Pope Sylvester II

Model of the addition 908+95 on part of Gerbert's abacus (with modern numerals, not Gerbert's ones)

Gerbert learned of Hindu–Arabic digits and applied this knowledge to the abacus, but probably without the numeral zero.[n 2] According to the 12th-century historian William of Malmesbury, Gerbert got the idea of the computing device of the abacus from a Moorish scholar.[6] The abacus that Gerbert reintroduced into Europe had its length divided into 27 parts with 9 number symbols (this would exclude zero, which was represented by an empty column) and 1,000 characters in all, crafted out of animal horn by a shieldmaker of Rheims.[7][8][9] According to his pupil Richer, Gerbert could perform speedy calculations with his abacus that were extremely difficult for people in his day to think through using only Roman numerals.[7] Due to Gerbert's reintroduction, the abacus became widely used in Europe once again during the 11th century.[9]

Although lost to Europe since the terminus of the Greco-Roman era, Gerbert reintroduced the astronomical armillary sphere to Latin Europe via the Islamic civilization of Al-Andalus, which was at that time at the "cutting edge" of civilization.[10][11] The details of Gerbert's armillary sphere are revealed in letters from Gerbert to his former student and monk Remi of Trèves and to his colleague Constantine, the abbot of Micy, as well as the accounts of his former student and French nobleman Richer, who served as a monk in Rheims.[12] Richer stated that Gerbert discovered that stars coursed in an oblique direction across the night sky.[13] Richer described Gerbert's use of the armillary sphere as a visual aid for teaching mathematics and astronomy in the classroom.

An armillary sphere in a painting by Sandro Botticelli, c. 1480

Historian Oscar G. Darlington asserts that Gerbert's division by 60 degrees instead of 360 allowed the lateral lines of his sphere to equal to six degrees.[14] By this account, the polar circle on Gerbert's sphere was located at 54 degrees, several degrees off from the actual 66° 33'.[14] His positioning of the Tropic of Cancer at 24 degree was nearly exact, while his positioning of the equator was correct by definition.[14] Richer also revealed how Gerbert made the planets more easily observable in his armillary sphere:

He succeeded equally in showing the paths of the planets when they come near or withdraw from the earth. He fashioned first an armillary sphere. He joined the two circles called by the Greeks coluri and by the Latins incidentes because they fell upon each other, and at their extremities he placed the poles. He drew with great art and accuracy, across the colures, five other circles called parallels, which, from one pole to the other, divided the half of the sphere into thirty parts. He put six of these thirty parts of the half-sphere between the pole and the first circle; five between the first and the second; from the second to the third, four; from the third to the fourth, four again; five from the fourth to the fifth; and from the fifth to the pole, six. On these five circles he placed obliquely the circles that the Greeks call loxos or zoe, the Latins obliques or vitalis (the zodiac) because it contained the figures of the animals ascribed to the planets. On the inside of this oblique circle he figured with an extraordinary art the orbits traversed by the planets, whose paths and heights he demonstrated perfectly to his pupils, as well as their respective distances.[15]

Richer wrote about another of Gerbert's last armillary spheres, which had sighting tubes fixed on the axis of the hollow sphere that could observe the constellations, the forms of which he hung on iron and copper wires.[16] This armillary sphere was also described by Gerbert in a letter to his colleague Constantine.[17] Gerbert instructed Constantine that, if doubtful of the position of the pole star, he should fix the sighting tube of the armillary sphere into position to view the star he suspected was it, and if the star did not move out of sight, it was thus the pole star.[18] Furthermore, Gerbert instructed Constantine that the north pole could be measured with the upper and lower sighting tubes, the Arctic Circle through another tube, the Tropic of Cancer through another tube, the equator through another tube, and the Tropic of Capricorn through another tube.[18]

Pope Sylvester II and the Devil in an illustration of c. 1460

The legend of Gerbert grows from the work of the English monk William of Malmesbury in De Rebus Gestis Regum Anglorum and a polemical pamphlet, Gesta Romanae Ecclesiae contra Hildebrandum, by Cardinal Beno, a partisan of Emperor Henry IV who opposed Pope Gregory VII in the Investiture Controversy. According to the legend, Gerbert, while studying mathematics and astrology in the Muslim cities of Córdoba and Seville, was accused of having learned sorcery.[22] Gerbert was supposed to be in possession of a book of spells stolen from an Arab philosopher in Spain. Gerbert fled, pursued by the victim, who could trace the thief by the stars, but Gerbert was aware of the pursuit, and hid hanging from a wooden bridge, where, suspended between heaven and earth, he was invisible to the magician.[23]

Gerbert was supposed to have built a brazen head. This "robotic" head would answer his questions with "yes" or "no". He was also reputed to have had a pact with a female demon called Meridiana, who had appeared after he had been rejected by his earthly love, and with whose help he managed to ascend to the papal throne (another legend tells that he won the papacy playing dice with the Devil).[24]

According to the legend, Meridiana (or the bronze head) told Gerbert that if he should ever read a Mass in Jerusalem, the Devil would come for him. Gerbert then cancelled a pilgrimage to Jerusalem, but when he read Mass in the church Santa Croce in Gerusalemme ("Holy Cross of Jerusalem") in Rome, he became sick soon afterwards and, dying, he asked his cardinals to cut up his body and scatter it across the city. In another version, he was even attacked by the Devil while he was reading the Mass, and the Devil mutilated him and gave his gouged-out eyes to demons to play with in the Church. Repenting, Sylvester II then cut off his hand and his tongue.

The inscription on Gerbert's tomb reads in part Iste locus Silvestris membra sepulti venturo Domino conferet ad sonitum ("This place will yield to the sound [of the last trumpet] the limbs of buried Sylvester II, at the advent of the Lord", mis-read as "will make a sound") and has given rise to the curious legend that his bones will rattle in that tomb just before the death of a pope.[25]

The alleged story of the crown and papal legate authority given to Stephen I of Hungary by Sylvester in the year 1000 (hence the title 'apostolic king') is noted by the 19th-century historian Lewis L. Kropf as a possible forgery of the 17th century.[26] Likewise, the 20th-century historian Zoltan J. Kosztolnyik states that "it seems more than unlikely that Rome would have acted in fulfilling Stephen's request for a crown without the support and approval of the emperor."[27]

Hungary issued a commemorative stamp honouring Pope Sylvester II on 1 January 1938,[28] and France honoured him in 1964 by issuing a postage stamp.[29]

• Buddhue, John Davis (1941). "The Origin of Our Numbers". The Scientific Monthly. 52 (3): 265–267. Bibcode:1941SciMo..52..265D.
• Darlington, Oscar G. (1947). "Gerbert, the Teacher". American Historical Review. 52 (3): 456–476. doi:10.2307/1859882. JSTOR 1859882.
• Kosztolnyik, Zoltan J. (1977). "The Relations of Four Eleventh-Century Hungarian Kings with Rome in the Light of Papal Letters". Church History. 46 (1): 33–47. doi:10.2307/3165157. JSTOR 3165157.
• Kropf, Lewis L. (1898). "Pope Sylvester II and Stephen I of Hungary". English Historical Review. 13 (50): 290–295. doi:10.1093/ehr/XIII.L.290. JSTOR 547228.
• Seife, Charles (2000). Zero: The Biography of a Dangerous Idea. New York: Penguin Books. Bibcode:2000zbdi.book.....S. ISBN 978-0-670-88457-5.
• Tester, S. Jim (1987). A History of Western Astrology. Rochester: Boydell & Brewer. ISBN 978-0-85115-446-6.