Summary: The true definition of wisdom and strength does not come from the world, but from God, whose foolishness is wiser than mans, and whose weakness is stronger than the strength of men.
Paul spends time defending his ministry. Evidently there were eminent "super-apostles (2 Cor 12:11), who were sharp in every way. Paul was unimpressive and even contemptible in comparison. These other leaders apparently had letters of commendation (2 Cor 3) which was impressive, they apparently boasted in their success, knowledge, and accomplishments (2 Cor 10-12), they apparently were skilled (2 Cor 11:6), unlike Paul, they were paid by the people they taught (2 Cor 11:7), which is what any eminent teacher/philosopher/etc. would do. Paul could have easily used many of these same methods but chose not to (2 Cor 2). He intentionally "de-exalted" himself. Apparently his trainees did the same(2 Cor 12:18).
There is a theme of spiritual warfare that seems to run through much of what he says, but it is a war that runs upside-down and backwards to conventional thought about ministry, strength, power, and success.
2 Cor 1:5 - "For just as the sufferings of Christ are ours in abundance, so also our comfort is abundant through Christ."
2 Cor 1:12b - "...not in fleshly wisdom but in the grace of God we have conducted ourselves in the world, especially toward you."
Paul rejected conventional wisdom and chose to operate in the grace of God instead. He recognized that God's grace is sufficient. He does not need anything else, and anything else may actually be detrimental.
2 Cor 3:fb - "...but our adequacy is from God."
2 Cor 3:18 - "But we all, with unveiled face, beholding as in a mirror the glory of the Lord, are being transformed into the same image from glory to glory (or, with ever increasing glory"), just as from the Lord, the Spirit.
The goal of his ministry was not amassing a large following like some of the "super-apostles" of the day. The goal came from his Lord - it was lives that are being transformed into the image of Christ. In other words, people lived like, thought like, and had the attitude of Christ. It was never about the greatness of the vessel, but the greatness of God.
2 Cor 3:7 - "We have this treasure in earthen vessels, so that the surpassing greatness of the power will be of God and not from ourselves;"
2 Cor 4:18 - "...we look not at the things which are seen, but at the things which are not seen..."
2 Cor 5:7 - "...we walk by faith, not by sight..."
Paul and his disciples had 20/20 spiritual vision. They could see, perceive, and understand the world around them. They also understood their own inadequacy, weakness, and brokenness. This is why Paul was able to correctly say "I am a nobody (2 Cor 12:11).
2 Cor 5:16 - "...from now on we recognize no one according to the flesh; even though we have known Christ according to the flesh, yet now we know (Him - this word supplied by the translators and not in the original text) in this way no longer..."
Paul does not look at anyone or anything from a fleshly point of view. He operates out of a different paradigm that is not of this world, which redefines greatness, success, and wisdom.
2 Cor 10:1-4 - "Now I, Paul, myself urge you by the meekness of gentleness of Christ - I who am meek when face to face with you, but bold toward you when absent! I ask that when I am present I need not be bold with the confidence with which I propose to be courageous against some, who regard us as if we walked according to the flesh. For though we walk in the flesh, we do not war according to the flesh, for the weapons of our warfare are not of the flesh, but divinely powerful for the destruction of fortresses."