> How do you see the synoptic problem?
I don't see it as a PROBLEM, really. It's one of millions of historical quandaries.
> Who wrote first and which are the other two that inspired from that?
There are four main theories of Gospel formation:
1. Two-source hypothesis (Markan Priority and Q): Mark and Q are claimed to be two major sources of Matthew and Luke.
2. The Farrer Hypothesis (Matthew and Luke were written independently. No Q. Both Matthew and Luke used Mark. Luke also used Matthew).
3. The Griesbach hypothesis (two-Gospel hypothesis), which is...
A. Matthew came first (Eusebius Eccl. Hist. 6.25, citing Origen)
B. Luke used Matthew
C. Mark utilized both Matthew and Luke. Mark, in fact, conflates Matthew & Luke
4. The Oral Tradition hypothesis (the orality and memory hypothesis). Oral instruction was widespread. The Gospels are the result of an oral tradition characterized by a flexible stability. While the sayings of Jesus were somewhat “fixed,” the narrative seem to have been handed down with greater flexibility. The Gospel writers tapped into the oral traditions to write their accounts, hence their similarity.
Peter Williams says,
"The chief takeaway is that we have multiple sources and multiple witnesses to things. We find an overall pattern that makes the compelling argument that the material was not all made up. Again and again we will find that supposing the authors handed on faithfully what they knew yields simple explanations, whereas supposing they made things up produces complex ones."
> Do we then truly have 3 accounts , or just 1 account?
We have one account from three vantage points: one from Matthew, from the vantage point of the law; one from Mark (from Peter), from the vantage point of the disciples; one from Luke, from the vantage point of a Gentile.
> Does the synoptic problem pose any real threat to the authenticity of the gospels?
Not one bit. Recent research has shown that the Gospel writers follow the practices of Greco-Roman biographers. Their flexibility in reflecting their sources, rearranging chronologies, simplifying material, and giving gists rather than quotes is the way historians of their era handled important writing. Their differences contribute more to authenticity than to their discredit.