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The numerals used in the Bakhshali manuscript, datedbetween the 2nd century BC and the 2nd century AD.

Brahmi numerals (lower row) in India in the 1st centuryAD

HistoryOrigins

By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimalpositional numeral system. The lack of a positional value (or zero) was indicated by a space betweensexagesimal numerals. By 300 BC, a punctuation symbol (two slanted wedges) was co-opted as aplaceholder in the same Babylonian system. In a tablet unearthed at Kish (dating from about 700 BC),the scribe Bêl-bân-aplu wrote his zeros with three hooks, rather than two slanted wedges.[7]

The Babylonian placeholder was not a true zero because it was not used alone. Nor was it used at theend of a number. Thus numbers like 2 and 120 (2×60), 3 and 180 (3×60), 4 and 240 (4×60) looked thesame because the larger numbers lacked a final sexagesimal placeholder. Only context coulddifferentiate them.

The decimal Hindu-Arabic numeral system was invented in India around AD 500.[8][9] The system wasrevolutionary by including a zero and positional notation. It is considered an important milestone in thedevelopment of mathematics. One may distinguish between this positional system, which is identicalthroughout the family, and the precise glyphs used to write the numerals, which vary regionally. Theglyphs most commonly used in conjunction with the Latin script since early modern times are 0 1 2 3 45 6 7 8 9. The first universally accepted inscription containing the use of the 0 glyph is first recorded inthe 9th century, in an inscription at Gwalior in Central India dated to 870. By this time, the use of theglyph had already reached Persia, and was mentioned in Al-Khwarizmi's descriptions of Indiannumerals. Numerous Indian documents on copper plates exist, with the same symbol for zero in them,dated back as far as the 6th century AD.[10]

The numeral system came to be known toboth the Persian mathematician Al-Khwarizmi, whose book On the Calculationwith Hindu Numerals written about 825 inArabic, and the Arab mathematician Al-Kindi, who wrote four volumes, "On the Useof the Indian Numerals" (Ketab fi Isti'mal al-

'Adad al-Hindi) about 830. Their work wasprincipally responsible for the diffusion of theIndian system of numeration in the MiddleEast and the West.[11] In the 10th century,Middle-Eastern mathematicians extended thedecimal numeral system to include fractions,as recorded in a treatise by Syrianmathematician Abu'l-Hasan al-Uqlidisi in

952–953. The decimal point notation was introduced by Sind ibn Ali, he also wrote the earliest treatiseon Arabic numerals.

A distinctive West Arabic variant of the symbols begins to emerge around the 10th century in theMaghreb and Al-Andalus, called ghubar ("sand-table" or "dust-table") numerals, which are the directancestor of the modern Western Arabic numerals used throughout the world. Ghubar numeralsthemselves are probably of Roman origin.[12]

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Modern-day Arab telephone keypad

with two forms of Arabic numerals:

Western Arabic/European numerals

on the left and Eastern Arabic

numerals on the rightWoodcut showing the 16th century astronomical

clock of Uppsala Cathedral, with two clockfaces,

one with Arabic and one with Roman numerals.

A German manuscript page teaching

use of Arabic numerals (Talhoffer

Thott, 1459). At this time, knowledge

of the numerals was still widely seen

as esoteric, and Talhoffer presents

them with the Hebrew alphabet and

astrology.

Folk etymologies

Some folk etymologies have argued that the original forms of

these symbols indicated their value through the number of angles

they contained, but no evidence exists of any such origin.[13]

Adoption in Europe

In 825 Al-

Khwārizmī

wrote a

treatise in

Arabic, OntheCalculationwith HinduNumerals,

[14]

which

survives only

as the 12th-

century Latin

translation, Algoritmi de numero Indorum.[15][16]

Algoritmi, the

translator's rendition of the author's name, gave rise to the word

algorithm (Latin algorithmus, "calculation method").[17]

The first mentions of the numerals in the West are found in the

Codex Vigilanus of 976.[18]

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.

Leonardo Fibonacci (Leonardo of Pisa), a mathematician born in

the Republic of Pisa who had studied in Béjaïa (Bougie), Algeria,

promoted the Indian numeral system in Europe with his 1202

book Liber 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."

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Late 18th-century French

revolutionary "decimal" clockface.

The numerals are arranged with their lowest value digit to the right, with higher value positions added to

the left. This arrangement was adopted identically into the numerals as used in Europe. Languages

written in the Latin alphabet run from left-to-right, unlike languages written in the Arabic alphabet.

Hence, from the point of view of the reader, numerals in Western texts are written with the highest

power of the base first whereas numerals in Arabic texts are written with the lowest power of the base

first.

The reason the digits are more commonly known as "Arabic

numerals" in Europe and the Americas is that they were

introduced to Europe in the 10th century by Arabic-speakers of

North Africa, who were then using the digits from Libya to

Morocco. Arabs, on the other hand, call the system "Hindu

numerals",[19][20]

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 (٠۰ - ١۱ - ٢۲ - ٣۳ -٧ - ٦ - ٥ - ٤۷

- ٨۸ - ٩۹ ) 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).[8]

The European acceptance of the numerals was accelerated by the

invention of the printing press, and they became widely known

during the 15th century. Early evidence of their use in Britain

includes: an equal hour horary quadrant from 1396,[21]

in England, a 1445 inscription on the tower of

Heathfield Church, Sussex; a 1448 inscription on a wooden lych-gate of Bray Church, Berkshire; and a

1487 inscription on the belfry door at Piddletrenthide church, Dorset; and in Scotland a 1470 inscription

on the tomb of the first Earl of Huntly in Elgin Cathedral. (See G.F. Hill, The Development of ArabicNumerals in Europe for more examples.) In central Europe, the King of Hungary Ladislaus the

Posthumous, started the use of Arabic numerals, which appear for the first time in a royal document of

1456.[22]

By the mid-16th century, they were in common use in most of Europe.[23]

Roman numerals

remained in use mostly for the notation of Anno Domini years, and for numbers on clockfaces.

Sometimes, Roman numerals are still used for enumeration of lists (as an alternative to alphabetical

enumeration), for sequential volumes, to differentiate monarchs or family members with the same first

names, and (in lower case) to number pages in prefatory material in books.

Adoption in Russia

Cyrillic numerals were a numbering system derived from the Cyrillic alphabet, used by South and East

Slavic peoples. The system was used in Russia as late as the early 18th century when Peter the Great

replaced it with Arabic numerals.

Adoption in China

Arabic numerals were introduced to China during the Yuan Dynasty (1271–1368) by the Muslim Hui

people. In the early 17th century, European-style Arabic numerals were introduced by Spanish and

Portuguese Jesuits.[24][25][26]

Evolution of symbols

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Iron plate with an order 6 magic

square in Persian/ Arabic numbers

from China, dating to the Yuan

Dynasty (1271–1368).

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, which may have evolved from the

Brahmi numerals, or developed independently from it. 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 script, in the table below labelled

European, descended from the West Arabic numerals developed in al-Andalus (Andalucía, Spain)

and the Maghreb. Spanish scholars because of the

geographic proximity, trade and constant warfare with the

Muslim kingdoms of Southern Spain saw a potential in the

simplicity of Arabic numbers, and decided to adopt those

symbols, later other Europeans followed and incorporated

them too. (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 script, 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.[27]

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

numerals.

The evolution of the numerals in early Europe is shown on a table created by the French scholar J.E.

Montucla in his Histoire de la Mathematique, which was published in 1757: