Editing Arabic numerals (section)

== History ==
{{main|History of the Hindu–Arabic numeral system}}
=== Origin ===
[[File:The Brahmi numeral system and its descendants.png|alt=|thumb|Evolution of Indian numerals into Arabic numerals and their adoption in Europe]]

Positional decimal notation including a [[0|zero]] symbol was [[History of the Hindu–Arabic numeral system|developed in India]], using symbols visually distinct from those that would eventually enter into international use. As the concept spread, the sets of symbols used in different regions diverged over time.

The immediate ancestors of the digits now commonly called "Arabic numerals" were introduced to Europe in the 10th century by Arabic speakers of Spain and North Africa, with digits at the time in wide use from Libya to Morocco. In the east from Egypt to Iraq and the Arabian Peninsula, the Arabs were using the [[Eastern Arabic numerals]] or "Mashriki" numerals: <span dir=ltr style="unicode-bidi: bidi-override; direction: ltr">٠, ١, ٢, ٣, ٤, ٥, ٦, ٧, ٨, ٩</span>.<ref name=":2">{{Cite book |last=Burnett |first=Charles |url=https://books.google.com/books?id=AG2XBCmxYcUC |title=From China to Paris: 2000 Years Transmission of Mathematical Ideas |year=2002 |publisher=Franz Steiner Verlag |isbn=978-3-515-08223-5 |editor-last=Dold-Samplonius |editor-first=Yvonne |pages=237–288 |editor-last2=Van Dalen |editor-first2=Benno |editor-last3=Dauben |editor-first3=Joseph |editor-last4=Folkerts |editor-first4=Menso}}</ref>

[[Alī ibn Ahmad al-Nasawī|Al-Nasawi]] wrote in the early 11th century that mathematicians had not agreed on the form of the numerals, but most of them had agreed to train themselves with the forms now known as Eastern Arabic numerals.<ref>{{harvnb|Kunitzsch|2003|p=7}}: {{lang|fr|"Les personnes qui se sont occupées de la science du calcul n'ont pas été d'accord sur une partie des formes de ces neuf signes; mais la plupart d'entre elles sont convenues de les former comme il suit."}}</ref> The oldest specimens of the written numerals available are from Egypt and date to 873–874&nbsp;AD. They show three forms of the numeral "2" and two forms of the numeral "3", and these variations indicate the divergence between what later became known as the Eastern Arabic numerals and the Western Arabic numerals.{{sfn|Kunitzsch|2003|p=5}} The Western Arabic numerals came to be used in the [[Maghreb]] and [[Al-Andalus]] from the 10th century onward.<ref>{{harvnb|Kunitzsch|2003|pp=12–13}}: "While specimens of Western Arabic numerals from the early period—the tenth to thirteenth centuries—are still not available, we know at least that Hindu reckoning (called ''ḥisāb al-ghubār'') was known in the West from the 10th century onward..."</ref> Some amount of consistency in the Western Arabic numeral forms endured from the 10th century, found in a Latin manuscript of [[Isidore of Seville]]'s ''{{lang|la|[[Etymologiae]]}}'' from 976 and the Gerbertian abacus, into the 12th and 13th centuries, in early manuscripts of translations from the city of [[Toledo, Spain|Toledo]].<ref name=":2" />

Calculations were originally performed using a dust board ({{tlit|ar|takht}}, Latin: {{lang|la|tabula}}), which involved writing symbols with a stylus and erasing them. The use of the dust board appears to have introduced a divergence in terminology as well: whereas the Hindu reckoning was called {{tlit|ar|ḥisāb al-hindī}} in the east, it was called {{tlit|ar|ḥisāb al-ghubār}} 'calculation with dust' in the west.{{sfn|Kunitzsch|2003|p=8}} The numerals themselves were referred to in the west as {{tlit|ar|ashkāl al‐ghubār}} 'dust figures' or {{tlit|ar|qalam al-ghubār}} 'dust letters'.{{sfn|Kunitzsch|2003|p=10}} [[Abu'l-Hasan al-Uqlidisi|Al-Uqlidisi]] later invented a system of calculations with ink and paper 'without board and erasing' ({{tlit|ar|bi-ghayr takht wa-lā maḥw bal bi-dawāt wa-qirṭās}}).{{sfn|Kunitzsch|2003|pp=7–8}}

