A common claim from the Muslim side is
Let us investigate these claims.
The Arabic numerals are more properly called Hindu-Arabic numerals because they did not originate in Arabia but originated with the Hindus as early as 200 B.C. The system was adopted by the Arabs by about A.D. 800 at the very earliest. They brought it to Spain about 900. It was brought to the rest of Europe about 1100...
Very few Arabs at the time of Mohammad could read or write or know arithmetics. Mohammad himself said we are a nation that does not know how to write or to do arithmetics (nahnu 'omah la takteb wa la tahseb).
It is the Jewish prisoners of war in early Islam that taught the early Muslims how to read and write etc. and in return they received their freedom.
The Arabs used the local tradesmen, architects and scholars of the conquered countries and learned their skills from them. The scientific measure of the Arabs at the time of Mohammad is best reflected in the Hadith and the Qur'an.
After this quick overview let us now be more specific in regard to the above claims:
They arabic symbols for the digits do look different from the Western way of writing them. Just look at the verse numbers in an Arabic Qur'an. The way of writing them (i.e. the symbols themself) are obivously not the same, so they are not "Arabic", therefore I guess the claim refers probably to the way of manipulating them, i.e. the positional number system. (The Greeks and Hebrews had signs for numbers long before the Arabs.) Assuming the positional number system is meant and not the symbols for the digits, I have to sadly pop this illusion as well since even that is not from the Arabs as we will see below in greater detail.
Algebra and Algorithm, I agree. But I am not so sure if you can add "MANY others" to this list as claimed. (But then exaggeration is a very Arabic thing also.)
Would you mind showing us where exactly the Qur'an did bring math to us? I have not found that yet. Please quote exact passages which explain those mathematical concepts you seem to allude to.
The Arabs kept learning from the local scholars until they began to reinterpret the Qur'an. But thank God for a man called Ghazali he squashed the new approach and put Islamic thinking hundred of years back because the new approach contradicted the hadith. If it was not for Imam Ghazali the Muslims not the Americans would have been the technological masters of this planet.
The words Algebra and Algorithm come from the Arabic, no question. But e.g. the word Arithmetics comes from the Greek word Arithmos meaning number. So, there are terms coming from one language and other terms coming from other languages, then what exactly are we to conclude from this? Also ponder this one: The word "computer" is English and that is used all over the world even though the first computers were built by the German engineer Konrad Zuse between 1930 and 1942. But it was the Americans who first built them on a large scale and distributed them, so that the English word became the standard word used for it in many languages.
In a similar way, the Arabs have taken over the work others have done [the Greeks and the Indians] and mainly have disseminated it and the Arabic name for it has stuck.
The positional number system was developed fully by the Hindu Indians in the 4th-6th century and adapted by the Arabs only in the 9-10th century. [Encyclopædia Britannica] Somehow many people still believe it was the Arabs who invented it while they only made it known world wide after they have taken it over from the Hindus. There is even a public inscription using the positional number system in India from the year 576, which shows that by this time it was in public use and not only used by the scholars in their studies. And you know that 576 is before the revelation of the Qur'an.
Let me quote in excerpts from Carl B. Boyer, "History of Mathematics", (a standard reference book):
The first century of the Muslim empire had been devoid of
scientific achievement. This period (from about 650 - 750)
had been, in fact, perhaps the nadir in the development of
mathematics, for the Arabs had not yet achieved intellectual
drive, and concern for learning in the other parts of the
world had pretty much faded. Had it not been for the sudden
cultural awakening in Islam during the second half of the
eighth centrury, considerably more of the ancient science
and mathematics would have been lost. To Baghdad at that
time were called scholars from Syria, Iran, and Mesopotamia,
including Jews and Nestorian Christians; under three great
Abbasid patrons of learning -- al-Mansur, Haroun al-Rashid,
and al-Mamun -- the city became a new Alexandria. During
the reign of the second of these calliphs, ... , part of
Euclid was translated. ...
Mohammed ibn-Musa al-Khwarizmi, ..., who died sometime before 850, wrote more than a half dozen astronomical and mathematical works, of which the earliest were probably based on the Sindhind derived from India. Besides ... [he] wrote two books on arithmetic and algebra which played very important roles in the history of mathematics. ... In this work, based presumably on an Arabic translatoin of Brahmagupta, al-Khwarizmi gave so full an account of the Hindu numerals that he probably is responsible for the widespread but false impression that our system of numeration is Arabic in origin. Al-Khwarizmi made no claim to originality in connection with the system, the Hindu source if which he assumed as a matter of course; ... [pages 227-228]
Through his arithmetic, al-Khwarizmi's name has become a common English word; through the title of his most important book, Al-jabr wa'l muqabalah, he has supplied us with an even more popular household term. From this title has come the word "algebra", for it is from this book that Europe later learned the branch of mathematics bearing this name. Diophantus sometimes is called "the father of algebra", but this title more appropriately belongs to al-Khwarizmi. It is true that in two respects the work of al-Khwarizmi represented a retrogression from that of Diaophantus. First, it is on a far more elementary level than that found in the Diophantine problems and, second, the algebra of al-Khwarizmi is thoroughly retorical, with none of the syncopation found in the Greek Arthmetica or in Brahmagupta's work. Even numbers were written out in words rather than symbols! It is quite unlikely that al-Khwarizmi knew of the work of Diophantus, but he must have been familiar with at least the astronomical and computational portions of Brahmagupta; yet neither al-Khwarizmi nor other Arabic scolars made use of syncopation or of negative numbers ... [page 228]
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