Numbers, origin of numerals

Roman numerals didn't support arithmetic as they were simply abbreviations for physical amounts. In fact business people in ancient Rome would use calculators whenever they needed work with Roman numerals. The calculator back then was the abacus.
To read about alphabet history, click here.

So while the Roman Empire came to dominate the world, their system of numbers was in reality not as good as what was to replace it.

Roman Numerals were superceded by the Arabic Numerals we use today. And how did the new signs, symbols emerged?


0. VI-IX centuries:
knowledge of the Indian number system was known in lands soon to become part of the Arab world as early as the seventh century.  
Severus Sebokht as a Christian bishop of Nisibis in Mesopotamia would have been interested in calculating the date of Easter (a problem to Christian churches for many hundreds of years). This may have encouraged him to find out about the astronomy works of the Indians and in these, of course, he would find the arithmetic of the nine symbols. As he speaks in a manuscript (662) of “this computation is done by means of nine signs,” the zero seems to have been unknown to him.

By 776 AD the Arab empire was beginning to take shape and we have another reference to the transmission of Indian numerals. We quote from a work of al-Qifti Chronology of the scholars written around the end the 12th century but quoting much earlier sources:-

... a person from India presented himself before the Caliph al-Mansur in the year [ 776 AD] who was well versed in the siddhanta method of calculation related to the movment of the heavenly bodies, and having ways of calculating equations based on the half-chord [essentially the sine] calculated in half-degrees ... This is all contained in a work ... from which he claimed to have taken the half-chord calculated for one minute. Al-Mansur ordered this book to be translated into Arabic, and a work to be written, based on the translation, to give the Arabs a solid base for calculating the movements of the planets ...

Now in his work (The Universal History of Numbers) Ifrah tries to determine which Indian work is referred to. He concludes that the work was most likely to have been Brahmagupta's Brahmasphutasiddhanta (The Opening of the Universe) which was written in 628. Irrespective of whether Ifrah is right, since all Indian texts after Aryabhata I's Aryabhatiya used the Indian number system of the nine signs, certainly from this time the Arabs had a translation into Arabic of a text written in the Indian number system. 


01.  What of the current numerals themselves ? (click on link)
We have seen in the article Indian numerals that the form of the numerals themselves varied in different regions and changed over time. Exactly the same happened in the Arabic world.

Here is an example of an early form of Indian numerals being used in the eastern part of the Arabic empire. It comes from a work of al-Sijzi, not an original work by him but rather the work of another mathematician which al-Sijzi copied at Shiraz and dated his copy 969.

The numerals from al-Sizji's treatise of 969

The numerals had changed their form somewhat 100 years later when this copy of one of al-Biruni's astronomical texts was made. Here are the numerals as they appear in a 1082 copy.

The numerals from al-Biruni's treatise copied in 1082

In fact a closer look will show that between 969 and 1082 the biggest change in the numerals was the fact that the 2 and the 3 have been rotated through 90°. There is a reason for this change which came about due to the way that scribes wrote

1. On the road to Europe, Did it enter thru Sicily, Italy? thru the Pyrenees?

The first Arabic numerals in Europe appeared in the Codex Vigilanus written in the Riojan St Martin's Albelda Cloister in the year 976.



we can learn about our numbers.


The origin of hindi and arabic numerals
The word "Shunya" for zero was translated into Arabic as "صفر" "sifr", meaning 'nothing, empty' which became the term "zero" in many European languages from Medieval Latin, zephirum (in Catalan it became 'xifra', English, cipher).

En realidad los números que conocemos en la actualidad son una evolución y estrictamente, tal vez este mal llamarlos arábigos ya que son una versión latina de lo que originalmente eran los números hindú arábigos. Los ideogramas (glifoa) usados en la actualizadad para representar los números fueron creados por Abu Ja’far Muhammad ibn Musa al-Khwarizmi (c.778 – c.850). Al-Khwarizmi nacio en Asia Central, actualmente Uzbekistan, donde desarrollo el actual sistema decimal manuscrito, basado en las notaciones para el ábaco.

2. From 9 to 10 figures.

Abacus and Hindu-Arabic numerals (wikipedia)

Reconstructed Ancient RomanAbacus.

