The oppression which thus fell upon the inhabitants of Palestine, and which gave rise to Hillel's calendar, augmented the importance and influence of Babylonia, and although Christianity could boast of having broken up the academies and destroyed, so to speak, the Temple of the Law in Judæa, the destruction was nevertheless merely local. In Babylonia the study of the Law acquired so vigorous an impetus that the achievements of ancient times were almost eclipsed; the study of the Law was now celebrating the period of its maturity. Two methods of instruction in the traditions especially had developed, namely, that of receiving the authentic terms of the traditions and handing them down in exactly the same words, and that of making a fruitful application of the same, and of further amplifying them. Each of these methods was represented by one of the academies of Babylonia; Sora was receptive, Pumbeditha creative. Altogether Sora can be regarded only as a continuation of the academies of Judæa, as a sort of Babylonian Tiberias; and although the spirit which reigned there underwent a change under the influence of the Babylonian method, still the Soranian school never furthered the cause of study to any appreciable extent. It was Pumbeditha that raised learning to its highest level. The acute scholars of Pumbeditha, produced by Judah ben Ezekiel's Academy, held sway at this period over Babylonia and the dependent countries. The leaders and representatives of this movement formed a triumvirate, consisting of Rabba, and his comrades and disciples, Abayi and Raba. It was these three that gave the finishing touch to the work of completing the Talmud, or rather who raised the study of the Halacha to the rank of an intellectual system of dialectics.

Rabba bar Nachmani (born about 270, died 330) possessed, like the family to which he belonged, certain original qualities. He was of a family from Mamal or Mamala, a city of Galilee, the inhabitants of which were for the most part descendants of Aaron, and members of the family of Eli; they asserted that they participated in the curse with which this house had been visited, and which prevented any of its members from ever attaining extreme old age. Whoever went to Mamala was astonished at seeing so many persons with black hair; a grey-haired man was a rarity.

Rabba had three brothers, whose names were Kailil, Ushaya, and Chananya; all of them lived in the greatest poverty, which misfortune they also ascribed to the curse resting on the house of Eli. Ushaya, the younger, and Chananya, who had returned to Judæa, obtained a precarious living as shoemakers. By reason of the scarcity of customers, they were sometimes obliged to sell their work to prostitutes. Nevertheless, their minds remained so pure and chaste that they were never reproached with a single immodest glance; they were consequently held in high esteem, and were known as the "saints of the land of Israel." These two brothers applied themselves to the Agada, the favorite study in Judæa, while Rabba, their sober brother, who as a child had shown signs of great acuteness of mind, evinced a predilection for the Halacha, in which province his labor was epoch-making. He had determined to remain in Babylonia, and his brothers, unable to quiet their apprehensions concerning his lot, used all their endeavors to persuade him to come to Judæa. "It is not all one," ran their message to him, "whether one dies in or out of Judæa; for the Patriarch Jacob attached great weight to being buried in the Holy Land. Although thou art learned, still it is better to have a master than to educate thyself. And if thou thinkest that there is no teacher of importance to be found in the academies of Judæa, we inform thee that thou wouldst indeed find such a one here." In consequence of this pressing invitation, and contrary to the principles of Judah, his teacher, Rabba emigrated to Judæa. Some time after, however, he returned to Babylonia, probably because he was dissatisfied with the Judæan method of teaching. Rabba's worldly affairs are described as most miserable, and are frequently contrasted with Chasda's uninterrupted happiness.