A popular myth claims that the symbols were designed to indicate their numeric value through the number of angles they contained, but there is no contemporary evidence of this, and the myth is difficult to reconcile with any digits past 4.<ref name=ifrah>{{cite book |last1=Ifrah |first1=Georges |year=1998 |title=The universal history of numbers: from prehistory to the invention of the computer |translator-last=Bellos |translator-first=David |location=London |publisher=Harvill |isbn=978-1-860-46324-2 |pages=356–357}}</ref>
[[File:Houghton Typ 520.03.736 - Margarita philosophica.jpg|thumb|Etching published 1503 showing usage of Arabic numerals]]

=== Adoption and spread ===
[[File:Codex Vigilanus Primeros Numeros Arabigos.jpg|thumb|right|The first Arabic numerals in the West appeared in the ''{{lang|la|[[Codex Albeldensis]]}}'' in Spain.]]

The first mentions of the numerals from 1 to 9 in the West are found in the 976 ''{{lang|la|[[Codex Vigilanus]]}}'', an [[Illuminated manuscript|illuminated]] collection of various historical documents covering a period from antiquity to the 10th century in [[Hispania]].<ref name=":1">{{Cite journal |last=Nothaft |first=C. Philipp E. |date=2020-05-03 |title=Medieval Europe's satanic ciphers: on the genesis of a modern myth |url=https://doi.org/10.1080/26375451.2020.1726050 |journal=British Journal for the History of Mathematics |volume=35 |issue=2 |pages=107–136 |doi=10.1080/26375451.2020.1726050 |s2cid=213113566 |issn=2637-5451}}</ref> Other texts show that numbers from 1 to 9 were occasionally supplemented by a placeholder known as [[Names for the number 0 in English|{{tlit|ar|sipos}}]], represented as a circle or wheel, reminiscent of the eventual symbol for [[0|zero]]. The Arabic term for zero is {{tlit|ar|ṣifr}} ({{Lang|ar|صفر}}), transliterated into Latin as {{lang|la|cifra}}, which became the English word ''[[cipher]]''.

From the 980s, Gerbert of [[Aurillac]] (later [[Pope Sylvester II]]) used his position to spread knowledge of the numerals in Europe. Gerbert studied in [[Barcelona]] in his youth. He was known to have requested mathematical treatises concerning the [[astrolabe]] from [[Lupitus of Barcelona]] after he had returned to France.<ref name=":1" />

The reception of Arabic numerals in the West was gradual and lukewarm, as other numeral systems circulated in addition to the older Roman numbers. As a discipline, the first to adopt Arabic numerals as part of their own writings were astronomers and astrologists, evidenced from manuscripts surviving from mid-12th-century Bavaria. Reinher of Paderborn (1140–1190) used the numerals in his calendrical tables to calculate the dates of [[Easter]] more easily in his text ''{{lang|la|Computus emendatus}}''.<ref>{{Cite web |last=Herold |first=Werner |year=2005 |title=Der "computus emendatus" des Reinher von Paderborn |url=https://ixtheo.de/Record/164418110X |access-date=2022-07-29 |website=ixtheo.de |language=German |url-status=live |archive-date=30 July 2022 |archive-url=https://web.archive.org/web/20220730020351/https://ixtheo.de/Record/164418110X}}</ref>

==== Italy ====
[[Image:Liber abbaci magliab f124r.jpg|thumb|A page of the ''Liber Abaci''. The list on the right shows the [[Fibonacci sequence]]: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377. The 2, 8, and 9 resemble Arabic numerals more than [[Eastern Arabic numerals]] or [[Indian numerals]].]]

