Pope Sylvester II (Latin: Silvester II; c. 946 – 12 May 1003), originally known as Gerbert of Aurillac, was a scholar and teacher who served as the bishop of Rome and ruled the Papal States from 999 to his death. He endorsed and promoted study of Moorish and Greco-Roman arithmetic, mathematics and astronomy, reintroducing to Western Christendom the abacus, armillary sphere, and water organ, which had been lost to Latin Europe since the fall of the Western Roman Empire. He is said to be the first in Christian Europe (outside of Al-Andalus) to introduce the decimal numeral system using the Hindu–Arabic numeral system.

Gerbert was born about 946, or at any rate between 945 and 950. His exact birthplace is unknown, but it must have been in what was then the Duchy of Aquitaine, part of the Kingdom of France. More precise proposals include the town of Belliac, near the present-day commune of Saint-Simon, Cantal, or Aurillac. Another speculated location is the province of Auvergne. Gerbert's parents, wanting him to have a quality education, took him to receive instruction at the nearby Benedictine Abbey. Here, Gerbert became a pupil of a monk named Raimund, who admired his desire of knowledge and assisted him in his studies.

Around 963, he entered the Monastery of St. Gerald of Aurillac. In 967, Count Borrell II of Barcelona (947–992) visited the monastery, and the abbot asked the count to take Gerbert with him so that the lad could study mathematics in Catalonia and acquire there some knowledge of Arabic learning. While away from the monastery, Gerbert pursued studies in Barcelona, and also received Arabic instruction at Seville and Córdoba.

Gerbert studied under the direction of Bishop Atto of Vich, some 60 km north of Barcelona, and probably also at the nearby Monastery of Santa Maria de Ripoll. Like all Catalan monasteries, it contained manuscripts from Muslim Spain and especially from Córdoba, one of the intellectual centres of Europe at that time: the library of al-Hakam II, for example, had thousands of books (from science to Greek philosophy). This is where Gerbert was introduced to mathematics and astronomy. Borrell II was facing major defeat from the Andalusian powers so he sent a delegation to Córdoba to request a truce. Bishop Atto was part of the delegation that met with al-Ḥakam II, who received him with honour. Gerbert was fascinated by the stories of the Mozarab Christian bishops and judges who dressed and talked like the Moors, well-versed in mathematics and natural sciences like the great teachers of the Islamic madrasahs. This sparked Gerbert's veneration for the Moors and his passion for mathematics and astronomy.

Gerbert learned of Hindu–Arabic digits and applied this knowledge to the abacus, but probably without the numeral zero. According to the 12th-century historian William of Malmesbury, Gerbert got the idea of the computing device of the abacus from a Moorish scholar from University of Al-Qarawiyyin. 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. 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. Due to Gerbert's reintroduction, the abacus became widely used in Europe once again during the 11th century.

Bernelinus of Paris, who was probably a pupil of Gerbert, wrote a book called the Liber Abaci (not to be confused with Fibonacci's Liber Abaci) where he discussed the abacus' design. In this book, he individually introduced the "Hindu-Arabic" symbols the abacus used and related them to the more common Latin numerical nouns. Bernelinus' Liber Abaci has survived in 11 manuscripts from the 11th and 12th centuries. In two of them, probably the oldest ones, the number 3 is reproduced in a form that differs from the other manuscripts. This symbol is reminiscent of the "Tironian note" for the Latin word "ter" from the Roman shorthand. The reason for this is not known, but it is speculated that Bernelinus did not want to use an "unbeliever" symbol to indicate the number that represents the Holy Trinity.

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. 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. Richer stated that Gerbert discovered that stars coursed in an oblique direction across the night sky. Richer described Gerbert's use of the armillary sphere as a visual aid for teaching mathematics and astronomy in the classroom.

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. By this account, the polar circle on Gerbert's sphere was located at 54 degrees, several degrees off from the actual 66° 33'. His positioning of the Tropic of Cancer at 24 degree was nearly exact, while his positioning of the equator was correct by definition. Richer also revealed how Gerbert made the planets more easily observable in his armillary sphere: