Rav Hai Gaon ben Rav Sherira Gaon was made Rosh Yeshiva in his father's lifetime in year 4757 [(and in Yuchsin in the order of the Geonim, generation 7, he wrote 4758)] and he spread Torah in Israel more than all the Geonim. Those seeking Torah came to his light from east to west, and there was none like him before him among the Geonim, and he was the last of the Geonim. He was twenty-nine years old when he reigned [(and in Shalshelet HaKabbalah, letter 37, part 3, he wrote twenty-eight years old)] and he reigned forty years. [And in the responsa of the Maharshal, section 29, they ordained him for the Gaonut at twenty years old in year 4736.

Yuchsin wrote in the order of the Geonim, generation 7, that his generation was the eighth generation of the Gaonut. And in Seder HaKabbalah of the Rema he wrote that the days of his life were about ninety years. He passed away in year 4798 (but it requires examination, since according to all opinions he was not more than twenty-nine when he reigned and he reigned forty, how were his life ninety years?).

In the Mordechai on Shabbat it appears that Rav Hai was in Rome. He composed the book Musar HaSekhel, rulings and customs in proverbs and ethics and in rhyme from year 4722. And the book of Sales and Purchases, and Laws of Oaths, and a new method from many on the Blessing of Yaakov and the construction of the work of the Mishkan from year 4762, and Sefer HaPikkadon. His burial is in the Metivta of Machsaya (some wrote) and in Gedolei Yisrael he wrote that Rav Hai Gaon is buried near Mount Sinai.] In those days the wicked of Israel reported on Rav Sherira Gaon and Rav Hai his son, and the Ishmaelite king seized them and plundered all they had and left them no sustenance.

Rav Sherira Gaon was hung by his one hand when he was already one hundred years old. [And Shalshelet HaKabbalah, letter 37, part 3, wrote that he died around year 4780.]

It is written [Yesod Olam at the end of the Yuchsin] that with Tzidkiyahu king of Yehuda the kingdom of the House of David ceased, but from his seed they were in the Babylonian exile and in the days of the Second Temple and for a long time after the destruction, Nesi'im and Reishei Galuta. The first was Shealtiel ben Yehoyakhin king of Yehuda; Pedaya his son; Zerubavel his son; Meshulam his son; Chananya his son; Berachya his son; Chasadya his son; Yeshaya his son; Ovadya his son; Shechanya his son; Shemaya his son; Nearya his son; Elyoenai his son; Chizkiya his son; the Nasi Shemaya his son; from him onwards are the Nesi'im of Eretz Yisrael; and Nechemya his brother came to Babylon and from him came the Reishei Galuta.

The Nasi Shemaya his son; Shmuel his son; Yehonatan his son; Yehonatan his son; Akuv his son; Shemaya his son; Anani his son; Hillel HaZaken ben Nasi Shemaya who was Nasi in Eretz Yisrael and others of the house of the Nesi'im who returned to Eretz Yisrael. And Shimon ben Hillel, Rabban Gamliel HaZaken his son, Rabban Shimon his son who was killed together with Rabbi Yishmael Kohen Gadol by the Romans, Rabban Gamliel of Yavneh his son, Rabban Shimon his son, Rabbi Yehuda HaNasi his son.

And the Reishei Galuta in the order written in Yuchsin: Nechemya, Shmuel his son, Yehonatan his son, Akuv his son, Shemaya his son, Anani his son, Nachum his son, and from him until Mar Zutra there were twenty-two Reishei Galuta in Babylon.

Mar Rav Yaakov HaChaver ben Mar Rav Nissim asked [from the city of Kairouan] the great teacher our master Sherira the Rosh Yeshiva Gaon Yaakov, and to the great teacher our master Hai, head of the yeshiva of Gaon Yaakov (Aruch, entry "Agei"), and on the entry "Hil" our teacher Meshulam bar Moshe bar Rabbi Itiel from the city of Mainz explained.

Rabbi Kalonymus, a Roman man [(see above year 4952 that he was in the days of Rashi)] I found in an old contract that he learned Torah from Rav Hai and was the teacher of the Rif [(Shalshelet HaKabbalah, letter 44, part 2)].

In the days of Rav Hai Gaon there was Rabbi Yosef bar Yitzchak ben Shatnas ben Avitor, a student of Rav Moshe the captive mentioned above [(see above year 4750)], and he translated the entire Talmud into Arabic for an Ishmaelite king named Alhakiya. Because of his greatness and wisdom he disdained Rav Chanoch, the rabbi who sat on his father's throne, and the congregation was divided in a great dispute after the passing of the great Nasi Rav Chasadai bar Yitzchak [(Shalshelet HaKabbalah wrote in letter 39, part 2)].