TheArabic numerals are tensymbols (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) used for writingnumbers. The term often also implies apositional notation number with adecimal base, in particular when contrasted withRoman numerals. However, the symbols are also used to write numbers in other bases, as well as non-numerical information such as trademarks or license plate identifiers.
They are also calledWestern Arabic numerals,Western digits,European digits,ASCII digits,Latin digits[1] orGhubār numerals to differentiate them from other types of digits.Hindu–Arabic numerals[2] is used due to positional notation. TheOxford English Dictionary uses lowercaseArabic numerals while using the fully capitalized termArabic Numerals forEastern Arabic numerals.[3] In contemporary society, the termsdigits,numbers, andnumerals often implies only these symbols, although it can only be inferred from context.
Europeans first learned of Arabic numerals in about the 10th century, though their spread was a gradual process. After Italian scholarFibonacci ofPisa encountered the numerals in the Algerian city ofBéjaïa, his 13th-century workLiber Abaci became crucial in making them known in Europe. However, their use was largely confined toNorthern Italy until the invention of theprinting press in the 15th century.[4] European trade, books, andcolonialism subsequently helped popularize the adoption of Arabic numerals around the world. The numerals are used worldwide—significantly beyond the contemporaryspread of the Latin alphabet—and have become common in the writing systems where other numeral systems existed previously, such asChinese andJapanese numerals.
Evolution of Indian numerals into Arabic numerals and their adoption in Europe
Positional decimal notation including azero symbol wasdeveloped in many ancient cultures, 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 theEastern Arabic numerals or "Mashriki" numerals:٠, ١, ٢, ٣, ٤, ٥, ٦, ٧, ٨, ٩.[5]
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.[6] The oldest specimens of the written numerals available are from Egypt and date to 873–874 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.[7] The Western Arabic numerals came to be used in theMaghreb andAl-Andalus from the 10th century onward.[8] Some amount of consistency in the Western Arabic numeral forms endured from the 10th century, found in a Latin manuscript ofIsidore of Seville'sEtymologiae from 976 and the Gerbertian abacus, into the 12th and 13th centuries, in early manuscripts of translations from the city ofToledo.[5]
Calculations were originally performed using a dust board (takht, Latin: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 calledḥisāb al-hindī in the east, it was calledḥisāb al-ghubār 'calculation with dust' in the west.[9] The numerals themselves were referred to in the west asashkāl al‐ghubār 'dust figures' orqalam al-ghubār 'dust letters'.[10]Al-Uqlidisi later invented a system of calculations with ink and paper 'without board and erasing' (bi-ghayr takht wa-lā maḥw bal bi-dawāt wa-qirṭās).[11]
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.[12]
Etching published 1503 showing usage of Arabic numerals
The first Arabic numerals in the West appeared in theCodex Albeldensis in Spain.
The first mentions of the numerals from 1 to 9 in the West are found in the 976Codex Vigilanus, anilluminated collection of various historical documents covering a period from antiquity to the 10th century inHispania.[13] Other texts show that numbers from 1 to 9 were occasionally supplemented by a placeholder known assipos, represented as a circle or wheel, reminiscent of the eventual symbol forzero. The Arabic term for zero isṣifr (صفر), transliterated into Latin ascifra, which became the English wordcipher.
From the 980s, Gerbert ofAurillac (laterPope Sylvester II) used his position to spread knowledge of the numerals in Europe. Gerbert studied inBarcelona in his youth. He was known to have requested mathematical treatises concerning theastrolabe fromLupitus of Barcelona after he had returned to France.[13]
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 ofEaster more easily in his textComputus emendatus.[14]
Leonardo Fibonacci was aPisan mathematician who had studied in the Pisan trading colony ofBugia (modern name Béjaïa), in what is nowAlgeria,[15] and he endeavored to promote the numeral system in Europe with his 1202 bookLiber Abaci:
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.
