User talk:Nepaheshgar/Al-Khwarizmi the Mathematician

In the Western World, a Muslim and Arab became synonymous thus confusion has risen amongst some non-specialized sources. This is starting to change, but at one point in the history of Western scholarship, the term Muslim and Arab were used interchangeably, although more 80% of Muslims today are not of Arab origin. Some of these scholars like Al-Khwarizmi, Rhazes wrote their works in Arabic only while others like Biruni and Avicenna wrote in both Persian and Arabic. I would note that there is a difference between scientific writing and say cultural writing: poetry. Poetry and language/culture are tied together and thus regardless of a background, a poet belong to the language/culture where his masterpiece was created. This is the case with say Pushkin, an important Russian poet and writer. But a scientific language is different than a cultural language. For example Latin was used by both Newton and Leibnitz, but they are not called Latin scholars. Of course the situation in the Muslim world at times might be more confusing and then the title Muslim scholar suffices. On the other hand, many times, it was not so.

This page is written for the purpose of clarifying the background of Muhammad Ibn Musa Al-Khwarizmi (about 780-850 A.D.). There is a special field of Mathematics called History of Mathematics. Within that field, there are a few Professors who specialize in the period of Islamic Mathematics. These professors have an excellent background on both the culture/history of the given time period as well as the Mathematics involved (which is now fairly thought in the High School level although the CRT (Chinese Remainder Theorem)(and many others) despite their antiquity are mainly college level materials).

Modern Opinion and Ibn Khaldun

Professor Oaks

An important article on Khwarizmi was recently written by Professor. Oaks. I have went through the modern sources recently, and amongst these modern sources, this well researched source by a Professor of Mathematical History specializing in the history of Mathematics in the Islamic era is noteworthy: [[3]] He also has an extensive website on the history of Islamic Mathematics [4]. Although the term Islamic Mathematics is not a term I like (just like I do not like Chinese or Indian or Western Mathematics, since Mathematics is valid irregardless of such appelatation).

Professor J. Oaks writes:

“ In a well-planned and broadly supported movement, the Ummayads were overthrown in 750 by a new dynasty, the ‘Abbasids. A key source of ‘Abbasid support lay in Khurasan, a region in northeastern Persia. Broad support existed in other regions as well, but this revolt can be seen largely as a re-assertion of Persian national identity, against the pro-Arab Ummayads. In fact, it can be said that Persian culture reemerged in full force, in

Islamic garb, under the ‘Abbasids. Al-Khwarizmi himself was of Persian stock, his ancestors coming from Khwarezm, in distant Transoxania. The Banu Musa, al-Mahani, and a host of others in the intellectual circle of ninth century Baghdad, were also Persians. Iran was the heartland of the toppled Sasanian monarchy, and it was Sasanian imperial ideology, based on Zoroastrian myth, which appealed to the second ‘Abbasid caliph al-Mansur (reigned 754-775). The caliph needed support from the Iranian nobility, mostly still Zoroastrian, so his appropriation of this Persian system was certainly a political move. The important aspect of it which interests us here is the tradition of translation.

”

(http://facstaff.uindy.edu/~oaks/MHMC.htm, Access Date March 2, 2008)

I also wrote to Professor Oaks that in Wikipedia at that time there was a debate on the issue. He wrote back:

“ Dear Ali,

I was quite surprised to see my article on al-Khwarizmi mentioned so often in the discussion section of the Wicopedia article on al-Khwarizmi! I'm writing to you now to help in two directons: (1) to give you an account of my background and more recent work, and (2) to steer you and others toward reliable sources on Islamic/Arabic mathematics.

(1) I began studying medieval mathematics in 1999, having studied Roman history for many years before. It is true that my article "Was al-Khwarizmi an applied algebraist?" relied heavily on secondary sources, but I can tell you, after several years of deep immersion in the field, that they are reliable sources. At the time I was just beginning to read Arabic---I have the good luck to have Haitham Alkhateeb, a native Arabic speaker, as a colleague. I continue to pester him with questions, though less and less as the years pass. Now I am finishing up writing my 3rd, 4th, and 5th articles on Arabic algebra. See my web page for a description of the first two:

http://facstaff.uindy.edu/~oaks/Oaks.htm

I can send you pdf versions if you like.

