There is debate concerning. whether Matthew wrote the Gospel of Matthew. It can be strongly argued that Matthew is in fact the author.
The earliest description of this Gospel that we have says that the Gospel was written by Matthew. The book was circulated with Matthew in the title.
Before the end of the second century, perhaps as early as AD 1251, it was indisputably acknowledged that Matthew was the author of this Gospel. There is absolutely no evidence that says otherwise.
One argument against Matthew being the author is that the titles are not part of the body of the Gospels, so it is suggested that the Gospels were anonymous. However, even if there is no internal evidence that Matthew is the author of the Gospel, the unanimous early tradition that ascribes this Gospel to Matthew is strong evidence that Matthew is indeed its author.
Matthew composed the logia in the Hebrew tongue and everyone interpreted them as he was able.Papias. Cited by Eusebius, HE, iii. 39. 16.
The Elder used to say: Mark, in his capacity as Peter’s interpreter, wrote down accurately as many things as he recalled from memory—though not in an ordered form—of the things either said or done by the Lord. For he neither heard the Lord nor accompanied him, but later, as I said, Peter, who used to give his teachings in the form of chreiai, but had no intention of providing an ordered arrangement of the logia of the Lord. Consequently Mark did nothing wrong when he wrote down some individual items just as he related them from memory. For he made it his one concern not to omit anything he had heard or to falsify anything.Papias. Cited by Eusebius.
What is Papias referring to when he says logia here? In the New Testament, logia refers to an oracular utterance that descriibes the Old Testament (e.g., Romans 3:2, Hebrews 5:12). Could Papias be referring to the Gospel of Matthew with the word logia, or is Papias referring to a writing that only records the oracles of Jesus?
The points above strongly suggest that Papias believed that Matthew wrote the Gospel of Matthew.
Papias says that Matthew was written in Hebrew, although he probably meant Aramaic. However, essentially every scholar agrees that Matthew’s Gospel was written in Greek. There are several possible explanations concerning this:
In any case, Papias’s testimony is not the only evidence we have concerning Matthew’s authorship.
Now Matthew published also a book of the Gospel among the Hebrews in their own dialect, while Peter and Paul were preaching the gospel in Rome and founding the Church.Adv. Haer. iii. I. I, cited by Eusebius. HE, v. 8.2. The translation. cited is that of D. THeron’s Evidence of. Tradition (1957), p. 43.
It is likely that here, Irenaeus is using and interpreting Papias’s statement. Since Irenaeus does not mention anyone who disagrees, it can be assumed that there was unanimous agreement concerning Matthew’s author of this Gospel at this time.
Eusebius says that Pantaenus discovered that Matthew’s Gospel was already in India when he arrived.3 Although there are doubts concerning this story, it contributes to the tradition that Papias is referring to Matthew’s Gospel when he uses the word logia.
Origin also says that Matthew wrote a Gospel in Hebrew. Munck says that Origin’s testimony is significant because Origin knew both Greek and Hebrew, yet did not question Papias’s statement.