What caused Arabic Numerals to be accepted world wide, but alphabets developed such a wide variety?

by Ehhhhhhhhhh
Jooseman

I can't really answer why compared to alphabets, but I can explain a little how they started to spread around. It's just a continuation of how throughout history, mathematics has spread between Mesopotamia and the Middle East, India, China and later on Europe, due to trade.

Well first, they are Hindu numerals, Arabia was just the first place they spread to on there way. The oldest definite reference outside of India came from Syrian scholar and bishop Severus Sebokht, in 662. Later on it was al-Fazārīs translation of the Sindhind into Arabic which quite possibly began to get the Islamic scientific world acquainted with Hindu Numerals. While this system began to be used all throughout the Arab World, many others were used concurrently, such as the Greek system, or other native systems.

Introduction into Europe

While the adoption of Hindu-Arabic Numerals into Europe was slow, the earliest French manuscript they are found in dates from 1275 for example, Europe seemed an obvious place for Hindu-Arabic Numerals to spread to, however this wasn't without opposition.

Anyway, the first spread of Hindu-Arabic numerals had trickled into Spain. In the 8th Century, the Umayyad Caliphate had started there conquest of Spain, and this meant that as Hindu Numerals spread across the Arab World, it also meant they traveled along into Spain, where they were introduced by the Arabs around 900. The oldest dated manuscript which contains the numerals produced in Europe, the Codex Vigilanus (a compilation of various historical documents accounting for a period extending from antiquity to the 10th century in Hispania), was first produced in Spain in in 881, but was updated up to 976, and it was in the 976 version which contains the first use of Hindu-Arabic numerals in Europe.

At the same time however, these numerals were being spread in other ways, through trade and movement between Europe, and Islamic Spain and the Levant. While this had been going on for some centuries before him, it was a later mathematician, Leonardo of Pisa (also known as Fibonacci) who had traveled the Arabic world as a merchant with his father, who directed a trading post in Bugia in modern day Algeria, it was here that he learned about that he learned about the Hindu–Arabic numeral system.

Recognising that this was easier to do mathematics with than Roman Numerals, Fibonacci traveled, studying under leading Arab Mathematicians. After returning from these travels he wrote what he had learned in Liber Abaci (1202) and did similar for Geometry and trigonometry in Practica Geometriae (1220).

While these were helping it spread into Europe, remember, adoption was very slow, and what little adoption there was, was met with opposition from the public, as they made merchant books difficult to read. This got to the point that in the statutes if the Arte del Cambio of 1299 and even later the money changers if Florence were forbidden from using Arabic Numerals and made to use Roman ones.

During the 14th century however you do begin to see some adoption of Hindu-Arabic numerals by Italian merchants, including some intermediate forms, such as II III XV for 2315.

This would then explain there spread into other parts of the world then colonised by Europe, such as the Americas etc.

Introduction into Japan

Prior to the widespread use of Hindu-Arabic numerals, they did most calculation, in the Chinese style, with an abacus, rather than on paper. They did have knowledge of some underlying concepts of algebra, with notations for unknown variables and ways of representing zeros, but they were more interested in discovering algorithms that had practical application on the abacus than they were in a general theory of mathematics. (Though incidentally there was a popular amateur mathematics scene, and those who came up with useful or interesting mathematical ideas would write them on votive tablets, called sangaku and hang them in shrines or temples to share there discoveries with others)

While the shogun kicked out all of the Europeans except the Dutch in the 1630s, before this there had been there had also been contact and trade with the Portuguese, Spanish, and English, which brought limited contact with Hindu-Arabic numerals. Later on, in the late 1700s / early 1800s, much more books on European Mathematics started to be imported into Japan, both from the Dutch, and from China. While it didn't spread much within the local population, especially those in more rural areas, it did give the Japanese access to functions for calculus that that Japanese mathematics lacked, and was the primary interest of study due to the military applications of it.

In 1855, soon after Japan had once again been opened up to the rest of the world, the Tokugawa Shogunate set up a naval academy in Nagasaki that taught Western mathematics, using the knowledge gained from those who had studied these earlier books.

Eventually they became much more widespread with the Meiji government's Education Order of 1872, which mandated that only Western mathematics should be taught in the newly compulsory school system. They did this because of Western dominance in science and technology fields around the world and the Meiji development campaign demanded a technologically literate populace.

Introduction into China

As I have mentioned above, China has always been included in the spread of developments between the Middle East, Europe and India, albeit slowly, through trade, conquest etc

So while Hindu-Arabic numerals had been introduced numerous times by Indian and Arabic mathematicians into China, they never found much popular use until much later on in History, using counting rods instead.

China has, through much of history, had an interest in astronomy, which lead to many of there developments in mathematics. There had always been a spread with the Arabic astronomy, even more so under the Mongol empire. They ended up establishing a Bureau of Western Astronomy in order to study Astronomy discovered by Muslims, this was alongside the bureau for Chinese Astronomy. Muslims were also being employed in and heading observatories, and with it would have brought there numerals.

There is early evidence of this Arabic spread of numerals into China, when in 1956, 5 magic squares of the 6th order from around the 13th-14th Centuries were found in China, written in Medieval Arabic numerals.

In the 16th Century, when they started there missions in China, Jesuit priests brought Western astronomy into China and with it more books, clocks, maps and knowledge of Hindu-Arabic numerals used in calculations.

Only in the 19th Century, as with Japan, did China adopt Hindu-Arabic numerals, especially in mathematics, though it still uses it's own Numeral Systems as well (2 have popularity, Chinese characters that correspond to numerals in the spoken language, and Suzhou numerals, or huama, a positional system, the only surviving form of the rod numerals) which shows that there is a wider variety of numerals still in use as well.

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