Editing Pope Sylvester II (section)

===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>