Matthew also uses the typically Jewish expression “kingdom of heaven,” thus avoiding unnecessary use of the word “God.” As we will see below, Matthew also seems to soften Mark’s negative approach to the Jewish law.
There are, however, important arguments against identifying the author as a Jew.
Matthew, whose name means "gift of the Lord," was a tax collector who left his work to follow Jesus (9:9-13).
In Mark and Luke he is called by his other name, Levi.
It is also the consensus position that the evangelist was not the apostle Matthew. 3.39, Papias states: "Matthew put together the oracles [of the Lord] in the Hebrew language, and each one interpreted them as best he could." In Adv. 3.1.1, Irenaeus says: "Matthew also issued a written Gospel among the Hebrews in their own dialect while Peter and Paul were preaching at Rome and laying the foundations of the church." We know that Irenaeus had read Papias, and it is most likely that Irenaeus was guided by the statement he found there. 7): This means, however, that we can no longer accept the traditional view of Matthew's authorship. First, the tradition maintains that Matthew authored an Aramaic writing, while the standpoint I have adopted does not allow us to regard our Greek text as a translation of an Aramaic original.None of the gospels mention the destruction of the Jewish temple in A. Acts also fails to mention the incredibly significant events of A. 70, which would have been extremely relevant and prophetically important and would require inclusion into Acts had it occurred before Acts was written. If what is said of Acts is true, this would mean that Luke was written at least before A. 63 and possibly before 55 - 59 since Acts is the second in the series of writings by Luke. Therefore, Matthew was in circulation well before Ignatius came on the scene. Since Luke agrees with Matthew, Mark, and John and since there is no contradictory information coming from any of the disciples stating that Luke was inaccurate and since Luke has proven to be a very accurate historian, we can conclude that Luke's account is very accurate. Remember, Acts is a book of history concerning the Christians and the Jews. We add to this the fact that Acts does not include the accounts of "Nero's persecution of the Christians in A. This means that the gospel of Luke was written within 30 years of Jesus' death. The various dates most widely held as possible writing dates of the Gospel are between A. As far as dating the gospel goes, Luke was written before the book of Acts and Acts does not mention "Nero's persecution of the Christians in A. by Maxim Cardew The author of the Gospel has traditionally been identified with “Matthew,” who according to this Gospel is one of Jesus’ twelve disciples (see Matthew 9:9; he is called “Levi” in Luke ).The main source of this tradition is Irenaeus (a second-century bishop) who writes: “Matthew also issued a written Gospel among the Hebrews in their own dialect” (Against Heresies 3.1.1).