As the Exilarchate declined, the respect increased for the school of Pumbeditha, because it was near the capital of the Bagdad Caliphate, whose Jewish community of influential men came under its jurisdiction. Pumbeditha now rose from the subordinate position into which it had been forced. It put itself on an equal footing with the sister academy of Sora, and its presidents likewise assumed the title of Gaon. It next made itself independent of the Exilarchate. Formerly the head of the school and the faculty of Pumbeditha had to go once a year to pay homage to the Exilarch, but now, if the Exilarch wished to hold a public assembly, he had to repair to Pumbeditha. This was probably brought about by the chief of the school, Paltoi ben Abayi (842–858), who heads the list of important Geonim, and who was noted for his free use of the Cherem (Excommunication). Dissensions about the succession to the Gaonate were not wanting during this period, although the Exilarchs could not make their influence felt.
A Gaon of Sora, Natronaï II, son of Hillaï (859–869), kept up a prolific correspondence with foreign communities in the Arabic language. His predecessors had employed a mixture of Hebrew and Chaldee as the medium of their communications. Natronaï II also corresponded with the Jewish-Spanish community at Lucena, whose members doubtless understood Arabic better than Hebrew. He opposed the Karaites as bitterly as the Geonim had done at the time of the rise of this sect, "because they despised the words of the sages of the Talmud, and set up for themselves an arbitrary Talmud of their own." His pupil and successor, Mar-Amram ben Sheshna (869–881), was the compiler of the liturgical order of prayers in use amongst European Jews. At the request of a Spanish community, preferred by their religious leader, Isaac ben Simeon, he collected everything that the Talmud and the custom of the schools had ratified concerning prayer and divine service (Siddur Rab Amram). The form which the prayers had assumed in the course of time was by him declared to have the force of fixed law. Every one that deviated from it was considered a heretic, and excluded from the community of Israel. The poetical compositions for the festivals were not yet in general use at this time, and Mar-Amram left the selection to the taste of the individual.
During Mar-Amram's Gaonate, there were two successive heads of the schools in Pumbeditha, Rabba ben Ami (869–872), of whom nothing is known, and Mar-Zemach I. ben Paltoi (872–890), who heads the list of literary Geonim. Hitherto, the leaders of the school had occupied themselves with the exposition of the Talmud, with the regulation of the internal affairs of the communities, and with answering questions which were submitted to them. The one or the other of them, it is true, made a collection of Agadic sayings, but for literary activity, they either had no leisure, or opportunity, or inclination. But when the zeal for the study of the Talmud increased in the different communities in Egypt, Africa, Spain and France, and students of the Talmud spent their time in studying obscure and difficult passages, they often had to appeal to the schools for the solution of their difficulties. Their questions soon concerned only theoretical points, and the Geonim found it necessary to write treatises on certain portions of the Talmud, instead of simple and short answers. These books were used by students as Talmudical handbooks. The Gaon Zemach ben Paltoi, of Pumbeditha, arranged an alphabetical index of difficult words in the Talmud, under the title of "Aruch." In it he shows acquaintance with the Persian language. This dictionary forms the first contribution to the constantly growing department of Talmudical lexicography. The second literary Gaon was Nachshon ben Zadok of Sora (881–889), Zemach's contemporary. He, too, wrote a book giving explanations of difficult words in the Talmud. Nachshon made himself famous through his discovery of a key to the Jewish calendar. He found that the order of the years and festivals repeat themselves after a cycle of two hundred and forty-seven years, and that the forms of the years can be arranged in fourteen tables. This key bears his name; it is known as the cycle of Rabbi Nachshon.
The third author of this time was Rabbi Simon of Cairo, or Misr, in Egypt, who, although not an official of the Babylonian school, was in a position to compose a code embracing all religious and ceremonial laws (about 900). This work, directed against the Karaites, bears the title "The Great Halachas" (Halachoth gedoloth), and forms a supplement to Jehudaï's work of a similar nature. The history of the post-exilic period till the destruction of the Temple was also written at this time; its author is unknown. It is written in Arabic, and is based partly upon Josephus, partly upon the Apocrypha, and partly upon tradition. It is called "The History of the Maccabees" or "Joseph ben Gorion." In later times an Italian translated it into Hebrew, and in its expanded form it bears the title Josippon (Pseudo-Josephus), and this work served to awaken in the Jews, who were ignorant of the original sources of Jewish history, interest in their glorious past.
