Yes, Matthew CAN Count to 14

In Matthew 1:1-17 we see one of two genealogies of the Lord Jesus Christ (the other is found in Luke 3:23-38). Matthew lists three groups of fourteen names. The second group is entirely kings of Judah:

  1. David
  2. Solomon
  3. Rehoboam
  4. Abijah
  5. Asaph
  6. Jehoshaphat
  7. Joram
  8. Uzziah
  9. Jotham
  10. Ahaz
  11. Hezekiah
  12. Manasseh
  13. Amos
  14. Josiah

What's interesting is that this is NOT the generation by generation genealogy that we find working through First and Second Kings. There we find this genealogy:

  1. David
  2. Solomon (First Kings 2:10-12) 
  3. Rehoboam (First Kings 11:43)
  4. Abijam/Abijah (First Kings 14:31)
  5. Asa/Asaph (First Kings 15:8)
  6. Jehoshaphat (First Kings 14:24)
  7. Jehoram/Joram (First Kings 22:50)
  8. AHAZIAH (Second Kings 8:24) 
  9. JOASH/JEHOASH (Second Kings 11:1, 12:1) 
  10. AMAZIAH (Second Kings 12:19-21) 
  11. Azariah/Uzziah (Second Kings 14:17-21)
  12. Jotham (Second Kings 15:7) 
  13. Ahaz (Second Kings 15:38)
  14. Hezekiah (Second Kings 16:20)
  15. Manasseh (Second Kings 20:21)
  16. Amon (Second Kings 21:18)
  17. Josiah (Second Kings 21:26) 
  18. JEHOAHAZ (Second Kings 23:30) 
  19. JEHOIAKIM (Second Kings 23:34)
  21. ZEDEKIAH (Second Kings 24:17) 
  22. Jechoniah (First Chronicles 3:16) 

Seven men are not mentioned by Matthew: Ahaziah, Joash, Amaziah, Jehoahaz, Jehoiakim, Jehoiachin, and Zedekiah. Why doesn't Matthew list them? 

First, because the Holy Spirit chosen to eliminate their names. It's not that they were particular wicked men; in fact, the records of Joash and Amaziah is positive, not negative. Besides, it's hard to find a king in Judah more evil than Ahaz, whom Matthew lists. 

We see that lines of descent were not always expected to be generation-by-generation in biblical times. If this was common practice, it certainly creates the possibility that the generations between Adam and Noah, and Noah and Abraham, also feature such gaps. At the same time, it must be said that for Matthew's purposes, there ARE no "gaps." A "gap" implies a mistake or error; this is a properly formatted and fully acceptable genealogy. 

What about Matthew's statement in Matthew 1:17, "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 knew his own history; the books of the Kings and the Chronicles of the kingdoms were clear. So we see that Matthew tells us that he has RECORDED 14 generations between the key figures of Abraham, David, Jeconiah, and Christ, who is the Son of David. The Hebrew language did not have numbers separate symbols; letters were given numerical value. The name "David" is equal to 14 in Hebrew numbering. The genealogy of the Christ, the Son of David, is given in three sets of 14 names, emphasizing His connection to the much beloved king. 

David Turner writes in his commentary on Matthew, 

It can be argued that Matthew made errors only if it can be demonstrated that Matthew intended to construct a comprehensive and exhaustive genealogy. Matthew’s “errors” are theologically motivated omissions, not mistakes in simple arithmetic. Matthew could evidently count to fourteen as well as his interpreters can.

Turner also writes,

"Some scholars think that Matthew chose fourteen because it is twice seven, the number of fullness or perfection. In this view, there are six sets of seven generations, and the Messiah inaugurates the seventh seven."

So, Matthew was not creating a record for, but writing the prologue for the arrival of the Christ, whose connection to king David was clearly established. The Christ was the fulfillment of the promises of God, the beginning of a new generation of the people of God, who through Christ become spiritual children of Abraham, who is "the father of all who believe without being circumcised" (Romans 4:9-12).