Matthew opens his gospel account with these words: “The book of the genealogy of Jesus Christ, the son of David, the son of Abraham” (1:1). We find the same wording in Genesis 2:4 (LXX), “The book of the genealogy of heaven and earth,” and 5:1 (LXX), “The book of the genealogy of Adam.” These are the only two places in the entire Old Testament where the phrase “the book of the genealogy” (Gk. Βίβλος γενέσεως) occurs. This suggests an intentional allusion by Matthew.
Continuity and Recapitulation
Why does Matthew make this allusion? Two reasons can be given.
First, Matthew demonstrates continuity: the promised line called out and separated by God earlier in redemptive-history and through which the eschatological blessing for the cosmos would be realized culminates in the person of Jesus Christ. As Matthew points out, Jesus is the “son of Abraham.” Herman Ridderbos notes, “The birth of Jesus Christ was the culmination of the great ancestral line of sacred history.”
Second, Matthew demonstrates recapitulation: something similar to what took place in Genesis is now occurring, namely the birth of Jesus Christ as the beginning of a new creation. The historical events of Genesis are repeating themselves on a higher plane with his birth. G.K. Beale observes,
Matthew is narrating the record of the new age, the new creation, launched by the coming, death, and resurrection of Jesus Christ. And, since Matthew is narrating a genealogy of Jesus, it is likely that the Gen. 5:1 reference is uppermost in mind, and that Jesus is being painted with the genealogical brush of Adam. And just as Adam created others “in his own likeness, according to his image” (Gen. 5:3), so would Christ.
It is interesting also to point out that just as the Spirit was present at the first creation hovering over the waters (Gen. 1:2), so in the Genesis-like genealogical opening of Matthew’s gospel the Spirit is present again: “[Mary] was found to be with child from the Holy Spirit” (Matt. 1:18). This further illumines Matthew’s opening intention of showing Jesus to be the new Adam, the beginning of the promised new creation.
The Seed and Redemptive-History
Both reasons stated above—continuity and recapitulation—need to be maintained. In the redemptive-historical period of Genesis, the revelation of God was in seed form and the idea of a new creation was not yet apparent. This was so much the case that Eve believed her merely human son Cain might be the one promised who would crush the head of the serpent—a bit of triumphant optimism may be found in her naming of him (Gen. 4:1). Of course she was mistaken, for Cain will go on to murder his brother Abel, manifesting his dark position in the great divide between the seed of the woman and the seed of the serpent (Gen. 3:15).
As the revelation of God organically blossoms through the course of redemptive-history, it becomes more evident and explicit, especially during the time of the prophets, that the promised seed of the woman will bring about a new creation (e.g., Isa. 65:17-25). Furthermore, there are super-human, even divine claims that are made about this seed (e.g., Dan. 7). While still the seed of Abraham (and later specified as the kingly seed of David), something about this seed would surpass even Abraham and David themselves (Ps. 110:1; cf. Matt. 22:41-46). All of this is confirmed in the birth of Jesus Christ: fully man and of the line of Abraham and David, but also fully God and the eternally begotten Son of God.
There is therefore not a mere one-to-one correspondence between the Βίβλος γενέσεως (“the book of the genealogy”) of Matthew and Genesis, as if nothing developed between the writing of the two books. Matthew demonstrates continuity and fulfillment by tapping into the redemptive-historical family tree that Jesus is not only a member of, but the consummate member of, that is, the very seed of the woman who was promised to one day crush the head of the serpent. The person and work of Jesus are rooted in the creation account, for he comes as the second and last Adam (Rom. 5:12-21; 1 Cor. 15:42-49), the son of David, the son of Abraham, to bring about God’s eschatological kingdom and unleash his cosmic blessing for the whole creation.
While this blessing was initially to spread by the obedience of the first Adam, according to the dominion mandate given to him in the garden (Gen. 1:28), now it will spread as Jesus, the last Adam, continues his work through his Holy Spirit-empowered church, commissioned to make disciples of all nations (Matt. 28:18-20).
This began to be fulfilled in the early church as the word of truth, the gospel, went forth. Paul observes in Colossians 1:6 that “in the whole world [the gospel] is bearing fruit and increasing [αὐξάνεσθε].” This is an allusion to Genesis 1:28 (LXX), “Be fruitful [αὐξάνεσθε] and multiply and fill the earth and subdue it…”  Like Matthew, Paul sees the original dominion mandate that the first Adam failed at when he distrusted God’s word and submitted himself to the serpent, now today being fulfilled by the exalted King Jesus as his church goes out to make disciples of all nations.
The Opening and Closing of Matthew’s Gospel
This points brings together Matthew’s entire gospel. We’ve been focusing on his opening words, “The book of the genealogy of Jesus Christ, the son of David, the son of Abraham (1:1). But now we can see how his closing words reveal that Jesus’ incarnation, life, death and resurrection have unleashed the covenant promises of God made to Abraham and David, that he is, in fact, the consummate member of this family tree. To David God promised that he would establish the throne of his son’s kingdom forever (2 Sam. 7:13). To Abraham God promised that all the nations of the earth would be blessed in him (Gen. 12:2-3). And so we read,
And Jesus came and said to them, “All authority in heaven and on earth has been given to me. Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age” (Matthew 28:18-20).
The birth of Jesus Christ—the son of Abraham, the son of David—is the dawning of a new age. He has begun to realize the eschatological goal of creation and will one day bring it to consummation when he comes again in the glory of his eternal kingdom.
 For further discussion on Βίβλος γενέσεως in Matthew 1 see D.A. Carson, “Matthew,” in Matthew & Mark, The Expositor’s Bible Commentary, eds. Tremper Longman III and David E. Garland, Revised Edition (Grand Rapids: Zondervan, 2010), 86-90.
Herman Ridderbos, Matthew, Bible Student’s Commentary, trans. Ray Togtman (Grand Rapids: Zondervan, 1987), 16.
 G. K. Beale, A New Testament Biblical Theology, 389; see also pp. 566ff; cf. Jonathan T. Pennington, “Heaven, Earth, and a New Genesis: Theological Cosmology in Matthew,” in Cosmology and New Testament Theology, ed. Jonathan T. Pennington and Sean M. McDonough, LNTS 355 (London: T&T Clark, 2008), 39-40.
 Note Luke, in his two volume work (Luke-Acts), does not say Jesus finished his work with his ascension, but that his work recorded in the gospel account was only the beginning! (cf. Acts 1:1)
 For an insightful discussion on this and further argumentation for the allusion see G.K. Beale, The Temple and the Church’s Mission: A Biblical Theology of the Dwelling Place of God, New Studies in Biblical Theology (Downers Grove, IL: InterVarsity Press, 2004), 263-68.