There have been several proposed reconciliations of the Matthew and Luke genealogies. Among the popular ones are:
- Matthew's genealogy traces legal heirs; Luke's traces biological ancestors.
- Matthew's genealogy traces the ancestry of Joseph; Luke's traces the ancestry of Mary. This view takes the phrase "as was supposed of Joseph" in 3:23 as a parenthetical expression.
- Matthew's genealogy traces the ancestry of Mary; Luke's traces the ancestry of Joseph. This view assumes the phrase "Joseph the husband of Mary" was originally written as "Joseph the father of Mary". This view is much less common than the previous two; no existing ancient biblical texts read "Joseph the father of Mary".
The reason Luke has more generations than Matthew is because Matthew has left some out in order to split the generations into three sets of 14. We can see evidence of this in the middle section, tracing Solomon to Jechoniah:
…and Solomon the father of Rehoboam, and Rehoboam the father of Abijah, and Abijah the father of Asaph, and Asaph the father of Jehoshaphat, and Jehoshaphat the father of Joram, and Joram the father of Uzziah, and Uzziah the father of Jotham, and Jotham the father of Ahaz, and Ahaz the father of Hezekiah, and Hezekiah the father of Manasseh, and Manasseh the father of Amos, and Amos the father of Josiah, and Josiah the father of Jechoniah and his brothers, at the time of the deportation to Babylon.
Compare this to the same genealogy in 1 Chronicles;
1 Chronicles 3:10-16 [emphasis mine]
The descendants of Solomon: Rehoboam, Abijah his son, Asa his son, Jehoshaphat his son, Joram his son, Ahaziah his son, Joash his son, Amaziah his son, Azariah his son, Jotham his son, Ahaz his son, Hezekiah his son, Manasseh his son, Amon his son, Josiah his son. The sons of Josiah: Johanan the firstborn, the second Jehoiakim, the third Zedekiah, the fourth Shallum. The descendants of Jehoiakim: Jeconiah his son, Zedekiah his son;
Asaph in Matthew is Asa in 1 Chronicles and Uzziah in Matthew is Azariah in 1 Chronicles. However, Joram's great-grandson Azariah from Chronicles is listed as his son in Matthew. This technique for shortening lengthy genealogies is known as telescoping.