||Monetary rules and oaths by R. Hai b. Sherira Gaon (939–1038), gaon of Pumbedita and molder of the halakhah and the most prominent figure of his time. Of his youth nothing is known. From 986 he was the av bet din in the academy of Pumbedita , acting as the deputy to his father Sherira gaon; in this role he left his mark upon the mode of studies and general orientation of the academy. According to some, he had a share in composing the Iggeret Rav Sherira. Some time after he and his father had been released from prison, where they had been kept on a false charge, he became the gaon of Pumbedita, while his father was still alive, a position which he held for 40 years (998–1038). Although his position had been vied for by R. Samuel b. Hophni the latter withdrew his claim to the gaonate when R. Hai married his daughter. Students came to R. Hai's academy from Byzantium and from western Christian countries, from where queries were also sent to R. Hai. His ties with Spain and his influence upon R. Samuel ha-Nagid in particular are well known.
Aside from his preeminence in rabbinic knowledge, he was well acquainted with the Persian and Arabic languages and with Arabic literature. While he permitted children to be taught Arabic writing and arithmetic, he warned against the study of philosophy (from a letter ascribed to him and addressed to R. Samuel ha-Nagid). He criticized his father-in-law, R. Samuel b. Hophni, "and others like him, who frequently read the works of non-Jews."
R. Hai occupies a central position in the history of the halakhah . Later generations regarded him as the supreme authority, declaring that "he, more than all the geonim, propagated the Torah in Israel … both in the east and in the west.… No one among his predecessors can be compared to him, who was the last of the geonim" (R. Abraham Ibn Daud , Sefer ha-Kabbalah). The measure of his influence and the volume of his responsa, decisions, and comments can be gaged from the fact that approximately a third of all extant geonic responsa are his (some of them in conjunction with his father).
In his writings R. Hai set out in detail his approach to the principles of faith and to the requirements of community leadership. In his piyyutim he expressed with much bitterness his sense of living in exile from Ereẓ Israel. He was a mystic, who ascribed sanctity to the heikhalot literature, believing that whoever studied it in holiness and purity could ascend to the world of the angels and of the divine chariot (merkavah). Contrary to the view of his father-in-law, he believed "that God performs signs and awe-inspiring acts through the righteous, even as He did through the prophets." But he vigorously opposed those who believed that the divine names and charms were efficacious in changing the course of nature, declaring emphatically that its laws cannot be modified by such means. Vehemently antagonistic to any tendency toward anthropomorphism, he maintained that anthropomorphic passages in the aggadah were to be interpreted metaphorically. In his formulation of the ideals and values of the complete Jew, he described the rewards for observing divine precepts. These rewards greet the righteous and form "groups that go to meet the Divine Presence" and say to the righteous: "Ascend to your grade, stand in your division (in heaven), you who have conquered your evil inclination … who have borne the yoke of the commandments, and in your fear of Him have endured suffering."
R. Hai drew special attention to the duty of the dayyanim to guide and admonish the people, to take responsibility for people's conduct and to be accountable for their sins. He demanded that strong measures be taken against dissenters and thieves, and under certain circumstances even permitted recourse to Jewish courts of law. He adopted a tolerant attitude towards traditional local liturgical practices, but was opposed to delving into the reasons for them, insisting on "the observance of institutions introduced by those superior to our generations in learning and in caliber" (lit. "number"). He retained his physical and mental energies to the end. At the age of 99, a few months before his death, he replied with remarkable vigor to questions submitted to him. After his death, R. Samuel ha-Nagid eulogized him, saying: "During his lifetime he acquired all the choicest wisdom," and though "he left no child, he has, in every land, both east and west, children whom he reared in the Torah" (Ben Tehillim, 11).
Of R. Hai's works the following are extant: (1) fragments of the Arabic original of Sefer Shevu'ot (Kitāb al-Aymān; "A Treatise on Oaths"), and a Hebrew rendering by an unknown translator of the entire work entitled Mishpetei Shevu'ot (Venice, 1602; Hamburg, 1782); (2) fragments of the Arabic original of Sefer ha-Mikkaḥ ve-ha-Mimkar (Kitāb al-Shirā wa-al-Baye; "Treatise on Commercial Transactions"). This, his chief literary production, was translated into Hebrew by Isaac Al-Bargeloni (Venice, 1602; Vienna, 1800), and another version is extant in manuscript; (3) Sefer ha-Shetarot ("Treatise on Documents"), containing the texts of various documents, such as a ketubbah, a get, etc. (published by Assaf in Tarbiz, 1 (1930), supplement). Fragments of R. Hai's commentary on several tractates of the Babylonian Talmud have also been preserved. The ascription of certain other works to Hai has, in recent years, been rejected. (4) R. Hai wrote numerous responsa. (5) To aid the study of Arabic, R. Hai wrote Kitab Al-Hawi, a comprehensive Hebrew/Aramaic-Arabic anagrammatic dictionary. It was very popular and in use through the end of the 13th century. Extant only in manuscript (see Tarbiz 69, 3 (2000), 341–422).
To R. Hai are ascribed some 25 poems, most of which are prayers, seliḥot, and piyyutim, a few of them didactic poems on laws and etiquette and eulogies of contemporary personalities. Most of these are in meter and rhyme, but in form and content reveal very little similarity to Arabic poetry. For poetic power, pride of place should be given to a group of five selihot (not kinot) for the Ninth of Av ; these are without meter and rhyme and voice a bitter and vehement complaint in the manner of Job against the suffering endured by the Jewish people in exile in the face of its great faith in G-d. R. Hai's authorship of several poems, and even the fact of his having written poetry at all, which was questioned in modern times (from the beginning of research into the poetry of the Middle Ages) has now been confirmed.