Editing Pope Sylvester II (section)

==Scholarly work==
Gerbert studied under the direction of Bishop [[Atto of Vich]], some 60&nbsp;km north of Barcelona, and probably also at the nearby [[Monastery of Santa Maria de Ripoll]].<ref>{{cite web|last1=Mayfield|first1=Betty|title=Gerbert d'Aurillac and the March of Spain: A Convergence of Cultures|url=http://www.maa.org/press/periodicals/convergence/gerbert-daurillac-and-the-march-of-spain-a-convergence-of-cultures|publisher=[[Mathematical Association of America]]|date=August 2010}}</ref> Like all Catalan monasteries, it contained manuscripts from [[Muslim Spain]] and especially from [[Córdoba, Andalusia|Cordoba]], 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]].<ref>[http://www-history.mcs.st-and.ac.uk/Biographies/Gerbert.html Gerbert biography<!-- Bot generated title -->]</ref> Borrell II was facing major defeat from the [[Al-Andalus|Andalusian]] powers so he sent a delegation to [[Córdoba, Spain|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 [[madrasah]]s. This sparked Gerbert's veneration for the Moors and his passion for mathematics and astronomy.

===Abacus and numerals===
[[File:Àbac de Gerbert.png|thumb|Model of the addition 908+95 on part of Gerbert's abacus (with modern numerals, not Gerbert's ones)]]

Gerbert learned of [[Hindu–Arabic numeral system|Hindu–Arabic digits]] and applied this knowledge to the [[abacus]], but probably without the numeral [[zero]].{{refn|group=n|[[Charles Seife]]: "He probably learned about the numerals during a visit to Spain and brought them back with him when he returned to Italy. But the version he learned did not have a zero."{{sfnp|Seife|2000|p=77}}}} According to the 12th-century historian [[William of Malmesbury]], Gerbert got the idea of the computing device of the abacus from a [[Moors|Moorish]] scholar<ref>{{Cite book|title=Medieval robots : mechanism, magic, nature, and art|last=Truitt|first=E. R.|publisher=University of Pennsylvania Press|year=2015|isbn=9780812291407|location=Philadelphia|pages=77|oclc=907964739}}</ref> from [[University of al-Qarawiyyin|University of Al-Qarawiyyin]].<ref>[https://www.herodote.net/2_avril_999-evenement-9990402.php herodote.net] {{Webarchive|url=https://web.archive.org/web/20170301212427/https://www.herodote.net/2_avril_999-evenement-9990402.php |date=1 March 2017}}</ref> 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 [[Horn (anatomy)|animal horn]] by a shieldmaker of Rheims.<ref name="darlington 472">{{harvtxt|Darlington|1947|p=472}}.</ref>{{sfnp |Tester|1987| pp=131–132}}{{sfnp |Buddhue|1941| p=266}} 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]].<ref name="darlington 472"/> Due to Gerbert's reintroduction, the abacus became widely used in Europe once again during the 11th century.{{sfnp |Buddhue|1941| p=266}}

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.<ref name=":02"/> In this book, he individually introduced the "Hindu-Arabic" symbols the abacus used and related them to the more common Latin numerical nouns.<ref name=":02">{{Cite journal |last=Freudenhammer |first=Thomas |date=2021 |title=Gerbert of Aurillac and the Transmission of Arabic Numerals to Europe |url=https://www.jstor.org/stable/48636817 |journal=Sudhoffs Archiv |volume=105 |issue=1 |pages=5 |doi=10.25162/sar-2021-0001 |jstor=48636817 }}</ref> Bernelinus' ''Liber Abaci'' has survived in 11 manuscripts from the 11th and 12th centuries.<ref>{{Cite journal |last=Freudenhammer |first=Thomas |date=2021 |title=Gerbert of Aurillac and the Transmission of Arabic Numerals to Europe |url=https://www.jstor.org/stable/48636817 |journal=Sudhoffs Archiv |volume=105 |issue=1 |pages=6 |doi=10.25162/sar-2021-0001 |jstor=48636817 }}</ref> 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.<ref>{{Cite journal |last=Freudenhammer |first=Thomas |date=2021 |title=Gerbert of Aurillac and the Transmission of Arabic Numerals to Europe |url=https://www.jstor.org/stable/48636817 |journal=Sudhoffs Archiv |volume=105 |issue=1 |pages=6–7|doi=10.25162/sar-2021-0001 |jstor=48636817 }}</ref> 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.<ref>{{Cite journal |last=Freudenhammer |first=Thomas |date=2021 |title=Gerbert of Aurillac and the Transmission of Arabic Numerals to Europe |url=https://www.jstor.org/stable/48636817 |journal=Sudhoffs Archiv |volume=105 |issue=1 |pages=8 |doi=10.25162/sar-2021-0001 |jstor=48636817 }}</ref>