The literary activity of the official heads of Judaism in the two schools confined itself to Talmudical subjects. They had no idea of scientific research, would have condemned it, in fact, as a leaning to Karaite doctrine. Outside of the Gaonate, in Egypt and Kairuan, there was a scientific movement among the Rabbanites, weak at first, but increasing in strength every year. The Rabbanite thinkers must have felt that so long as Talmudic Judaism maintained a hostile position towards science, it could not hold its own against the Karaites. Biblical exegesis and Hebrew philology formed the special studies of the Karaites, and in connection with these was developed a kind of philosophy, though only as an auxiliary science. It was in this branch that, towards the end of the ninth century, several Rabbanites emulated them. Famous amongst these was Isaac ben Suleiman Israeli (845–940). He was a physician, philosopher, and Hebrew philologist. He was an Egyptian, and was called to Kairuan about the year 904 as physician to the last Aghlabite prince, Ziadeth-Allah. When the founder of the Fatimide dynasty, Ubaid-Allah, the Messianic Imam (Al-Mahdi, who is said to have been the son of a Jewess), conquered the Aghlabite prince, and founded a great kingdom in Africa (909–933), Isaac Israeli entered his service, and enjoyed his full favor. Israeli had a great reputation as a physician, and had many pupils. At the request of the Caliph Ubaid-Allah, he wrote eight medical works, the best of which is said to be that on fever. His medical writings were translated into Hebrew, Latin, and part of them into Spanish, and were zealously studied by physicians. A Christian physician, the founder of the Salerno school of medicine, made use of his researches, and even republished some of his works without giving credit to Israeli for them. He was thus an important contributor to the development of medical science, but as a philosopher he did not do much. His work on "Definitions and Descriptions" shows scarcely the rudiments of philosophical knowledge.
His lectures must have made a greater impression than his writings. He instructed two disciples, a Mahometan, Abu-Jafar Ibn-Aljezzar, who is recognized as an authority in medicine; and a Jew, Dunash ben Tamim, who continued the work of his master. Isaac Israeli lived to be more than one hundred years old, and survived his patron the Caliph Ubaid-Allah, whose death was hastened by his disregard of the advice of his Jewish physician. When Isaac Israeli died, about 940, his example had made a place in the Rabbanite studies for the scientific method that shaped the activity of succeeding generations.
Whilst the Rabbanites were making the first attempt to follow a scientific method, the Karaites were disporting on the broad beaten path of Mutazilist philosophy. Although young in years, Karaism showed signs of advanced old age. All its strength was given to Biblical exposition, combined with philology, but even here it made no progress. In the central community of the Karaites, in Jerusalem, it assumed an ascetic character. Sixty Karaites agreed to leave their homes, their property and their families, live together, abstain from wine and meat, go poorly clad, and spend their time in fasting and prayer. They adopted this mode of living, as they said, with the object of promoting Israel's redemption. They called themselves the mourners of Zion and Jerusalem (Abele Zion), and every one of them added to his signature the term "The Mourner." It was through them that the religious life of the Karaites took on an ascetic tinge. They not only observed the Levitical laws of purity in the strictest manner, but they shunned intercourse with non-Jews. They would not buy bread from them, nor eat anything they had touched. The more rigorous the Karaites became, the more they looked upon the Rabbanites as reprobates and sinners, whose houses it was a sin to visit. The Karaites gradually spread from Babylonia and Judæa to Egypt on the one side and to Syria on the other, and northwards as far as the Crimea. There were large Karaite communities in Alexandria and Cairo, and also in the Crimea, on the Bosporus (Kertch), Sulchat and Kaffa (Theodosia). The zeal of individuals contributed much to spread Karaism. By means of disputations, sermons, and letters, they endeavored to secure followers amongst the Rabbanites. Like every other essentially weak sect the Karaites relied upon propaganda, as though numbers could atone for lack of real strength. There was amongst them a certain proselytizer, a cunning man, Eldad by name, who related wonderful adventures, and made a great stir in his day. Eldad's romantic travels throw a lurid light upon the Jewish history of the time. He belongs to that class of deceivers who have a pious end in view, know how to profit by the credulity of the masses, and can easily catch men in a web of falsehood. The Geonim themselves were almost deceived into believing his pretended traditions, which he affirmed had been received direct from Moses.
