Paul in Galatians 1:17 begins describing his movements and travels after his conversion. The simple statement ἀπῆλθον εἰς Ἀραβίαν ("I went into Arabia") is as enigmatic as it is short. It is rather simple to understand: Paul went to Arabia. The difficulty comes in determining exactly where this place was and why Paul traveled there. The contemporary geo-political entity of Saudi Arabia does cover much of the same area as the ancient term, but when applied to the ancient Near East the term could refer to territories further north and west. In Roman terminology Arabia extended further north than present-day Saudi Arabia, comprising parts of Transjordan, the Negev, southern Syria, and the northwestern portion of the Arabian peninsula. Within this general geographic region kingdoms independent from Rome, like that of the Nabateans south of Damascus, could also be referred to by this name. But the name could also refer to territories to the west, such as the Sinai Peninsula, evidenced by Paul’s usage in Gal 4. So the question here is, did Paul stay in the general region of Damascus after his conversion, or did he undertake a longer trip to the Sinai Peninsula? It is difficult to be certain of the answer, but given the fact that he mentions a return to Damascus as the next stop on his post-conversion journey, the most reasonable assumption is that he intended this term to mean the desert area south of Damascus in the kingdom of the Nabateans. Traveling within the general area of Damascus—instead of an arduous trek of hundreds of miles to the Sinai Peninsula—makes much more sense of what we do know of Paul’s travels.
The purpose for the journey is even more difficult to ascertain. Paul gives no rationale for the travel other than the general argument of this paragraph, that is, as proof that the gospel he preached was not received from any human source. Thus his travels to Arabia serve only that negating purpose: Instead of making a trip to Jerusalem to visit key Christian leaders, which would have been eminently logical and appropriate, Paul instead makes a trip to the desert, thus proving his disassociation from the Jerusalem apostles. Paul makes no positive statement of the trip’s value. It is reasonable to assume that it gave Paul time for reflection and communion with God, given the radical nature of his conversion, but this judgment has to be tentative. Paul simply does not say why he took this trip or what he did while there.