The First Gospel circulated anonymously and acquired the name of Matthew early. The oldest surviving statement, from Papias in the early second century, says that Matthew compiled the sayings in the Hebrew tongue, and each interpreted them as he could, a sentence much argued over.
Modern scholarship generally doubts that the apostle wrote the Gospel as it stands. The canonical Matthew is in fluent Greek, not translated from Hebrew or Aramaic; it draws heavily on the Gospel of Mark, reproducing much of it almost word for word, which is a strange thing for an eyewitness apostle to do with a non-apostle's book; and its polished form points to a later author. What Papias described, perhaps a collection of sayings, may lie somewhere behind it, but the attribution is treated as traditional rather than established.
The traditions of his mission scatter widely: Ethiopia, Persia, or Parthia, with martyrdom in some accounts and a peaceful death in others. None is early or secure. His emblem among the four evangelists is the man or angel, because his Gospel opens with the human genealogy of Jesus, and he is invoked as patron of tax collectors, accountants and bankers, a wry legacy of the trade he was called to leave.