Rav Hai Gaon (939-1038) was the son of Rav Sherira Gaon, head of the Pumbedita academy, and the son-in-law of Rav Shmuel ben Chofni Gaon. His family descended from the Exilarchs of Babylon, but his forebears had given up the leadership to devote themselves to the yeshiva; his father, grandfather and great-grandfather were all Geonim of Pumbedita.

As a young man he helped his father run the yeshiva. In 986 he became av beit din of Pumbedita, in effect sharing the gaonate with his aged father; in 1005, when Rav Sherira died at a hundred, he succeeded him as Gaon and led the academy for more than thirty years. He is regarded as the last of the great Geonim.

The supreme authority of the Jewish world in his day, he answered thousands of questions from Asia, Europe and North Africa on every area of Judaism; his responsa remain authoritative, and the Ramban called him "equal to the greater part of a Sanhedrin". He also wrote Sefer HaMekach VehaMimkar on commercial law, commentaries on the Bible, Mishnah and Talmud, liturgical poems and linguistic works.

After his death the centre of Torah study gradually moved from Babylonia to North Africa and Europe.