Gerbert

also known as Gerbert d’Aurilla , later Pope Sylvester II

(b. Aquitaine, France, ca. 945; d Rome, 12 May 1003)

mathematics.

Gerbert received his early education at the Benedicitine convent of Saini Géraud in Aurillac. He left it in 967 in the company of Borel, count of Barcelona. In Catalonia he continued his studies under Atto, bishop of Vich; he concentrated on mathematics, Probably on the works of such authors as Boethius, Cassiodorus, and Martianus Capella. How much Moorish science Gerbert was able to study as far north as Vich is uncertain. In 970 he accompanied Borel and Atto to Rome, where he attracted the attention of Pope John XIII and, through him, of Otto I, Holy Roman Emperor, who was then residing in Rome.

This was the beginning of Gerbert’s career, which was based not only on his intellectual gifts but also on his allegiance to the Saxon imperial house and its political dream—the restoration of the empire of Charlemagne, rule in harmony of emperor and pope, Gerbert was assigned to Adalbero, the energetic and learned archbishop of Rheims; there he reorganized the cathedral school with such success that pupils began to flock to it from many parts of the empire. Equal attention was paid to Christian authors and to such pagan writers as Cicero and Horace; great pains were taken to enrich the library.

For many years experts have tried, without reaching full agreement, to date the many exisiting mathematical manuscripts dating from the tenth to the thirteenth centuries and ascribed to Boethis or Gerbert or their pupils. From what most authorities believe are transcripts of Boethius and Gerbert themselves, it seems that in arithmetic some Phythagorean numbers theory was taught in the spirit of Nicomachus, and in geometry, some statements (without proofs) of Euchlid together with the mensuration rules of ancient Roman surveyors; the art of computing was taught with the aid of a special type of abacus. For his lessons in astronomy Gerbert constructed some armillary spheres.

Among Gerbert’s pupils were Robert, son of Hugh Capet (later Robert II of France): Adalbold, later bishop of Utrecht; Richer of Saint-Remy, who wrote Gerbert’s biography; and probably also a certain Bernelinus, the Paris author of a Liber abaci that mentions Gerbert as pope and may well represent his teaching, Gerbert’s influence probably extended to other cathedral or monastic schools, especially in Lorraine. This school of training in the quadrivium (music, geometry, arithmetic, astronomy), which is also represented by the Quadratura circuli of Franco of Liège (ca. 1050), indicate the vivid interest in mathematics that was beginning to appear in western Europe. The only works available, however, were poor remains of Greek knowledge transmitted in the later Roman period. These prepared the way for Arabic science; a work entitled De astorlabia which shows Arabic influence and of which the earliset manuscript is form the eleventh century, has occasionally been ascribed to Gerbert.

In 983 Otto II, a great admirer of Gerbert, appointed him abbot of Bobbio in the Apennines, but by 984 he was back in Rheims. From then on, he took an active part in the political schemes among the Saxons, Carolingians, and Capets; he and Adalbero were deeply involved on the side of the emperor. The Carolingian dynasty came to an end, and in 987 Gerbert assisted in the coronation of Hugh Capet as king of France. In 991 he became archbishop of Rheims, but in 997 he left his see amid controversy and intrigue. He followed the court of young Otto III through Germany to Italy. At Magdeburg between 994, and 995 he constructed an oralogium, either a sundial or an astrolabe, for which he took the altitude of the pole star. In 998 Gerbert became archbishop of Ravenna; and in 999, through Otto’s influence, he was the first Frenchman to be elected pope. A lover of arts and sciences, Otto hoped that emperor and pope would revive the Carolingian Renaissance. Significantly, Gerbert assumed the name Sylvester II, Sylvester I Having been pope at the time of Constantine and, thus, a participant in the first holy alliance of pope and emperor.

The great scheme, however, came to naught with the death of Otto in 1002 and of Gerbert the following year. Legendary ascriptions to Gerbert of supernatural and demonic powers (which even found their way into Victor Hugo’s Welf, castellan d’Osbor) testify to the impression that this learning made on posterity.

