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First look at Luke 3:23 ;23 Furthermore, Jesus himself, when he commenced [his work], was about thirty years old, being the son, as the opinion was,
of Joseph,
[son] of He′li,
Now read Matthew 1:16; 1 6 Jacob became father to Joseph the husband of Mary, of whom Jesus was born, who is called Christ.
Problem number one. Here we read that Joseph has two fathers. In Matthew it says his father is Jacob, but in Luke it's He'li. Doesn't add up.
Second problem. Read Matthew 1:17; 17 All the generations, then, from Abraham until David were fourteen generations, and from David until the deportation to Babylon fourteen generations, and from the deportation to Babylon until the Christ fourteen generations.
It say that all the generations from Babylon to Christ are fourteen generations. So, lets add them up.
Matthew 1: 12-16;12 After the deportation to Babylon Jec·o·ni′ah became father to She·al′ti·el;
She·al′ti·el became father to Ze·rub′ba·bel;
13 Ze·rub′ba·bel became father to A·bi′ud;
A·bi′ud became father to E·li′a·kim;
E·li′a·kim became father to A′zor;
14 A′zor became father to Za′dok;
Za′dok became father to A′chim;
A′chim became father to E·li′ud;
15 E·li′ud became father to El·e·a′zar;
El·e·a′zar became father to Mat′than;
Mat′than became father to Jacob;
16 Jacob became father to Joseph the husband of Mary, of whom Jesus was born, who is called Christ.
Jec·o·ni′ah (1), She·al′ti·el; (2), Ze·rub′ba·bel (3), A·bi′ud (4), E·li′a·kim (5), A′zor (6), Za′dok (7), A′chim (8), E·li′ud (9), El·e·a′zar (10), Mat′than (11), Jacob (12) , Joseph (13)
There is one generation missing. Some might think that they forgot to put in He'li, but that won't make it work either. In Luke it tells you a completely different family line starting from David. I do believe there is an answer to this.
First thing you must know is that Matthew was originally written in Hebrew. Among scholars, it was determined that New Testament if not parts were written in Hebrew . Nehemia Gordon, a Dead Sea Scroll scholar, in research, came across a book written by an early Jewish man named Shem-Tob. In the book he refutes Catholicism arguing that they really don't follow the teachings of Jesus, and and the end of the book he included a Hebrew version of the Gospel of Matthew in Hebrew. Many refer to this book of Matthew as Shem-Tob's Hebrew Matthew.
In the Hebrew language, a dot can change the word. While translating Matthew into Greek a translator could easily take no note of a dot, jot or tittle, and therefore he mistranslates a word. In the Hebrew language, a dot can change the word from Husband to Father. So what it should read in Matthew is;
“Jacob became father to Joseph the father of Mary, of whom Jesus was born, who is called Christ.”
Mary's fathers name was Joseph, and she married a man by the name of Joseph.
Mary was apart of David's kingly line, not Joseph her husband. If you read in Luke, it say Nathan son of David. Nathan wasn't a king, whereas in Matthew it reads David became father to Sol'omon. Sol'omon who was king. We know that Joseph, the Husband of Mary was not the father of Jesus, so to keep the promise to David that Jesus would come through the kingly line, a woman would have to birth the Messiah.
This also gives you the fourteenth generation, making Matthew all add up.