TheLiber 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.[16] Fibonacci's work coincided with the Europeancommercial 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.[16]
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.[16] This may in part have been due to language barriers: although Fibonacci'sLiber 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 theprinting press, and they became widely known during the 15th century. Their use grew steadily in other centers of finance and trade such as Lyon.[17] Early evidence of their use inBritain includes: an equal hour horaryquadrant from 1396,[18] in England, a 1445 inscription on the tower ofHeathfield Church,Sussex; a 1448 inscription on a wooden lych-gate ofBray Church,Berkshire; and a 1487 inscription on the belfry door atPiddletrenthide church,Dorset; and inScotland a 1470 inscription on the tomb of the first Earl of Huntly inElgin Cathedral.[19] In central Europe, theKing of HungaryLadislaus the Posthumous, started the use of Arabic numerals, which appear for the first time in a royal document of 1456.[20]
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.
Prior to the introduction of Arabic numerals,Cyrillic numerals, derived from theCyrillic alphabet andGreek numerals, were used bySouth andEast Slavs. The system was used in Russia as late as the early 18th century, although it was formally replaced in official use byPeter the Great in 1699.[21] 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 1698during his Grand Embassy and was likely informally exposed to Western mathematics during this time.[22] The Cyrillic system was found to be inferior for calculating practicalkinematic 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 ofballistics, whereas Western mathematicians such asJohn Napier had been publishing on the topic since 1614.[23]
The ChineseShang dynasty numerals from the 14th century BC predates the Indian Brahmi numerals by over 1000 years and shows substantial similarity to the Brahmi numerals. Similar to the modern Arabic numerals, the Shang dynasty numeral system was also decimal based andpositional.[24][25]
While positional Chinese numeral systems such as thecounting rod system andSuzhou numerals had been in use prior to the introduction of modern Arabic numerals,[26][27] the externally-developed system was eventually introduced to medieval China by theHui people. In the early 17th century, European-style Arabic numerals were introduced by Spanish and PortugueseJesuits.[28][29][30]
The numerals are encoded in virtually allcharacter sets includingASCII,Unicode (which includes ASCII) and evenMorse code.[31] With ASCII and therefore Unicode,masking all but the four least-significant binary digits gives the value of the decimal digit, a design decision facilitating the digitization of text.EBCDIC uses a different offset, but is designed for a similar masking operation.
^Kunitzsch 2003, p. 7:"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."
^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 (calledḥisāb al-ghubār) was known in the West from the 10th century onward..."
^Ifrah, Georges (1998).The universal history of numbers: from prehistory to the invention of the computer. Translated by Bellos, David. London: Harvill. pp. 356–357.ISBN978-1-860-46324-2.
^Danna, Raffaele; Iori, Martina; Mina, Andrea (22 June 2022). "A Numerical Revolution: The Diffusion of Practical Mathematics and the Growth of Pre-modern European Economies".SSRN4143442.
^abThe Shorter Science & Civilisation in China Vol 2, An abridgement by Colin Ronan of Joseph Needham's original text, Table 20, p. 6, Cambridge University PressISBN0-521-23582-0
^Shell-Gellasch, Amy (2015).Algebra in context : introductory algebra from origins to applications. J. B. Thoo. Baltimore.ISBN978-1-4214-1728-8.{{cite book}}: CS1 maint: location missing publisher (link)
^Uy, Frederick L. (January 2003). "The Chinese Numeration System and Place Value".Teaching Children Mathematics.9 (5):243–247.doi:10.5951/tcm.9.5.0243.ISSN1073-5836.
Burnett, Charles (2006). "The Semantics of Indian Numerals in Arabic, Greek and Latin".Journal of Indian Philosophy.34 (1–2). Springer-Netherlands:15–30.doi:10.1007/s10781-005-8153-z.S2CID170783929.
Hayashi, Takao (1995).The Bakhshālī Manuscript: An Ancient Indian Mathematical Treatise. Groningen, Netherlands: Egbert Forsten.ISBN906980087X.
Ifrah, Georges (2000).A Universal History of Numbers: From Prehistory to Computers. New York: Wiley.ISBN0471393401.
Katz, Victor J., ed. (20 July 2007).The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton, New Jersey: Princeton University Press.ISBN978-0691114859.
