THE PROBLEM: Matthew, Mark, and Luke use almost identical narratives of everything but the Birth of Christ and the Crucifixion -- their accounts of His ministry are nearly identical, though they differ greatly in what teachings He did where and when. And that similarity is not merely a matter of three reporters telling the same story, but a near-verbatim identity of phrasing, with differences attributable to some simple rules. E.g., Matthew will use Heaven in place of God, as in "Kingdom of Heaven"; Mark emphasizes "the Messianic secret," where Jesus is adamant that His Messiahship not be widely spread during His earthly ministry.
Now, traditionally they were supposedly written in the order they are found in the Bible. But some modern scholars think that Mark wrote first. However, either order leaves us with a case of a ridiculous assumption: Either (1) God inspired verbatim, separately, two or three near-identical accounts of Jesus's ministry; (2) Matthew Levi, one of the Twelve, used John Mark's report of Peter's reminiscences and preaching about Christ's life rather than writing what he was himself an eyewitness to; or (3) Mark produced a "Readers Digest Condensed Matthew" by leaving out two-thirds of Jesus's teachings. All three presumptions leave us going "Why?"
Further, Matthew and Luke both report many of the same teachings of Jesus -- but they place them at different times, for different purposes, and sometimes making quite disparate points. Why might this be?
This summary is, in a nutshell, what scholars call "The Synoptic Problem."
THE Q THEORY: Many scholars, seemingly unwilling to allow that anybody who actually appears in the Bible stories had anything to do with writing the books bearing their names, think that Matthew and Luke were later developments based on using Mark as a "frame story" into which they inserted Birth and Passion narratives, separately, and Jesus's teachings, getting the majority of them from a source that has not been preserved called "the Q Source." (This is something of a solecism, like "VCR recorder," because Q stands for the German word Quelle, which means "source." So they're calling it "the Source Source.")
The problem is that, with one exception, no writer, even those writing the days contemporaneous with John's last days, ever makes any reference to such a source having ever existed.
MY THEORY: The very early Church writer Papias reports that "Matthew first wrote down the logia of Jesus in the Hebrew language, though not in order." Logia is a Greek plural related to logos, word, meaning, roughly, "teachings, utterances" -- "words" in the more figurative sense.
Matthew, however, gives every evidence of having been composed in Greek, not translated from Hebrew, and in any case is a full narrative gospel, not a collection of sayings like the so-called Gospel of Thomas is.
But one can work from these facts and come up with a logical analysis of what must have happened that makes only one assumption about editors and compilation not documented in Scripture or early church history.
I came up with this theory independently, but I've since learned that there are reputable scholars who think that it's the logical way to resolve the Synoptic Problem.
1. As Papias reports, Matthew Levi, elderly tax collector become Apostle, collects Jesus's teachings before his own death.
2. After Peter's martyrdom, John Mark compiles his account of Jesus's life based on Peter's reminiscences and sermons.
3. Luke says explicitly in 1:1-4 that he is compiling for Theophilus a report of which among the many stories and teachings about Jesus can be trusted to be the truth. We can assume that he worked with Mark's Gospel, Matthew's collection of teachings, and his own researches, which would include, as very early Church tradition says, his friendship with Mary the mother of Jesus, and speaking to whatever eyewitnesses to Jesus's ministry he encountered.
4. Independently of Luke, a gentleman whom we will call "Matthew of Antioch" makes a free translation of Matthew's collection of Jesus's teachings into Greek. Either Matthew Levi or "Matthew of Antioch" arranged them into a topical collection, with stuff on moral obligations in one place, stuff about the Last Days in another, etc.
5. Then "Matthew of Antioch" took Mark, and inserted into it this Greek translation of Matthew's collection of Jesus's teachings. As was a widespread custom in those days, before tape recorders or shorthand reporting, he reconstructed five of Jesus's sermons, known to have been made at particular times and places, from the teachings Matthew Levi had recorded. This was completely in accord with standard literary practice in those days -- it was no more fraudulent or an act of misrepresentation than my saying "Jesus said that we should love all our fellow men" -- the 'that' in the middle of that sentence makes clear that I am making an indirect, paraphrased statement of His teaching, not a verbatim direct quote. And it would be automatically assumed by First Century readers that what purports to be an account of a sermon or speech is not a verbatim record of the sermon/speech, but an accurate reconstruction based on things the man (in this case, Jesus) had actually said at one time or another on the topic that the sermon/speech was about.
With the complete text of Matthew's collection available in the context of Jesus's life (as borrowed from Mark), the original Matthew collection, which probably did not circulate widely, fades from the scene. And because the Antioch gospel includes the complete Matthew collection of teachings, it becomes known by his name, and becomes the First Gospel.
This minimizes the number of assumptions that one needs to make, and yet resolves the questions raised in the Synoptic Problem without suggesting that anyone did something silly.