Information about Gerbert’s life is in the “Historiate” writtern from 996 to 998 by his pupil Richer, in 224 published letters, and in contemporary chronicles. Many theological and scientific writing testify to his work and influence. Among those that seem to be authentic are Regulae de numerorum abaci rationibus (also called Libellus de numerorum divisione), De sphaera, sections of a Geometria,, a letter to Adalbold on the area of an isoseles triangle, and a Libellus de rationali et ratione uti (997 or 998) with considerations on the rational and the use of reason. A text that Olleris entitled Regula de abaco computi and ascribed to Gerbert is ascribed to Heriger by Bubnov. The authenticity of the Geometria has been the subject of much controversy, often in connection with that of Boethiu’s work of the same title.

The abacus connected with Gerbert was a board with as many as twenty-seven columns, combined in groups of three. From left to right they were headed by the letters C (centum, hundred),D(decem, ten), and S or M(singularis of monad, one); other columns (and other letters) were expressed by counters (apices) which carried symbols equivalent to our 1, 2 … 9 (which many indicate some Arabic influence), so that 604, for instance, was expressed by an apex with 6 in the C column and an apex with 4 in the S column. There was no apex for zero. With such an apparatus Gerbert and his school were able to perform addition, subtraction, multiplication, and even division, something considered complicated. This art of computation probably remained confined to ecclesiastical schools, never replacing older forms of reckoning, and went cut of fashion with the gradual introduction of Hindu-Arabic numerals. A letter from Adalbold to Gerbert “de ratione inveniendi crassitudinem sperar” metnions the equivalent of π 22/7, which was probably considered as exact. For Gerbert accepted 26/15 (at another place 12/7), and for , 17/12.

Low as the level of Gerbert’s mathematical knowledge was, it surpassed that of his monstic contemporaries and their pupils. This is shown in eight letters exchanged between two monastic friends of Adalbold, edited by P. Tannery and Abbé Clerval (see Mémories scientifiques volume 5).

BIBLIOGRAPHY

I. Original Works. Gerbert’s extant work can be found in Oeuvres de Gebert, A. Olleris, ed. (Paris-Clermontferrande, 1867); Letters de Gerbert, J. Havet, ed. (Paris, 1889); and Gerberi Opera mathematica, N. Bubnov, ed. (Berlin, 1899). An added document is found in H. Omont, “Opuscules mathématiques de Gerbert et de Hériger de Lobbes,” in Notices et extraits des manuscrits de la Bibliothèque nationale et autres bibliothèques, 39 (1909), 4-15.

II. Secondary Literature. Works on Gerbert include moritz Cantor, Vorlesungen übr Geschichie dew Mathematik, 3rd ed., I (Leipzig, 1907), 848-878; O.G. Darlingston, “Gerbert the Teacher,” in American Historical Review, 52 (1947), 456-476, with titles of the articles published at the time of Gerbert’s millennary commemoration in 1938; J. Leflon, Gerbert, humanisme et chrétienté au X’ Siècle (Abbhaye Saint Wandrille, 1946); F. Picavet, Gerbert, un pape philosophe (Parios, 1917); P. Tannery, ed., Mèmories scientifiques, V. (Toulouse-Paris, 1922), arts. 5, 6, and 10; M. Uhlirz, Untersucungen über Inhablt und Datierung der Briefe Gerberts von Aurillac, Papst Sylvester II (Göttingen, 1957); ane J.M. Milláa Vallicrosa, Nueve estudios sobre historia de la ciencia espanola (Barcelona, 1960).

Richer’s “Historiae” wer published in R. Latouche, Richer, Historie de France (88-995) (Paris, 1937), with French trans, and in Monumenta Germaniae historica, Scriptorum, III. G.H. Pertz, ed. (Hannover, 1839). See also A.J. E. M. Smeur, “De verhandeling over de cirkelkwadratuur van Franco van luik van omstreeks 1050,” in Mededelingen van de K. Vlaamsche academie voor wetenschappen, letteren en schoone kunsten van België, Klasse der wetenshcappen, 30 no. 11 (1960).

D. J. Struik