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Arabic-Hindu Numeral System


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Positional decimal numeral systemdeveloped by the 9th century by

Indian mathematicians

Adopted by Persian (Al-Khwarizmi's

circa 825 book On the Calculationwith Hindu Numerals)

Adopted by Arabic mathematicians(Al-Kindi's circa 830 volumes On

the Use ofthe Indian Numerals)

Spread to the western world by theHigh Middle Ages.

The HinduArabic numeral system is a


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BriefHistory

The numeral system

was developed in

ancient India, and

was well established

by the time ofthe

Bakhshali manuscript

(ca. 3d c. CE).


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BriefHistory

Despite its Indian origins itwas initially known in theWest as "Arabic numerals"because ofits introductionto Europe through Arabictexts such as Al-Khwarizmi's "On theCalculation with Hindu

Numerals" (ca. 825), andAl-Kindi's four volumework "On the Use oftheIndian Numerals" (ca. 830)


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Predecessors

The Brahmi numerals are the basis ofthe system. It replaces the earlier Kharosthi numerals indigenous toIndia following the conquests ofAlexander the Great inthe 4th century BC

Brahmi and Kharosthi numerals were used alongsideone another in the Maurya Empire period, bothappearing on the 3rd century BC edicts ofAshoka.

Brahmi numerals are the ancestors ofthe HinduArabicglyphs 1 to 9, but they were not used as a positionalsystem with a zero, and there were rather separatenumerals for each ofthe tens (10, 20, 30, etc.).

The actual numeral system, including positionalnotation and use ofzero, is in principle independent ofthe glyphs used, and significantly younger than theBrahmi numerals.


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Development

The development ofthe positional decimalsystem takes its origins in Indian mathematicsduring the Gupta period.

Around 500 CE the astronomer Aryabhatauses the word kha ("emptiness") to mark"zero" in tabular arrangements ofdigits.

The 7th century Brahmasphuta Siddhantacontains a comparatively advancedunderstanding ofthe mathematical role ofzero


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The Sanskrit translation ofthe lost 5th centuryPrakrit Jaina cosmological text Lokavibhaga

preserve an early instance ofpositional use ofzero.

These Indian developments were taken up inIslamic mathematicsin the 8th century, asrecorded in al-Qifti's Chronologyofthe scholars(early 13th century).

The numeral system came to be known to boththe Persian mathematician Al-Khwarizmi whowrote a book, On the Calculation with Hindu

Numerals in about 825, and the Arabmathematician Al-Kindi, who wrote four volumes,On the Use ofthe Indian Numerals ( ] kitab fi isti'malal-'adad al-hindi])

around 830


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These books are principally responsible for thediffusion ofthe Indian system ofnumeration

throughout the Islamic world and ultimately

also to Europe.

The first dated and undisputed inscriptionshowing the use ofzero at is at Gwalior, dating

to 876 AD.

In 10th century Islamic mathematics, the

system was extended to include fractions, asrecorded in a treatise by Syrian mathematician

Abu'l-Hasan al-Uqlidisi in 952953


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976

In Christian Europe, the first mention and

representation ofHindu-Arabic numerals(from one to nine, without zero), is in the

Codex Vigilanus, an illuminated compilation

ofvarious historical documents from theVisigothic period in Spain, written in the

year 976 by three monks ofthe RiojanmonasteryofSan Martn de Albelda.

In the last few centuries, the European

variety ofArabic numbers was spreadaround the world and gradually became the

most commonly used numeral system in

the world.

1202

Fibonacci, an Italian mathematician whohad studied in Bjaa (Bougie), Algeria,

promoted the Arabic numeral system inEurope with his book "Liber Abaci", which

was published in 1202.

Even in many countries in languages which

have their own numeral systems, theEuropean Arabic numerals are widely used

in commerce and mathematics.

Adoption in

Europe


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Adoption

in East

Asia

Chinese and Japanesefinally adopted the

HinduArabic numerals

in the 19th century,

abandoning counting

rods.

In China, Gautama Siddhaintroduced Indian numerals

with zero in 718, but Chinesemathematicians did not find

them useful, as they hadalready had the decimal

positional counting rods

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