[[Leonardo Fibonacci]] was a [[Republic of Pisa|Pisan]] mathematician who had studied in the Pisan trading colony of [[Béjaïa|Bugia]], in what is now [[Algeria]],<ref name="K. K. Tung">{{cite book|first=K. K. |last=Tung|title=Topics in Mathematical Modeling |year=2016|publisher=Princeton University Press |isbn=978-1-4008-8405-6|pages=1}}</ref> and he endeavored to promote the numeral system in Europe with his 1202 book ''{{lang|la|[[Liber Abaci]]}}'':

<blockquote>When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art very soon pleased me above all else and I came to understand it.</blockquote>

The ''{{lang|la|Liber Abaci}}''{{'}}s analysis highlighting the advantages of positional notation was widely influential. Likewise, Fibonacci's use of the Béjaïa digits in his exposition ultimately led to their widespread adoption in Europe.<ref name=":0">{{Cite thesis |first=Raffaele |last=Danna |date=2021-07-12 |title=The Spread of Hindu–Arabic Numerals in the European Tradition of Practical Arithmetic: a Socio-Economic Perspective (13th–16th centuries) |url=https://www.repository.cam.ac.uk/handle/1810/325042 |publisher=University of Cambridge |degree=PhD |doi=10.17863/cam.72497 |access-date=29 July 2022 |archive-url=https://web.archive.org/web/20210727110444/https://www.repository.cam.ac.uk/handle/1810/325042 |archive-date=27 July 2021 |url-status=live}}</ref> Fibonacci's work coincided with the European [[commercial revolution]] of the 12th and 13th centuries centered in Italy. Positional notation facilitated complex calculations (such as currency conversion) to be completed more quickly than was possible with the Roman system. In addition, the system could handle larger numbers, did not require a separate reckoning tool, and allowed the user to check their work without repeating the entire procedure. Late medieval Italian merchants did not stop using Roman numerals or other reckoning tools: instead, Arabic numerals were adopted for use in addition to their preexisting methods.<ref name=":0" />

==== Wider Europe ====
[[File:Ms.Thott.290.2º 150v.jpg|thumb|A German manuscript page teaching use of Arabic numerals ([[Hans Talhoffer|Talhoffer]] Thott, 1459), presented together with the [[Hebrew alphabet]] and [[astrology]]]]
[[File:EuropeanFormOfArabianDigits.png|thumb|upright=1.5|Table of numerals in many variants, 1757, by [[Jean-Étienne Montucla]]]]

By the late 14th century, only a few texts using Arabic numerals appeared outside of Italy. This suggests that the use of Arabic numerals in commercial practice, and the significant advantage they conferred, remained a virtual Italian monopoly until the late 15th century.<ref name=":0" /> This may in part have been due to language barriers: although Fibonacci's ''{{lang|la|Liber Abaci}}'' was written in Latin, the Italian abacus traditions were predominantly written in Italian vernaculars that circulated in the private collections of abacus schools or individuals.

The European acceptance of the numerals was accelerated by the invention of the [[printing press]], and they became widely known during the 15th century. Their use grew steadily in other centers of finance and trade such as Lyon.<ref>{{Cite SSRN |last1=Danna |first1=Raffaele |last2=Iori |first2=Martina |last3=Mina |first3=Andrea |date=2022-06-22 |title=A Numerical Revolution: The Diffusion of Practical Mathematics and the Growth of Pre-modern European Economies |ssrn=4143442}}</ref> Early evidence of their use in [[Great Britain in the Middle Ages|Britain]] includes: an equal hour horary [[quadrant (instrument)|quadrant]] from 1396,<ref>{{cite news |title=14th century timepiece unearthed in Qld farm shed |work=ABC News |url=http://www.abc.net.au/news/2011-11-09/one-man27s-trash-is-another27s-centuries-old-treasure/3654974 |access-date=10 November 2011 |archive-date=29 February 2012 |archive-url=https://web.archive.org/web/20120229232807/http://www.abc.net.au/news/2011-11-09/one-man27s-trash-is-another27s-centuries-old-treasure/3654974 |url-status=live }}</ref> in England, a 1445 inscription on the tower of [[Heathfield and Waldron|Heathfield]] Church, [[Sussex]]; a 1448 inscription on a wooden lych-gate of [[Bray, Berkshire|Bray]] Church, [[Berkshire]]; and a 1487 inscription on the belfry door at [[Piddletrenthide]] church, [[Dorset]]; and in [[Scotland]] a 1470 inscription on the tomb of the first Earl of Huntly in [[Elgin, Moray|Elgin]] Cathedral.<ref>See G. F. Hill, ''The Development of Arabic Numerals in Europe'', for more examples.</ref> In central Europe, the [[King of Hungary]] [[Ladislaus the Posthumous]], started the use of Arabic numerals, which appear for the first time in a royal document of 1456.<ref>Erdélyi: Magyar művelődéstörténet 1-2. kötet. Kolozsvár, 1913, 1918.</ref>

