 (NLT)

The Messiah is the one who brings this time to an end, defeating the enemies of God and rescuing his people. Upon his arrival, the time of trampling is over.

Conclusion

In Jon Ericson's answer, he links to an article by Bob Deffinbaugh, who points out the strong connections between Matthew 1 and Genesis 1. Indeed, what we see here is that just as God created progressively over six days, so God revealed himself progressively for six weeks, until on the seventh God himself appeared on earth and became our rest.

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Please note that the total of 42 is also the Kabbalist number for one of the special names of God. –  R Rue Oct 21 '13 at 1:49
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The numerical values of David's name adds up to 14, as has already been stated. Besides there were exactly 14 generations between Abraham and David. But Matthew had to skip 3 generations to make 14 from David to the captivity in Babylon, and had to skip many more to make only 14 from Babylon to Jesus. The numerical value of David's name itself may explain why the number 14 is chosen, but does not explain why any number had to be chosen at all: why not list every person in the genealogy?

I think the answer lies in the fact that Matthew is more interested in theology and parallelism than in historicity and chronology. Often Matthew will mention only briefly what Mark describes in great detail, and will move the accounts of events around to make them fit his structure and theological emphasis (note, however, that he never claims that these events are in chronological order). In the genealogy, I believe he is drawing parallels between each set of 14 names in order to emphasize two points: David (from whom the Messiah would come), and Babylon (which took away from Israel the kingdom which Christ was to restore). In addition to emphasizing these two points in the chronology, the 14x3 generations may be meant as a mnemonic aid for anyone wanting to memorize them (as was more common in their time than in ours).

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The sons of some of the people were adopted as their father's sons...not their own so maybe there are cases in the genealogies that Matthew knew about that we don't know about. Some examples I've found of these sons being adopted even though he has his own parents are 1. Jacob claiming Joseph’s children as his own. Gen 48:5 And now your two sons, who were born to you in the land of Egypt before I came to you in Egypt, are mine; Ephraim and Manasseh shall be mine, as Reuben and Simeon are. 2. Joseph’s grandchildren were credited as his children. Gen 50: 23 And Joseph saw Ephraim's children of the 3rd generation. The children also of Machir the son of Manasseh were counted as Joseph’s own.

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Drawing on "The Adoption of Jesus" by Ra McLaughlin, I'd suggest that the counting here is not intended as a hidden numerological code or fulfillment of any prophecy but is simply a literary device used to place Jesus in squarely as part of Israel's history. Says McLaughlin:

The generations are not counted in a precisely similar fashion — Jeconiah is counted twice. This is not inappropriate given that [the genealogy] is primarily a literary device intended to highlight the four markers [viz., Abraham, David, the exile, and Christ]. Moreover, Jeconiah rightly belongs in both groups: in the first group, he is in a line of kings; in the second group, having been deposed, he is merely counted as a man.

In particular, Matthew was self-consciously writing, Michael Kruger argues, to complete the story of Israel recorded in the Old Testament and that he saw Jesus as the continuation and consummation of that story:

[Matthew] turns immediately to a genealogy, placing the Jesus story into the story of Israel, with a special emphasis on David. The genealogy, of course, is a well-known Old Testament genre that is frequently used to demonstrate the historical unfolding of God’s redemptive activities among his people. In this regard, Matthew’s closest parallel is the book of Chronicles which also begins with a genealogy that has an emphasis on the Davidic line.

If by the first century Chronicles was regarded as the final book in the Hebrew canon, as some scholars have argued, then Matthew’s gospel would certainly be a fitting sequel. An Old Testament canon ending with Chronicles would have placed Israel in an eschatological posture, looking ahead to the time when the messiah, the son of David, will come to Jerusalem and bring full deliverance to his people.

If so, then Matthew’s opening chapter would be a clear indication that he is intending to finish this story. He is picking up where the Old Testament ended, with a focus on David and the deliverance of Israel.

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