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First Matthew calls Jesus son of David, a title of the rightful heir to Israel's throne (as in Jer 23:5; 33:15; Ps. Sol. 17:21-23; 4QFlor). Other lines of evidence support the claim that Jesus' family stemmed from this royal lineage (for example, Rom 1:3; b. Sanhedrin 43a bar.; Euseb. H.E. 3.20; see also Meier 1991:216-19), and ancient Jewish polemicists never bothered to try to refute it. Thus Matthew opens and closes the genealogy with a title for Jesus that is significant but rare in his Gospel: Jesus Christ, that is, the messianic king (1:1, 18).
Next Matthew calls Jesus son of Abraham. This is especially significant because subsequent chapters further portray Jesus as Israel's representative, the epitome of its history (for example, 2:15; 4:2; see Kingsbury 1975:12; Longenecker 1975:141-43). As the heir of Abraham par excellence, Jesus can communicate Abraham's promised blessings to his people. (Some teachers regarded Abraham as the first Gentile convert to Judaism, which may also fit Matthew's theme.)