Arabic numerals, known formally as Hindu-Arabic numerals, and also known as Indian numerals, Hindu numerals, European numerals, and Western numerals, are the most common symbolic representation of numbers around the world. They are considered an important milestone in the development of mathematics.

One may distinguish between the decimal system involved, also known as the Hindu-Arabic numeral system, and the precise glyphs used. 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.

The numerals arose in India between 400 BCE and 400 CE.Ifrah, Georges. 1999. The Universal History of Numbers

From Prehistory to the Invention of the Computer, Wiley. ISBN 0-471-37568-3.O'Connor, J.J. and E.F. Robertson. 2000. 'Indian Numerals', MacTutor History of Mathematics Archive, School of Mathematics and Statistics, University of St. Andrews, Scotland. They were transmitted first to West Asia, where they find mention in the 9th century CE, and eventually to Europe in the 10th century CE. Since knowledge of the numerals reached Europe through the work of Arab mathematicians and astronomers, the numerals came to be called "Arabic numerals."In Arabic language itself, the Eastern Arabic numerals are called "Indian numerals," أرقام هندية, (arqam hindiyyah) and a different set of symbols are used as numerals.

The symbols for 1 to 9 in the Hindu-Arabic numeral system evolved from the Brahmi numerals. Buddhist inscriptions from around 300 BC 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.

Use of the 0 glyph is first recorded in the 9th century, in an inscription at Gwalior dated to 870, and in the work of Al-Khwarizmi.




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, 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, are 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.

In the Arab World—until modern times—the Arabic numeral system was used only by mathematicians. Muslim scientists used the Babylonian numeral system, and merchants used the Abjad numerals. Therefore, it was not until Fibonacci that the Arabic numeral system was used by a large population.

A distinctive "West Arabic" variant of the symbols begins to emerge in ca. the 10th century in the Maghreb and Al-Andalus, called the ghubar ("sand-table" or "dust-table") numerals.

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 Silvester II) began to spread knowledge of the numerals in Europe. Gerbert studied in Barcelona in his youth, and he is known to have requested mathematical treatises concerning the astrolabe from Lupitus of Barcelona after he had returned to France.

Al-Khwarizmi, the Persian scientist, wrote in his 825 treatise On the Calculation with Hindu Numerals was translated into Latin in the 12th century, as Algoritmi de numero Indorum (Algoritmi being the translator's rendition of the author's name, , ultimately leading to the term algorithm).

Fibonacci, an Italian mathematician who had studied in Bejaia (Bougie), Algeria, promoted the Arabic numeral system in Europe with his book Liber Abaci, which was written in 1202, still describing the numerals as "Indian" rather than "Arabic".

"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.."