Gerbert learned of Hindu-Arabic digits and applied this knowledge to the abacus, but according to Charles Seife without the numeral of zero.^[8] According to William of Malmesbury (c. 1080–c. 1143), Gerbert got the idea of the computing device of the abacus from a Spanish Arab. The abacus that Gerbert reintroduced into Europe had its length divided into 27 parts with 9 number symbols (this would exclude zero, which was represented by an empty column) and 1,000 characters in all, crafted out of animal horn by a shieldmaker of Rheims.^[4][9][10] According to his pupil Richer, Gerbert could perform speedy calculations with his abacus that were extremely difficult for people in his day to think through in using only Roman numerals.^[4] Due to Gerbert's reintroduction, the abacus became widely used in Europe once again during the 11th century.<sup>[10]




To read about the topic, please click on Development of shapes of the numbers, glyphs, (our other post).</sup>

A history of mathematical notations, byFlorian Caiori:

"The forms varied considerably. the number five was the most freakish. An upright 7 was rare in the earlier centuries.

3. But in the north of Spain we have the figure of Gerbert:


Gerbert compiled a list of rules for computing with his abacus, Regula de Abaco Computi, in which he painstakingly explained how to multiply and divide, as well as add and subtract, in the new system.  A companion work, Liber Abaci, by his student Bernelin, is often included in the collected works of Gerbert;


It predates the book of the same name by Leonardo of Pisa (ca. 1180-1250), a.k.a. Fibonacci, by two hundred years. During the 1100's the "Arabic" numerals were a topic of great interest among European scholars, and several translations of the Algebra appeared. In 1202, he published a famous book Liber abaci explaining and popularizing the Hindu-Arabic system, the use of the zero, the horizontal fraction bar, and the various algorithms of the Algebra. Leonardo (better known today by his patronymic Fibonacci, "son of Bonaccio.")

writes in his famous book Liber abaci published in Pisa in 1202:-

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, for whatever was studied by the art in Egypt, Syria, Greece, Sicily and Provence, in all its various forms.

4. The road towards recognition: Genoa-Pisa-Normans-Papacy

The Holy Roman emperor was Frederick II. He had been crowned king of Germany in 1212 and then crowned Holy Roman emperor by the Pope in St Peter's Church in Rome in November 1220. Frederick II supported Pisa in its conflicts with Genoa at sea and with Lucca and Florence on land, and he spent the years up to 1227 consolidating his power in Italy. State control was introduced on trade and manufacture, and civil servants to oversee this monopoly were trained at the University of Naples which Frederick founded for this purpose in 1224.

Scholars at his court had corresponded with Fibonacci since his return to Pisa around 1200. These scholars included Michael Scotus who was the court astrologer, Theodorus Physicus the court philosopher and Dominicus Hispanus who suggested to Frederick that he meet Fibonacci when Frederick's court met in Pisa around 1225.

Johannes of Palermo, another member of Frederick II's court, presented a number of problems as challenges to the great mathematician Fibonacci. Three of these problems were solved by Fibonacci and he gives solutions in Flos which he sent to Frederick II. Liber abaci, published in 1202 after Fibonacci's return to Italy, was dedicated to Scotus.

5. The Jews connection
Why do we Europeans use the 'O' figure instead of the dot of the Arabic language (Arabs use the "." = the number 5)?

The connexion seems to stem from the Jews.

Ibn Ezra, in the 12^th century, wrote three treatises on numbers which helped to bring the Indian symbols and ideas of decimal fractions to the attention of some of the learned people in Europe. The Book of the Number describes the decimal system for integers with place values from left to right. In this work ibn Ezra uses zero which he calls galgal (meaning wheel or circle).

In Ibn Ezra’s translation of al-Bīrūnī’s Ta’amē lūhōt al-Chowārezmī(“Commentary on the Tables of al-Khwārizmī”; the Arabic original is lost) there is interesting information on the introduction of Indian mathematics and astronomy into Arabic Science during the eighth century.

Ibn Ezra wrote a number of astrological works ... translated into French in 1213 by Hagin, a Jew in the employ of Henry Bate at Malines (Mechelen), who in turn translated the French into Latin. Both the French and the Catalan translations are of great philological interest.

Epilogue. The book origin of the arabic numerals.net



hispanic connections by R. Lemay