In the Matthew and Luke we can read the genealogy of Jesus. While in Matthew 1 it dates back to Abraham, in Luke 3 it goes back to Adam.
What's the significance of this difference?
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Matthew's Gospel is first for the Jews and Luke's Gospel is for the Gentile.
The focus of Matthew is that Jesus is "the King of the Jews", the Messiah promised to Abraham, Isaac, Jacob, who would be a direct-line descendant of King David, etc. The original purpose of Matthew's Gospel was for the Jews, and Papias tells us that Matthew's Gospel was first written in Hebrew for the Jews of Judaea, and only later translated into Greek. Matthew's Gospel seeks to answer the question "Is Jesus of Nazareth the promised Messiah of the Old Testament, the King of the Jews?"
If the royal line of David had continued to rule then, when Joseph, Jesus's adoptive father, died Jesus would have ascended the throne, being the eldest son in the family. (Adoption made no difference, an adopted son in those days having equal rights of inheritance with biological sons.)
So in Matthew's Gospel the focus is on Joseph and not Mary - the genealogy is that of Joseph (Matthew 1:16) and for the same reason in Matthew's Gospel the Lord speaks to Joseph, rather than Mary, about the coming birth; whereas in Luke's Gospel the focus is on Mary with the Angel Gabriel speaking to Mary, and not Joseph.
Notice how Joseph and not Mary is the focus of attention in Matthew's Gospel in Matthew 1:18-25, Matthew 2:13-14 and Matthew 2:19-23.
And notice how the opposite is true in Luke's Gospel: Mary and not Joseph is the focus of attention in Luke's Gospel.
In Luke's Gospel (Luke being a Gentile himself) the focus is that Jesus is the Saviour of the World, both Jews and Gentiles. So Jesus is the fulfilment of the promise God gave to the whole human race when He spoke to Satan in the hearing of Adam and Eve after they sinned:
I will put enmity between you and the woman, and between your seed and her seed; he shall bruise your head, and you shall bruise his heel.
It was by faith in this promise that one day a Saviour would come and destroy the power of the Devil that men, before the Deluge and right up to the time of Abraham, were enabled to call upon the name of the LORD and be saved (Genesis 4:26).
The coming Saviour would be "the seed of the woman", not the seed of a man, hinting that the Saviour when he comes into the world would be born of a virgin. And so Luke 3:23 ought to read
Jesus, when he began his ministry, was about thirty years of age, (being as was supposed of Joseph,) being of Heli, of Matthat...etc.
or to put it another way, to give the proper sense:
Jesus, (being as was supposed of Joseph), when he began his ministry was about thirty year of age, being of Heli, of Matthat, etc.
Meaning Jesus was a descendant of Heli, where Heli was the father of Mary.
Jesus, then, was a descendant of David both through his mother and his adoptive father, his mother to fulfil the promise of 2 Samuel 7:12 and his adoptive father to fulfil the promise of, for example, 2 Samuel 7:16 and 7:26.