Head of the college of Pumbedita at the end of the Geonic period (see GEONIM) (939–1038). Hai served in the Gaonite of Pumbedita together with his father, Sherira Gaon. When Sherira died, Hai was inducted formally into the office with the pomp and ceremony typical of the institution. It is reported that there was read in the Babylonian synagogues the narrative of Solomon's succession to the throne of David (1 Kings 2: 10–12), adapted to the occasion: ‘And Sherira slept with his fathers … And Hai sat upon the throne of Sherira his father; and his kingdom was established firmly.’ Hai was the son-in-law of the Gaon of Sura, Samuel Ibn Hofni, whose rationalism in Bible interpretation was not to Hai's taste.
As a theologian of note, Hai was among the earliest Jewish thinkers to discuss, in a Responsum, the vexed question of how to reconcile God's foreknowledge with human freedom, a problem of concern to the Arabic thinkers in Hai's day. In another Responsum, Hai reacts to Islamic fatalism when he considers the idea that every man has a life-span fixed beforehand. When a man is murdered, Hai was asked, does this mean that even had he not been slain, he would have died, in any event, at that particular moment? Hai replies that we simply do not know. We can either suppose that if he had not been murdered he would have died at that moment in any event, or we can suppose that if he had not been murdered he would have lived on until a later date. But, it might be objected, supposing a murderer killed a large number of persons on the same day, is it plausible to suggest that they would all have died in any event on the same day? ‘Why not?’ replies Hai. Experience shows us that a large number of people do sometimes die at the same time, when, for example, a building collapses or when a ship goes down and all the passengers are drowned. But if the victim of a murder would have died in any event, Hai asks, why is the murderer punished for his crime? Hai replies that it is the act of murder that constitutes the crime. The murderer deserves to be punished for the evil act that was his and his alone.
This Responsum has been quoted at length to demonstrate Hai's theological approach, one in which he is thoroughly familiar with the Islamic thought of his day (he knew Arabic and some of his writings are in this language) but proudly defends Judaism against its critics.