Meanwhile, the institution to which the memories of the former political independence of Judaism were attached was rapidly approaching dissolution. The Exilarchate fell into disregard through the rivalry of the school of Pumbeditha, and also lost the revenue which was its mainstay. Even though questions from abroad continued to be directed to the Geonim of Sora, the sister academy was considered even in Babylonia to be the chief authority, and to have most influence. This influence was increased still more through the choice as Gaon of Pumbeditha of Haï ben David (890–897), who had hitherto held the post of rabbi and judge in the capital of the Caliphate. It was just at this time, at the end of the 9th century, that the Jews again enjoyed a high position in the Caliphate, under the Caliph Al-Mutadhid (892–902). His vizir and regent Ubaid-Allah Ibn-Suleiman appointed Jews and Christians alike to state offices.
The community of Bagdad gained most through the favor shown to the Jews by the vizir. As Haï had occupied his post in the capital for a long time, and had made himself popular in the community, he was elected Gaon of Pumbeditha by the influential members. Their object was to make the school of Pumbeditha of greater importance, and the academy at Sora declined more and more. Haï's successors, who, like himself, had commenced their career with the rabbinate of Bagdad, worked in the same spirit, and were assisted by the powerful members of the community in the effort to make Pumbeditha the center of the Babylonian community and of Judaism generally, and to put an end to the Exilarchate as well as to the school of Sora. One of them was Mar Kohen-Zedek II. b. Joseph (held office 917–936). He was passionate and energetic, and was one of those who are, indeed, free from personal selfishness, but seek an increase of power for the community, regardless of every other consideration. As soon as he entered upon his office, Kohen-Zedek demanded that the school of Pumbeditha should have the greater share of the revenue which was contributed by the various communities. He based his demand upon the fact, that the pupils of the college at Pumbeditha were more numerous than those at Sora, and therefore deserved greater consideration. So many quarrels arose between the two schools in consequence of this demand that several important people found it necessary to interfere. A compromise was made, and it was agreed that in future the money should be equally divided, whereby the academy at Sora lost the last trace of its superiority. Kohen-Zedek then endeavored to deprive the Exilarchate of its little remnant of power. The Exilarch at the time was Ukba, a man of Arabic culture, who wrote poems in Arabic. Kohen-Zedek demanded that the appointment of judges in the communities of Khorasan should be vested in, and the revenues derived from the same, should be devoted to, the school of Pumbeditha. Ukba would not give up any portion of his dignity, and appealed to the Caliph. But Kohen-Zedek had friends at Bagdad, who had influence at court, and these succeeded in inducing the Caliph Al-Muktadir (908–932), or rather the vizir Ibn Furat, since the Caliph spent his time in riotous living, to deprive Mar-Ukba of his post, and banish him from Bagdad. The Exilarch went to Karmisin (Kermanshah, east of Bagdad), and Kohen-Zedek rejoiced that the Exilarchate was now destroyed. The weak president of Sora, Jacob ben Natronaï, permitted all these usurpations without interfering.
Meanwhile matters took a favorable turn for the banished Exilarch, by which he was able to frustrate the plans of Kohen-Zedek. Just at this time there came to Kermanshah the young and pleasure-seeking Caliph. The banished Exilarch Ukba frequently met him, and greeted and praised him in well-measured Arabic verses. His verses pleased Al-Muktadir's secretary so well that he had them copied, and called to the attention of the Caliph the many changes rung by the Jewish poet upon the one simple theme, allegiance.