After the death of his teacher Judah in 299, the Pumbedithan College, which was composed of lovers of dialectics, esteemed Rabba to be the only person worthy of occupying the vacancy thus created in the school. He was therefore offered the honor of becoming Judah's successor, but his exceeding modesty induced him to decline the post. The vacancy was eventually filled by Huna ben Chiya, whose wealth was so immense that he furnished his audience in the lecture-room with gilded seats. Although the greater number of the disciples frequented Sora, the Pumbedithan Academy nevertheless counted 400 students. Both Rabba and his friend Joseph associated themselves with the local academy, and subordinated themselves to the principal, in order to prevent the school from being deprived of the reputation which it had at last succeeded in gaining. When it came to be known in what manner Huna ben Chiya had acquired his wealth, which had been amassed by the farming of tolls, he was given to understand that the dignity of teacher must not be stained by association with that hateful trade, and that he must give up either one or the other. Having abandoned the calling of farmer of tolls, he was recognized by the college, which followed Rabba's example, as a worthy principal of the academy. Joseph was the only person who refused to acquiesce in the appointment. The not altogether spotless reputation of its principal, however, threatened to become a cause of ruin to the Pumbedithan Academy; care was therefore taken after the death of Huna to make a better choice, in order to enlist the sympathy of the people and to attract a numerous audience. Two men appeared worthy to fill this post, Rabba bar Nachmani and Joseph ben Chiya, the one distinguished for Talmudical dialectics, and the other for Halachic erudition. The choice between the two was so difficult that it was determined to take counsel of Judæa, and the following question was accordingly asked: "Who possesses the superiority, Sinai (man of learning), or the remover of mountains (man of acuteness)?" In Tiberias, where the acute method of teaching, although not hated, was nevertheless held in low esteem, the decision was given in favor of the former. But Joseph entertained scruples against accepting this dignity. His nativity had once been cast by a Chaldean, who had informed him that he would obtain a position of great authority, but would not be able to retain it longer than two years and six months, after which he would die. In spite of the legal prohibition forbidding credence to be given to the wisdom of the Chaldeans, the most noted teachers of the Law were unable to free themselves from its influence; daily example was stronger than the Law. Joseph having refused the post thus offered to him, it was conferred upon Rabba (309), and in him the Pumbedithan Academy found its ideal.

Rabba restored anew to the academy its extinguished fame, and attracted to his discourses a crowd of students, amounting at times to as many as 1200. He did not confine his lectures to the practical part of jurisprudence alone, as Judah had done, but treated of all the subjects contained in the Mishna; he sought to reconcile the various contradictions existing in the Mishna, the Boraitas, and the additions made by the Amoraic authorities (Memra), and generally to introduce clearness into the study of the Halacha. He even turned his attention to the remote subject of the laws of Levitical purity, which he succeeded in making comprehensible; but in this branch of study, which had vanished out of every-day life, he stood quite alone, a fact that he frequently lamented. He was distinguished by a desire to enter deeply into the motives not only of the Pentateuch, but also of the Sopheric and Mishnaic laws, and to draw conclusions from them. The formulæ which he employed as an introduction to these investigations ran as follows: "Wherefore has the Law commanded this?" or "Why are such-and-such things prohibited by the teachers of the Law?" His luminous conception and treatment of his subject invested it with life, while the variety which he succeeded in imparting to a dry theme by means of the occasional introduction of an Agadic sentence made it both interesting and captivating. At times he would entertain the students with interesting anecdotes before beginning his discourse, and as soon as he thought that he had put them in a cheerful temper, he would begin to treat of more serious and weighty subjects. His guiding principle was that the soul must be prepared for the reception of serious thoughts, and that this receptivity was best awakened by cheerfulness. Rabba often put catch questions to his pupils, or expressed paradoxical opinions, in order to test their judgment or sharpen their intellect. Rabba holds the same important position among the Amoraim, as Akiba among the Tanaites. He collected scattered and fragmentary subjects under general heads. For this reason the reverence in which he was held by the teachers of the Law equaled that which was entertained for the founder of Babylonian Jewish life. But in proportion as he was beloved by this circle, he was obnoxious to the populace of Pumbeditha. His fellow-countrymen could not forgive this severe censor for the sharp, reproachful words with which, in his honesty and stern morality, he strove to combat their deceits and artifices. Once, on the occasion of a drought, when Rabba had proclaimed a public fast, and had ordered prayers to be offered up, without succeeding in obtaining rain, he exclaimed reproachfully to the populace: "It is not because we leaders of the people are worse than in the time of my master Judah, that Heaven refuses to gratify our wishes; nor is it because we are less diligent in the study of the Law. But what can be done by the representatives of the people when the entire race is degenerate?"

On account of their needy circumstances Rabba and another Amora, Ada, appear to have become the colleagues (Chacham) of Mar-Ukban, a grandchild of Rab, and at that time Prince of the Captivity, at whose expense they were probably supported. While the principals of the Soranian Academy were wealthy, often supporting the entire expenses of the schools, and maintaining a large number of disciples from their own purse, those of Pumbeditha generally possessed but small means. This circumstance necessitated the establishment of an academical fund at Pumbeditha, to which the communities and the Prince of the Captivity probably contributed.

