The Empire suffered only less than Italy. Carthage and north Africa, farthest from the invaders, flourished; but Egypt decayed under destructive factionalism, Caracalla’s massacre, Zenobia’s conquest, high taxes, listless forced labor, and Rome’s annual exaction of grain. Asia Minor and Syria had borne invasion and pillaging, but their ancient and patient industries had survived all tribulations. Greece, Macedonia, and Thrace had been devastated by the barbarians, and Byzantium had not recovered from Septimius’ siege. As war brought Roman garrisons and supplies to the German frontier new cities rose along the rivers- Vienna, Karlsburg, Strasbourg, Mainz. Gaul had been disordered and discouraged by German attacks; sixty of her cities had been sacked; most of her towns and cities were shrinking within new walls, and were abandoning the broad straight streets of Roman design for the more easily defended irregular alleys of early antiquity and the Middle Ages. In Britain, too, the cities were becoming smaller, the villas larger; class war and high taxation had destroyed wealth or driven it into rural concealment. The Empire had begun with urbanization and civilization; it was ending in reruralization and barbarism.


The cultural graph of the third century follows loosely the curve of declining wealth and power. Nevertheless, in these tragic years we have the rise of notational algebra, the highest names in Roman jurisprudence, the finest example of ancient literary criticism, some of Rome’s most majestic architecture, the oldest romantic novels, the greatest of mystic philosophers.

The Greek Anthology summarizes the life of Diophantus of Alexandria (A.D. 250) with algebraic humor: his boyhood lasted one sixth of his life, his beard grew after one twelfth more, he married after another seventh, his son was born five years later and lived to half his father’s age, and the father died four years after his son- therefore at the age of eighty-four. Of his works the chief survivor is the Arithmetica – a treatise on algebra. It solves determinate equations of the first degree, determinate quadratic equations, and indeterminate equations up to the sixth degree. For the unknown quantity which we denote by x, and which he called arithmos (the number)- he used a Greek sigma; and for the other powers he used the letters of the Greek alphabet. An algebra without symbols had existed before him: Plato had recommended, for training and amusing the youthful mind, such problems as the distribution of apples in certain proportions among several persons; Archimedes had propounded like puzzles in the third century B.C.; and both the Egyptians and the Greeks had solved geometrical problems by algebraic methods without algebraic notation. Probably Diophantus systematized methods already familiar to his contemporaries; the accident of time has preserved him; and to him, through the Arabs, we trace that bold and esoteric symbolism which aspires to formulate all the quantitative relations of the world.

Papinian, Paulus, and Ulpian, the culminating trio of Roman law, all rose to power under Septimius Severus; all, as prefects of the Praetorian Guard, were the prime ministers of the realm; and all justified absolute monarchy on the ground that the people had delegated their sovereignty to the emperor. Papinian’s Quaestiones and Responsa were so distinguished by clarity, humanity, and justice that Justinian’s collections leaned heavily on these works. When Caracalla killed Geta, he bade Papinian write a legal defense of the act; Papinian refused, saying that it was “easier to commit fratricide than to justify it.” Caracalla ordered him beheaded, and a soldier performed the deed with an ax in the presence of the Emperor. Domitius Ulpianus continued Papinian’s labors as jurist and humanitarian. His legal opinions defended slaves as by nature free, and women as endowed with the same rights as men. Like most landmarks in the history of law, his writings were essentially a co-ordination of his predecessors’ work; but his judgments were so definitive that nearly a third of them survive in the Digest of Justinian. “It was because Alexander Severus ruled Chiefly in accord with Ulpian’s advice,” says Lampridius, “that he was so excellent an emperor.” However, Ulpian had had some of his opponents put to death; and in 228 his enemies in the Guard killed him in turn, with less legality and equal effect. Diocletian encouraged and financed schools of law, and commissioned the codification of post-Trajanic legislation in the Codex Gregorianus. Thereafter the science of jurisprudence hibernated till Justinian.