What did Paul and Barnabas try to prove to the leadership in Jerusalem?
Paul and Barnabas sought to demonstrate to the Jerusalem leadership that nothing may be added to the relationship between Christ and the believer except faith, and faith alone in Paul's Gospel. They came from Antioch to establish this point, showing that salvation rests entirely on faith rather than additional requirements.
Les explains that Paul and Barnabas, as they came from Antioch, were going to try to prove to the leadership of Jerusalem that you cannot add anything to the relationship between Christ and the believer except faith, and faith alone in Paul's Gospel. He notes they did not just flippantly say what they believed, but sat down and looked at it point by point, line upon line, because the revelations that came through the Apostle Paul were so above and beyond Judaism that it took time for these people to understand where he was coming from. Les also connects this to Romans 1:16, where Paul says he is not ashamed of the Gospel of Jesus Christ, for it is the power of God unto salvation, and explains that salvation in Paul's teaching involves justification, sanctification, forgiveness, redemption, baptism into the Body of Christ, and indwelling with the Holy Spirit.
And I went up by revelation, and communicated unto them that gospel which I preach among the Gentiles, but privately to them which were of reputation, lest by any means I should run, or had run, in vain.
More Questions
What does Paul mean when he says he 'communicated' his gospel to the Jerusalem leaders?
When Paul says in Galatians 2:2 that they 'communicated,' he means they did not flippantly state their beliefs, but sat down and went over the matter point by point, line upon line.
Who were the 'those of reputation' Paul met with privately in Jerusalem?
Those 'of reputation' in Jerusalem were the leadership of the church, which would include Peter and the eleven, and maybe a few other Jewish elders in that church.