Hindu-Arabic numerals are ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). They are descended from the Hindu-Arabic numeral system developed by Indian mathematicians, in which a sequence of numerals such as "975" is read as a whole number. The Indian numerals were adopted by the Persian mathematicians in India, and passed on to the Arabs further west. They were transmitted to Europe in the Middle Ages. The use of Arabic numerals spread around the world through European trade, books and colonialism. Today they are the most common symbolic representation of numbers in the world.

As befitting their history, the digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) are also known as Hindu numerals or "Hindu-Arabic numerals". The reason they are more commonly known as "Arabic numerals" in Europe and the Americas is that they were introduced to Europe in the 10th century by Arabs of North Africa, who were then using the digits from Libya to Morocco.

Europeans did not know about the numerals' origins in ancient India, so they named them "Arabic numerals". Arabs, on the other hand, call the system "Hindu numerals", referring to their origin in India. This is not to be confused with what the Arabs call the "Hindi numerals", namely the Eastern Arabic numerals ( . . . . . . . . .٠ ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩) used in the Middle East, or any of the numerals currently used in Indian languages (e.g. Devanagari: ०.१.२.३.४.५.६.७.८.९).

In English, the term Arabic numerals can be ambiguous. It most commonly refers to the numeral system widely used in Europe and the Americas. Arabic numerals is the conventional name for the entire family of related systems of Arabic and Indian numerals. It may also be intended to mean the numerals used by Arabs, in which case it generally refers to the Eastern Arabic numerals.

The decimal Hindu-Arabic numeral system was invented in India around 500 CE. The system was revolutionary in that it included a zero and positional notation. It is considered an important milestone in the development of mathematics. One may distinguish between this positional system, which is identical throughout the family, and the precise glyphs used to write the numerals, which vary regionally. The glyphs most commonly used in conjunction with the Latin alphabet since early modern times are 0 1 2 3 4 5 6 7 8 9.

Although the phrase "Arabic numeral" is frequently capitalized, it is sometimes written in lower case: for instance, in its entry in the Oxford English dictionary. This helps distinguish it from "Arabic numerals" as the East Arabic numerals specific to the Arabs.

The digits 1 to 9 in the Hindu-Arabic numeral system evolved from the Brahmi numerals. Buddhist inscriptions from around 300 BCE use the symbols which became 1, 4 and 6. One century later, their use of the symbols which became 2, 7 and 9 was recorded.

The first universally accepted inscription containing the use of the 0 glyph is first recorded in the 9th century, in an inscription at Gwalior in Central India dated to 870. By this time, the use of the glyph had already reached Persia, and was mentioned in Al-Khwarizmi's descriptions of Indian numerals. Numerous Indian documents on copper plates exist, with the same symbol for zero in them, dated back as far as the 6th century CE.[10]

The numerals used in the Bakhshali manuscript, dated between the 2nd century BCE and the 2nd century CE.

Brahmi numerals (lower row) in India in the 1st century CE 

 Modern-day Arab telephone keypad

with two forms of Hindu-Arabic numerals: Western Arabic/European numerals on the left and Eastern Arabic numerals on the right

The numeral system came to be known to both the Persian mathematician Al-Khwarizmi, whose book On the Calculation with Hindu Numerals written about 825 in Arabic, and the Arab mathematician Al-Kindi, who wrote four volumes, "On the Use of the Indian Numerals" (Ketab fi Isti'mal al-'Adad al-Hindi) about 830. Their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West In the 10th century, Middle-Eastern mathematicians extended the decimal numeral system to include fractions, as recorded in a treatise by Syrian mathematician Abu'l-Hasan al-Uqlidisi in 952–953. The decimal point notation was introduced by Sind ibn Ali he also wrote the earliest treatise on Arabic numerals.

A distinctive West Arabic variant of the symbols begins to emerge around the 10th century in the Maghreb and Al-Andalus, called ghubar ("sand-table" or "dust-table") numerals, which are the direct ancestor of the modern Western Arabic numerals used throughout the world.

The first mentions of the numerals in the West are found in the Codex Vigilanus of 976. 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.

The numeral system employed, known as algorism, is positional decimal notation. Various symbol sets are used to represent numbers in the Hindu-Arabic numeral system, all of which evolved from the Brahmi numerals. The symbols used to represent the system have split into various typographical variants since the Middle Ages:

The widespread Western Arabic numerals used with the Latin alphabet, in the table below labelled European, descended from the West Arabic numerals developed in al-Andalus and the Maghreb. (There are two typographic styles for rendering European numerals, known as lining figures and text figures).

The Arabic-Indic or Eastern Arabic numerals used with the Arabic alphabet developed primarily in what is now Iraq. A variant of the Eastern Arabic numerals used in the Persian and Urdu languages is shown as East Arabic-Indic. There is substantial variation in usage of glyphs for the Eastern Arabic-Indic digits, especially for the digits four, five, six, and seven.

The Devanagari numerals used with Devanagari and related variants are grouped as Indian numerals.

References (6 books/articles) G Ifrah, A universal history of numbers : From

prehistory to the invention of the computer (London, 1998).

G G Joseph, The crest of the peacock (London, 1991). R Kaplan, The nothing that is : a natural history of zero

(London, 1999). L C Karpinski, The history of arithmetic (New York,

1965). K W Menninger, Number words and number symbols :

A cultural history of numbers (Boston, 1969). D E Smith and L C Karpinski, The Hindu-Arabic

numerals (Boston, 1911).  

Other Web sites: Astroseti (A Spanish translation of this article) Islamic City

Main Web site http://www-history.mcs.st-andrews.ac.uk/HistTopics/

References/Arabic_numerals.html

Talha ÇÖGEN & Hakan ÇOLAKTalha ÇÖGEN & Hakan ÇOLAK