None of the four gospels contains a formal statement of authorship. Many critics latch on to this point and suggest that the gospels were written much later than the first century, and reflect the growth of unreliable traditions about Jesus.
This viewpoint will not stand up to close scrutiny. It is true that there is no “by-line” on the gospels. Such a practice was uncommon. But this is not the same as arguing they were anonymous. There would be no need to formally fix a name until there were several documents of the same kind together.
The other factor to consider is that because the gospels were written so closely to the time of Jesus, the actual eyewitnesses of Jesus and the apostles could authenticate the origin of the gospels.
Here are the basic historical facts:
1. There is zero evidence attributing the four gospels to anyone other than their traditional authors.
2. The early Christians unanimously accepted the traditional authorship of the four gospels.
3. It is highly implausible that the early church would have invented such unlikely characters as Matthew, Mark and Luke as authors of the gospels.
Papias (AD 60-130)
Papias, bishop of Hierapolis in Asia Minor, wrote a five-volume work entitled Expositions of the Sayings of the Lord. Only scattered fragments of his work survived, but they are quoted in various authors in early church history.
Here is what he said regarding Mark:
And the Elder used to say this: “Mark, having become Peter’s interpreter, wrote down accurately everything he remembered, though not in order, of the things either said or done by Christ. For he neither heard the Lord nor followed him, but afterward, as I said, followed Peter, who adapted his teachings as needed but had no intention of giving an ordered account of the Lord’s sayings. Consequently Mark did nothing wrong in writing down some things as he remembered them, for he made it his one concern not to omit anything which he heard or to make any false statement in them.”
Regarding Matthew: “So Matthew composed the oracles in the Hebrew language and each person interpreted them as best he could.”
(this is quoted by Eusebius, Ecclesiastical History 3.39.15-16, taken from The Apostolic Fathers, ed. by Holmes).
Eusebius mentions Papias again in Ecclesiastical History 2.15.2
Clement in the sixth of the Hypotyposes [Outlines] cites the story, and the bishop of Hierapolis named Papias joins him in testifying that Peter mentions Mark in the first epistle, which they say he composed in Rome herself, and that he indicates this, calling the city more figuratively Babylon by these: "She who is in Babylon, chosen together with you, sends you greetings and so does my son Mark."
Irenaeus (AD 130-200)
Irenaeus was a bishop in Roman Gaul (modern France), writing around AD 180. In a book refuting various heresies, he said the following about the gospels:
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. After their departure, Mark, the disciple and interpreter of Peter, did also hand down to us in writing what had been preached by Peter. Luke also, the companion of Paul, recorded in a book the Gospel preached by him. Afterwards, John, the disciple of the Lord, who also had leaned upon His breast, did himself publish a Gospel during his residence at Ephesus in Asia. (Against Heresies 3.1.1 Roberts & Coxe, The Ante-Nicene Fathers Vol.I : Translations of the writings of the Fathers down to A.D. 325)
The Muratorian Fragment (AD 170)
This fragment, discovered by Antonio Muratori and published in 1740, listed books of the New Testament in response to an early heretic named Marcion.
. . . at which nevertheless he was present, and so he placed. The third book of the Gospel is that according to Luke. Luke, the well-known physician, after the ascension of Christ, when Paul had taken with him as one zealous for the law, composed it in his own name, according to belief. Yet he himself had not seen the Lord in the flesh; and therefore, as he was able to ascertain events, so indeed he begins to tell the story from the birth of John. The fourth of the Gospels is that of John, of the disciples.
What we know about the authors of the gospels based on the internal evidence complies with this strong historical testimony.
Notice the frequent reference to money—more frequent than the other gospel writers in fact. He uses unique monetary terms (drachma in 17:24; stater in 17:25; talent in 18:24, 25). Matthew contains the only two parables on talents (chs. 18, 25); and he uses tax-collector-type terminology (“debts” in 6:12 where the Lukan parallel has “sins”); “bankers” (25:27), etc. Especially when one compares the synoptic parallels, Matthew’s use of monetary terms seems significant.
John Mark was an associate of the apostles (Acts 12:12; 13:5, 13; 2 Tim 4:11; and especially 1 Peter 5:13). Many commentators have pointed out the similarity in the structure of Mark’s gospel and Peter’s summary of the gospel in Acts 10:36-43.
Luke was a companion of Paul’s as the “we” passages in Acts (16:10-17; 20:5-15; 21:1-18; 27:1–28:16) suggest. He is also mentioned in his letters (Col. 4:14, Phm 24; 2 Tim 4:11). Paul apparently quotes from Luke 10:17 in 1 Tim 5:18.
The author of the fourth gospel calls himself the “beloved disciple” (13:23; 19:26; 21:7, 20). He belongs to a group of seven in 21:2 (Peter, Thomas, Nathanael, the sons of Zebedee, and two others)—and here, he must be one of the last four unnamed disciples. Nowhere in this gospel does John the disciple appear by name (even though he is named twenty times in the synoptics). This strongly infers either that the author of this work was absolutely unaware of John the disciple—a possibility which seems quite remote—or he was John the disciple.