Chizuk Emunah (Pt 2) Under the Microscope: Chapter 35

Luke 3:23, The genealogy of Jesus, as treated in this and the subsequent verses, is contradictory to that in Matthew 1. For Luke commences thus: "The list of the descent of Jesus"—"And Jesus was the son of Joseph, the son of Heli, the son of Matthat, the son of Levi, the son of Malachi," etc. etc. In Matthew, where the origin of Joseph is traced back to Solomon, the Son of David, the enumeration of the ancestors of Joseph closes in the following manner:—"And Eliud begat Eleazar, and Eleazar begat Matthan, and Matthan begat Jacob, and Jacob begat Joseph, the husband of Mary, of whom was born Jesus." We have already shown above that Matthew enumerates forty-two generations, from Abraham our father; but Luke counts only twenty-six. From these contrary statements one might fairly ask, which Joseph was the husband of Mary? Was it Joseph, the son of Heli, the son of Matthat, the son of Levi, as Luke supposes; or was it Joseph, the son of Jacob, the son of Matthan, the son of Eleazar, as Matthew supposes? If we are to believe the words of Luke, then the statement of Matthew must be incorrect, and vice versa. Luke, in tracing back the descent of Jesus to the first ancestor, says that Jesus was the son of Adam, the Son of God. Hence it would seem that Jesus has no better title to the designation of the Son of God, than every other descendant of Adam.

This is the common genealogy objection, which can be illustrated in this chart.


One observation is that Matthew is using the practice of gematria in his genealogy. Gematria is the practice of assigning the numerical value of the letters in a word in order to derive some significance. The numerical value of David is 14.
 
Compare this to Matthew 1:17 which states "So all the generations from Abraham to David were fourteen generations, and from David to the deportation to Babylon fourteen generations, and from the deportation to Babylon to the Christ fourteen generations." Matthew is not saying that the lineage of each of these was exactly 14 people, but instead picks out the 14 most significant people in the lineage.

Risto Santala also has explanations of Matthew's use in terms of rabbinical writings. For example, tractate Avot states that there were 10 generations from Adam to Noah, and 10 from Noah to Abraham. Technically, this requires some trickery to get right.

The lineage of Noah is:
1. Adam
2. Seth
3. Enosh
4. Kenan
5. Mahalalel
6. Jerod
7. Enoch
8. Methuselah
9. Lamech
10. Noah

The lineage in Genesis 11 is:
1. Noah
2. Shem
3. Arphaxad
4. Shem
5. Salah
6. Eber
7. Peleg
8. Reu
9. Serug
10. Nahor
11. Terah
12. Abraham

So there are 10 generations from Adam to Noah if you count Adam and Noah. There are 10 generation from Noah to Abraham if you do not count Noah or Abraham.

As explained by Jewishroots.net "If the genealogies in Matthew and Luke were identical, then one of them would have been unnecessary. And since God is the ultimate economizer of space, logic dictates that the differences between the genealogies must be purposeful."