===Armillary sphere and sighting tube===
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.{{sfnp |Tester|1987| pp=130–131}}<ref>{{harvtxt|Darlington|1947|pp=467–472}}.</ref> The details of Gerbert's armillary sphere are revealed in letters from Gerbert to his former student and monk Remi of [[Trier|Trèves]] and to his colleague Constantine, the [[abbot]] of [[Micy Abbey|Micy]], as well as the accounts of his former student and French nobleman Richer, who served as a monk in [[Rheims]].<ref>{{harvtxt|Darlington|1947|pp=464, 467–472}}.</ref> Richer stated that Gerbert discovered that stars coursed in an oblique direction across the night sky.<ref name="darlington 467">{{harvtxt|Darlington|1947|p=467}}.</ref> Richer described Gerbert's use of the armillary sphere as a visual aid for teaching mathematics and astronomy in the classroom.

[[Image:Sandro Botticelli 052.jpg|thumb|right|upright|An [[armillary sphere]] in [[Saint Augustine in His Study (Botticelli, Ognissanti)|a painting]] by [[Sandro Botticelli]], {{Circa|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.<ref name="darlington 468">{{harvtxt|Darlington|1947|p=468}}.</ref> By this account, the [[polar circle]] on Gerbert's sphere was located at 54 degrees,  several degrees off from the actual 66° 33'.<ref name="darlington 468"/> His positioning of the [[Tropic of Cancer]] at 24 degree was nearly exact, while his positioning of the [[equator]] was correct by definition.<ref name="darlington 468"/> Richer also revealed how Gerbert made the planets more easily observable in his armillary sphere:

{{Blockquote|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.{{sfnp |Darlington|1947| pp=468–469}}}}

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.<ref name="darlington 469">{{harvtxt|Darlington|1947|p=469}}.</ref> This armillary sphere was also described by Gerbert in a letter to his colleague Constantine.<ref name="darlington 469 470">{{harvtxt|Darlington|1947|pp=469–470}}.</ref> 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.<ref name="darlington 470">{{harvtxt|Darlington|1947|p=470}}.</ref> 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.<ref name="darlington 470"/>

=== Scientific library ===
In late 984, Gerbert sent a letter to abbot Eberhard of Tours concerning the foundation of a large scientific library.<ref name="Freudenhammer 2020 142">{{Cite journal |last=Freudenhammer |first=Thomas |date=2020 |title=Lupitus of Barcelona - Lupitus von Barcelona: On the identity of a tenth century scientific translator |url=https://www.jstor.org/stable/48616035 |journal=Sudhoffs Archiv |volume=104 |issue=2 |pages=142 |doi=10.25162/sar-2020-0005 |jstor=48616035 |issn=0039-4564 }}</ref> He dedicated immense sums of money to establishing the library and purchasing texts from a wide variety of western European authors.<ref name="Freudenhammer 2020 142"/>  He wrote to many monks and abbots in Europe requesting classical literature from their monasteries.<ref name="Freudenhammer 2020 142"/> Gerbert was also able to acquire some work from earlier era authors such as [[Cicero]] and [[Statius]].<ref name="Freudenhammer 2020 142"/> Two specific requests Gerbert made that documentation exists for are letters sent to Lupitus of Barcelona and Bishop Miró Bonfill of Girona, asking the former for an astrology book and the latter for an arithmetic book.<ref name="Freudenhammer 2020 142"/> It can be inferred from this that the library contained many volumes of books covering a wide variety of topics, but the exact size and influence the library had is seemingly unknown.