The Dialect that Matthew Wrote and the Gospel of Matthew

Hmm.. my mistake. While it is widely held that Matthew wrote originally in Aramaic [Papias, Jerome, Irenaeus, Nicephorus], the gospel of Matthew we have today is not a translation from Aramaic (apart from Hebrew expressions written, not translated, in Greek). What the heck does that mean? It means that what we have now is not directly translated from what Matthew originally wrote (in Aramaic).