By the mid-16th century, they had been widely adopted in Europe, and by 1800 had almost completely replaced the use of counting boards and Roman numerals in accounting. Roman numerals were mostly relegated to niche uses such as years and numbers on clock faces.

==== Russia ====
Prior to the introduction of Arabic numerals, [[Cyrillic numerals]], derived from the [[Early Cyrillic alphabet|Cyrillic alphabet]], were used by [[South Slavs|South]] and [[East Slavs]]. The system was used in Russia as late as the early 18th century, although it was formally replaced in official use by [[Peter the Great]] in 1699.<ref>{{Cite thesis |title=Orthographic Reform and Language Planning in Russian History |url=https://baylor-ir.tdl.org/handle/2104/10914 |date=2020-05-26 |degree=Honors |first=Sylvia |last=Conatser Segura |access-date=29 July 2022 |url-status=live |archive-date=30 July 2022 |archive-url=https://web.archive.org/web/20220730020351/https://baylor-ir.tdl.org/handle/2104/10914}}</ref> Reasons for Peter's switch from the alphanumerical system are believed to go beyond a surface-level desire to imitate the West. Historian Peter Brown makes arguments for sociological, militaristic, and pedagogical reasons for the change. At a broad, societal level, Russian merchants, soldiers, and officials increasingly came into contact with counterparts from the West and became familiar with the communal use of Arabic numerals. Peter also covertly travelled throughout Northern Europe from 1697 to 1698 [[Grand Embassy of Peter the Great|during his Grand Embassy]] and was likely informally exposed to Western mathematics during this time.<ref>{{Cite journal |last=Brown |first=Peter B. |date=2012 |title=Muscovite Arithmetic in Seventeenth-Century Russian Civilization: Is It Not Time to Discard the "Backwardness" Label? |journal=Russian History |volume=39 |issue=4 |pages=393–459 |doi=10.1163/48763316-03904001 |issn=0094-288X |url=https://brill.com/view/journals/ruhi/39/4/article-p393_1.xml |access-date=29 July 2022 |archive-url=https://web.archive.org/web/20220730020352/https://brill.com/view/journals/ruhi/39/4/article-p393_1.xml |archive-date=30 July 2022 |url-status=live}}</ref> The Cyrillic system was found to be inferior for calculating practical [[kinematic]] values, such as the trajectories and parabolic flight patterns of artillery. With its use, it was difficult to keep pace with Arabic numerals in the growing field of [[ballistics]], whereas Western mathematicians such as [[John Napier]] had been publishing on the topic since 1614.<ref>{{Cite journal |last=Lockwood |first=E. H. |date=October 1978 |title=Mathematical discoveries 1600-1750, by P. L. Griffiths. Pp 121. £2·75. 1977. ISBN 0 7223 1006 4 (Stockwell) |journal=The Mathematical Gazette |volume=62 |issue=421 |pages=219 |issn=0025-5572 |url=https://www.cambridge.org/core/journals/mathematical-gazette/article/abs/mathematical-discoveries-16001750-by-p-l-griffiths-pp-121-275-1977-sbn-0-7223-1006-4-stockwell/444F9C9ADA0D2634DDA7C34EF5F08F66 |doi=10.2307/3616704 |jstor=3616704 |access-date=29 July 2022 |archive-date=30 July 2022 |archive-url=https://web.archive.org/web/20220730020352/https://www.cambridge.org/core/journals/mathematical-gazette/article/abs/mathematical-discoveries-16001750-by-p-l-griffiths-pp-121-275-1977-sbn-0-7223-1006-4-stockwell/444F9C9ADA0D2634DDA7C34EF5F08F66 |url-status=live}}</ref>

