The greatest among the apostles

There are three gospels that record Peter's confession that Jesus is the Christ. Matthew records Christ saying to Peter during this conversation , "You are Peter, and on this rock I will build my church." It is soon afterwards that the gospels record the apostles arguing among themselves, asking "Who is the greatest?" When Jesus asked them about it, they were embarrassed; they knew that arguing over greatness was worldly. This period of time was full of conflict among the disciples. Not only do we see the argument about who was the greatest, we also see James and John trying to privately secure high positions for themselves, and Peter doing something that looks a lot like tattling on Andrew: "Lord, how many times must I forgive my brother when he sins against me?" (I know it's traditional to interpret this as a figurative brother, and no doubt we should apply it that way for general purposes; but with Peter's literal brother at hand I doubt that Peter's original question was about some hypothetical spiritual brother rather than Andrew.)

It is interesting to note that when Christ hears the disciples wondering who is the greatest among the apostles, he does not say, "It's Peter, weren't you listening?" as if the question were answered by the earlier "You are Peter" comments. In answer, he does not name any disciple, but describes how to recognize the greatest, telling us that "the greatest" is proved by actions. What kind of actions accompany the greatest?

If anyone wants to be first, he must be the very last, and the servant of all.