The hypothesis holds that Matthew was written first, by Matthew the Evangelist (see the Gospel According to the Hebrews and the Jewish-Christian Gospels).
Instead, slight disagreement is actually in favor of multiple, near identical traditions.
According to Irenaeus, Papias was "a hearer of John and a companion of Polycarp, a man of primitive times," who wrote a volume in "five books." The benefit of historical immediacy, as argued by D. Fischer is one of the key determinants of historicity, and the church father Papias is a very early source in regard to testimony that the Matthew wrote his gospel first.
A modified version of the Augustinian hypothesis, known as the Griesbach hypothesis, agrees that Matthew wrote first and that Mark depended on Matthew, and does not dispute that the original text was in Hebrew thereafter translated into Greek, but argues that Mark also depended on Luke and therefore that Luke’s gospel precedes Mark's.
Because of the similarity on primary points of contention, this hypothesis is also treated as a possible amendment to the Augustinian hypothesis.
A radical thesis; the intractable problem; building a synoptic theory - the relation of Luke to Mark, the relation of Luke to Matthew, the relation of Matthew to Mark; ancient testimony to Matthew's gospel; ancient testimony to Mark's gospel; the date of Peter's going to Rome; Mark's gospel - further considerations; ancient testimony to Luke's gospel; how were the gospels written?