Let's see if I can unravel some of this....Papias's (bishop in Hieropolis) assertion that Matthew wrote in Hebrew is generally dated ca. AD130, in a work entitled "Exposition of the Oracles of the Lord." This writing, however, is known only in fragments quoted by later Christian writers. They report that Matthew, the disciple, complied the *sayings* of Jesus in Hebrew. Those who have quoted Papias seem to have accepted his statement without question as referring to the First Gospel.
The difficulties with such assumption are generally these:
a) The Gospel consists of a rather full account of the public ministry of Jesus, not merely a series of *sayings* (such as we believe Q to have been);
b) Detailed analysis of Matthew shows that the author used Mark (usually dated AD 70) as one of his sources;
c) Therefore, Mark and therefore Matthew, for whom Mark was a source, were both written in Greek, not Hebrew.
In view of these difficulties, it's plausible to assume that Papias is referring, not to the Gospel of Matthew as we know it, but perhaps to a now lost collection of sayings of Jesus.
Because the Gospel of Matthew so clearly uses Mark as a major source of material, (in Greek), and the Gospel of Mark is believed, according to its internal evidence, to have been composed shortly after the Roman destruction of Jerusalem in AD 70; and because the executions of both Peter and Paul are believed to have occurred in Rome following the burning of the city and the subsequent persecution of Christians in Rome (including Peter and Paul) by Emperor Nero in ca AD 66, which is *prior* to the composition of either Mark or Matthew, scholars reject the idea that Matthew was composed during the lifetimes of Peter and Paul. The belief that the Gospel of Matthew was written in Hebrew, during the period when Peter and Paul were still alive does not withstand scrutiny. The further assertion that Paul wrote the letter to the Hebrews is also demonstrably false. "Detailed study in modern times has led to almost unanimous agreement that the language, style and ideas differ so markedly from those of Paul that it is almost inconceivable that he could have been the author," as one commentary puts it.
Did I get close to what you were asking, Coach?
(Jeepers, I'm rustier than I thought.)