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I will omit all discussion of the science of the Indians, ... , of their subtle discoveries in astronomy, discoveries that are more ingenious than those of the Greeks and the Babylonians, and of their valuable methods of calculation which surpass description. I wish only to say that this computation is done by means of nine signs. If those who believe, because they speak Greek, that they have arrived at the limits of science, would read the Indian texts, they would be convinced, even if a little late in the day, that there are others who know something of value.

In his authoritative work The Arithmetic of Al-Uqlîdisî (Dordrecht: D. Reidel, 1978), A.S. Saidan's studies were unable to answer in full how the numerals reached the Arab world:

It seems plausible that it drifted gradually, probably before the seventh century, through two channels, one starting from Sind, undergoing Persian filtration and spreading in what is now known as the Middle East, and the other starting from the coasts of the Indian Ocean and extending to the southern coasts of the Mediterranean.

He notes, however, that Al-Uqlidisi's work, Kitâb al-FusÞl fî al-Hisâb al-Hindî, "the earliest extant Arabic work of Hindu-Arabic arithmetic", written in Damascus in AD 952–953, showed “this system at its earliest stages and the first steps in its development.” (ibid, p. xi.), especially so that "The manuscript claimed to have a collection of all past knowledge on arithmetic" and "a clear exposition of what was currently known about the subject". Saidan also writes:

Whatever the case may be, it should be pointed out that Arabic works give no reference whatsoever to any Sanskrit text or Hindu arithmetician, nor do they quote any Sanskrit term or statement.

This is in line with what Professor Lam Lay Yon, member of the International Academy of the History of Science, points out in her 1996 paper titled "The Development of Hindu-Arabic and Traditional Chinese Arithmetic":

There are no descriptions of the Hindu-Arabic numeral system and the fundamental operations of arithmetic among the early Hindu treatises. With the exception of the Bakhshali Manuscript, whose date is controversial (could be as late as the 12th century), the treatises do not use the Hindu-Arabic numerals to represent numbers. Rather, numbers are generally written in Sanskrit in a terse stanza form. The Aryabhatiya, written by Aryabhata (b. 476 AD), contains a description of an alphabetic notation for numerals.(Kripa S. Shukla (ed.), Aryabhatiya of Aryabhata (New Delhi: Indian National Science Academy, 1976), pp. 3–5; S. N. Sen, “Aryabhata’s Mathematics,” Bulletin of the National Institute of Sciences of India no. 21 (1962), pp. 298–305.)

Until Al-Uglidisi's work, the Indian numerals and arithmetics required the use of a sand board, which was an obstacle to their use in official manuscripts. As-Suli in the first half of the tenth Century:

Official scribes nevertheless avoid using because it requires equipment and they consider that a system that requires nothing but the members of the body is more secure and more fitting to the dignity of a leader.

In his work cited above, Al-Uglidisi showed required modification to the numerals and arithmetics to make them suitable for use by pen and paper, which was a major improvement.

Al-Uqlidisi book was also the earliest known text to offer treatment of decimal fraction.

The numerals though were already in wide use throughout the Arab empire, as Avicenna who was born in 980 tells in his autobiography that he learnt them, as a child, from a humble vegetable seller. He also tells that when his father, in Bukhara, was visited by scholars from Egypt in 997, including Abu Abdullah al-Natili, they taught him more about them. J J O'Connor and E F Robertson point out:

He also tells of being taught Indian calculation and algebra by a seller of vegetables. All this shows that by the beginning of the eleventh century calculation with the Indian symbols was fairly widespread and, quite significantly, was known to a vegetable trader.

Of prime importance in the Hindu-Arabic Numeral system is the use of 0 (zero). There are two different concepts here, the first is the use of zero as a place holder (a mathematical punctuation mark), and then as a number.

It should not be assumed that 0 was the invention of the Hindu-Arabic numeral system however, since the Babylonians were in fact the first known to use it. The 0 is thought by some to have come from O, which is omicron, the first letter in the Greek word for nothing, namely "ouden". An alternative theory is that it stood for "obol", a coin of almost no value, and that it arose when counters were used on sand board, so that a removed coin would leave a depression in the sand that looked like an O. Ptolemy, writing in 130 AD in his work the Almagest, used the Babylonian system with the empty place holder O.

The first written record of the Indian use of zero (denoted by a dot) is dated to the 5th-3rd century BC in the Chhandah-shastra written by Indian mathematician Pingala as part of his binary number system. There were also other Indian texts dated between the 6th-3rd century BC that used the Sanskrit word Shunya to refer to zero, which suggests that such a symbol was in existence by 500 BC. The first documented evidence of the use of zero for mathematical purposes is presented in the Bakhshali manuscript written by Indian Jaina mathematicians between the 2nd century BC and 2nd century CE but most agree on it being written in the 2nd century CE. At around 500 however, the Indian mathematician Aryabhata devised a number system which apparently had no zero yet was a positional notation numeral system (there are some historians who contest this view however). The first documented use of zero in a positional notation numeral system is presented in the Brahma-sphuta-siddhanta written by Brahmagupta in 628. Many scholars believe its use in India evolved from the Mesopotamian use of zero as a placeholder.

The numerals came to fame due to their use in the pivotal work of the Arab mathematician Al-Khwarizmi, whose book On the Calculation with Hindu Numerals was written about 825, and the Arab mathematician Al-Kindi, who wrote four volumes (see ) "On the Use of the Indian Numerals" (Ketab fi Isti'mal al-'Adad al-Hindi) about 830. They, amongst other works, contributed to the diffusion of the Indian system of numeration in the Middle-East and the West.

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 published in 1202. The system did not come into wide use in Europe, however, until the invention of printing (See, for example, the 1482 Ptolemaeus map of the world printed by Lienhart Holle in Ulm, and other examples in the Gutenberg Museum in Mainz, Germany.)

In the last few centuries, the European variety of Arabic numbers was spread around the world and gradually became the most commonly used numeral system in the world. Even in many countries in languages which have their own numeral systems, the European Arabic numerals are widely used in commerce and mathematics.

Symbols

The Arabic numeral system has used many different sets of symbols. These symbol sets can be divided into two main families — namely the West Arabic numerals, and the East Arabic numerals. East Arabic numerals — which were developed primarily in what is now Iraq — are shown in the table below as Arabic-Indic. East Arabic-Indic is a variety of East Arabic numerals. West Arabic numerals — which were developed in al-Andalus and the Maghreb —are shown in the table, labelled European. (There are two typographic styles for rendering European numerals, known as lining figures and text figures).

Table of numerals

It is interesting to note that, like many numbering systems, the numbers 1, 2, and 3 represent simple tally marks. 1 being a single line, 2 being two lines (now connected by a diagonal) and 3 being three lines (now connected by two vertical lines). After three, numbers tend to become more complex symbols (examples are the Chinese numbers and Roman numerals). Theorists believe that this is because it becomes difficult to instantaneously count objects past three.

External links

• Unicode reference charts:
  • Arabic (See codes U+0660-U+0669, U+06F0-U+06F9)
  • Devanagari (See codes U+0966-U+096F)
• Charles Seife (2000). Zero: The Biography of a Dangerous Idea (paperback ed.). Crown Publishing. ISBN 0140296476.

• History of the Numerals
  • "The Development of Hindu-Arabic and Traditional Chinese Arithmetic" by Professor Lam Lay Yon, member of the International Academy of the History of Science
  • Indian numerals:
  • Arabic numerals:
  • Hindu-Arabic numerals:

• Numerals page at http://St-Takla.org
• http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Arabic_numerals.html - The Arabic numeral system by: J J O'Connor and E F Robertson