In Rabba's time the Babylonian Jews were the victims of a transitory persecution, which, although insignificant when compared with those which had occurred in the Roman empire, was nevertheless calculated to arouse the sufferers from their feeling of profound safety. It was during the long reign (310–380) of Shabur II, the new king of the Sassanian dynasty, who had been acknowledged as ruler while yet unborn, that the friendly relation in which the Jews had stood to the Persian court became disturbed, and it is possible that they would have been as cruelly persecuted as the Christians, had it not been that Ifra-Ormuzd, the king's mother, was prepossessed in favor of Judaism and the Jews. The account briefly narrates that a body of troops marched into Pumbeditha, whereupon Rabba and Joseph took to flight. A serious charge had been brought against Rabba, the king or his councillors having been secretly informed that, by means of Rabba's discourses during the Kalla months, his 1200 students had been induced to evade the payment of the poll-tax. A royal bailiff was sent out with orders to seize the person of the principal of the Pumbedithan Academy. Being warned in advance, Rabba fled, and in order to escape detection he wandered about in the surrounding country. His death was caused by fright at the rustling of the wind in the trees, which the fugitive mistook for the tramp of advancing soldiery. Abayi and Raba, his most distinguished disciples, together with the rest of the members of the academy, went in search of his corpse, which they eventually found covered over and hidden by birds. They mourned during seven days for this highly esteemed Amora (330). The charge, which was the occasion of Rabba's death, does not seem to have been further prosecuted. The queen-mother, Ifra, even sent a purse of denars to his successor, leaving it to him to make the best and most pious use of it, whereupon he employed it in ransoming Jewish prisoners.

Rabba's successor and friend, Joseph ben Chiya (born about 270, died about 333), was sickly and sensitive, and possessed a passionate disposition. He was aware of his failings and complained that they prevented him from enjoying life. He seems to have been very wealthy, and to have possessed fields, palm-trees and vineyards, from which latter—as he cultivated them more carefully than was generally the case—he obtained better wine than was commonly produced. Upon being afflicted with blindness, he grieved less for the loss of his sight than on account of his being thereby relieved from performing various religious duties.

Joseph was exceptional among the principals of the Pumbedithan Academy, inasmuch as he attached more weight to the acquisition of a knowledge of the Mishna and the Boraïtas by committing them to memory, than to the drawing of ingenious conclusions. For this reason he was known by the title of "Sinai" and "Possessor of Storehouses." Besides studying the Halacha, he turned his attention to the Targum or Chaldaic translation of the Holy Scriptures. The Torah, and probably also isolated portions of the Prophets, which were used for public reading (Haftara), had long ago been translated into the Aramaic dialects—both the Syriac and the Chaldaic. There existed various Chaldaic translations of the Torah for the use of those who were ignorant of Hebrew: one of these, based probably on the favorite Greek version of Akylas, bore the name of Targum Onkelos; the Syrian translation, employed by such of the Jews of Syria and Mesopotamia as spoke Syriac, was called Peshito (the simple). The greater portion of the Prophets, however, had not been translated, and it was Joseph who first took in hand a Chaldaic translation thereof. Some persons believed that this was a work of piety, as Joseph was prevented by his blindness from reading, and was unwilling to recite the Hebrew text by heart, on account of the prohibition against oral quotation of the written Law. He therefore set about translating the Prophets on his own account, in order to be able to quote any desired passage in Chaldaic. Joseph's translation was incorporated in the Targum, and was accepted as a decisive authority on questions relating to the explanation of doubtful words.

He was exceedingly severe in maintaining discipline in his capacity of principal of the Academy; he flogged one of the students—Nathan bar Assa—for journeying on foot from the Academy to Pumbeditha on the second day of one of the festivals. The few years during which he retained his office were in many ways embittered. He was stricken by a severe illness, through which he lost his memory, and it was consequently often necessary for his pupils to remind him that he himself had formerly taught them the very facts which he was then disputing. Although they endeavored to spare his feelings when drawing his attention to his absurd mistakes, nevertheless, in his irritation, he regarded these corrections as a slight, and complainingly exclaimed: "Be indulgent with an old man whom misfortune has caused to forget all he learnt; and forget not that the fragments of the first tables of the Law were preserved by the side of the unbroken tables."