==== China ====
[[File:Shang_numerals_to_brahmi.jpg|thumb|right|250px|Chinese [[Shang dynasty]] oracle bone numerals of 14th century BC<ref name="Taylor & Francis">{{Cite book |last1=Campbell |first1=Douglas M. |url=https://books.google.com/books?id=PFNsm_IaymYC&dq=shang+numerals+brahmi&pg=PA31 |title=Mathematics: People, Problems, Results |last2=Higgins |first2=John C. |year=1984 |publisher=Taylor & Francis |isbn=978-0-534-02879-4}}</ref><ref name="The Shorter Science p. 6">The Shorter Science & Civilisation in China Vol 2, An abridgement by Colin Ronan of Joseph Needham's original text, Table 20, p. 6, Cambridge University Press {{isbn|0-521-23582-0}}</ref>]] 
The Chinese [[Shang dynasty]] numerals from the 14th century BC predates the Indian Brahmi numerals by over 1000&nbsp;years and shows substantial similarity to the Brahmi numerals. Similar to the modern Arabic numerals, the Shang dynasty numeral system was also decimal based and [[positional notation|positional]].<ref name="Taylor & Francis"/><ref name="The Shorter Science p. 6"/>

While positional Chinese numeral systems such as the [[Counting rods|counting rod system]] and [[Suzhou numerals]] had been in use prior to the introduction of modern Arabic numerals,<ref>{{Cite book |last=Shell-Gellasch |first=Amy |title=Algebra in context : introductory algebra from origins to applications |year=2015 |others=J. B. Thoo |isbn=978-1-4214-1728-8 |location=Baltimore}}</ref><ref>{{Cite journal |last=Uy |first=Frederick L. |date=January 2003 |title=The Chinese Numeration System and Place Value |journal=Teaching Children Mathematics |volume=9 |issue=5 |pages=243–247 |doi=10.5951/tcm.9.5.0243 |issn=1073-5836}}</ref> the externally-developed system was eventually introduced to medieval China by the [[Hui people]]. In the early 17th century, European-style Arabic numerals were introduced by Spanish and Portuguese [[Jesuits]].<ref>{{cite book|editor-first=Helaine |editor-last=Selin|editor-link=Helaine Selin|title=Encyclopaedia of the history of science, technology, and medicine in non-western cultures|url=https://books.google.com/books?id=raKRY3KQspsC&pg=PA198|year=1997|publisher=Springer|isbn=978-0-7923-4066-9|page=198|access-date=18 October 2015|archive-date=27 October 2015|archive-url=https://web.archive.org/web/20151027201326/https://books.google.com/books?id=raKRY3KQspsC&pg=PA198|url-status=live}}</ref><ref>{{cite book|last=Meuleman|first=Johan H.|title=Islam in the era of globalization: Muslim attitudes towards modernity and identity|url=https://books.google.com/books?id=YNArhqy4emwC&pg=PA272|year=2002|publisher=Psychology Press|isbn=978-0-7007-1691-3|page=272|access-date=18 October 2015|archive-date=27 October 2015|archive-url=https://web.archive.org/web/20151027201326/https://books.google.com/books?id=YNArhqy4emwC&pg=PA272|url-status=live}}</ref><ref>{{cite book|author=Peng Yoke Ho|title=Li, Qi and Shu: An Introduction to Science and Civilization in China|url=https://books.google.com/books?id=_P6C4JO4JCUC&pg=PA106|year=2000|publisher=Courier Dover Publications|location=Mineola, NY|isbn=978-0-486-41445-4|page=106|access-date=18 October 2015|archive-date=27 October 2015|archive-url=https://web.archive.org/web/20151027201326/https://books.google.com/books?id=_P6C4JO4JCUC&pg=PA106|url-status=live}}</ref>