Paul's separation from Barnabas doubled the missionary effort. Barnabas took John Mark and sailed to his home, the Island of Cyprus. Paul took Silas, the prophet whom the church in Jerusalem sent with the letter to the Gentiles to explain it and teach it to them. These men took the shortest route overland west into eastern Galatia and the city of Derbe, their last stop on the first missionary journey. They journeyed west to Lystra, the city where Paul was stoned earlier. Here he met Timothy, a young believer whose mother was Jewish. His father was a Hellenist Gentile. Because of this, Timothy was never circumcised.
Paul found Timothy to be a valuable asset to his missionary endeavor. It is likely that Timothy's mother and grandmother were converted to Christ on Paul's first trip there (2 Tim. 1:5). How Timothy came to faith is not recorded, however, he was raised to know the Word of God (2 Tim. 3:14, 15). Paul wanted to take Timothy, but first wanted to have him circumcised. This seems to go contrary to the decision of the council in Jerusalem and the letter from them that he was presenting to the church at Lystra (see Acts 16:4).
The best solution to this question is to see it as consistent with Paul's philosophy of ministry‚ÄĒto be all things to all people (1 Cor. 9:19-23). In other words, the circumcision was not for Timothy's benefit, but to keep him from being a stumbling block to Jews to whom he would minister. That he was willing to undergo this painful procedure speaks volumes to his own spiritual character.