(2) For good sources on various aspects of medieval Islamic mathematics, see my online bibliography:

http://facstaff.uindy.edu/~oaks/Biblio/Intro.htm

Over 2,500 books and articles are arranged by topic. Many books & articles are for the general public, which I label "Introductory". Let me know if you want any guidance here.

Regarding the ethnicity of al-Khwarizmi: he was a Persian who wrote in Arabic and who worked in Baghdad. Most scholars in Baghdad at the time were Persians, and many were still Zoroastrian (though al-Kh was apparently a Muslim). This is not to slight the Arabs: the great (perhaps greatest?) Islamic philosopher, al-Kindi, was an Arab. The predominance of Persians in intellectual fields was due to cultural trends. Persia had an old tradition of learning, which had been supported by the vast Sasanian state and earlier Persian dynasties. The Arabs, up to the time of the prophet, had been traders and herdsmen, with little motive to study science (though they had a rich tradition of folk poetry). But of course, once the Muslims had conquered the Persian empire, things changed. As the decades passed, the Persian element faded. By, say, the 12th c., a scholar in the Muslim world could have just about any ethnic or cultural background.

I must add that it is a pity that just saying "Persian astronomer/mathematician" should raise so many objections! The word "Persian" to me places al-Khwarizmi geographically, and tells me something of his cultural background. Iranians can feel proud of this label if they like, while Arabs can point out in return that the man wrote in Arabic.

Best wishes, ---Jeff Oaks

--

”

The above E-mail was received on 21 June , 2006 and was forwarded to Admin Khoikhoi who I met at around time and who was involved in mediating the article. The actual E-mail is still available for anyone interested.

Professor Berggren, an important response from an important person

Professor Berggren [5][6] is a very well known mathematician and a scholar of mathematical history specializing in the history of Mathematics in the Islamic era. He also has a very interesting article: (LEN BERGGREN, Simon Fraser University, Burnaby, BC V5A 1S6 Creating Mathematics Textbooks in the Thirteenth Century: The Case of Nasir al-Din al-Tusi and Aristarchos of Samos)[7].

On March 12, 2006, I wrote an E-mail to Professor Berggren:

“

Dear Professor Bergrren,

I was reading the following article by you:

http://autocww.colorado.edu/~blackmon/E64ContentFiles/Mathematics-Algebra,etc./algebra.htm

In it, it is claimed that: "In the 9th century, the Arab mathematician Al-Khwarizmi wrote one of the first Arabic algebras, a systematic exposure of the basic theory of equations, with both examples and proofs"

You might want to take a look at this web-page also where I have listed all the ancient sources available on al-Khawarazmi's background: (a webpage I created then with regards to this issue). But after doing research, it has become clear that Al-Khawarazmi was not of Arabic background. Indeed he was from Chorasmia (Khawarazm) and thus this make him of Persian background. The difference here is like saying someone if Hungarian and another one is German.

Thanks for your response and best wishes ....

”

He wrote back on March 21, 2006:

“ Dear Professor ...,

Thank you for your letter. You are, of course, right and I make the same point myself in a book I published (with Springer-Verlag) in 1986, titled Episodes in the Mathematics of Medieval Islam. I write, on p. 6, speaking of the early period of Islamic science, that "the Central Asian scholar Muhammad ibn Musa al-Khwarizmi came from the old and high civilization that had grown up in the region of Khwarizm . . . near the delta of the Amu Dar'ya (Oxus) River on the Aral Sea." (This book has been translated into Farsi, by the way, and is available in Iran.) The article you wrote to me was one I wrote at a time when I was not as aware of the wide ethnic differences within medieval Islam as I was when I came to write my book. Anyway, happy "Nau Rooz" and I wish you success in your researches. I was very impressed with the sources you have gathered and I look forward, when I have finished teaching this term, to having the leisure to read them carefully. Yours sincerely, Len Berggren

”

The e-mail was forwarded to user Admin Khoikhoi in Wikipedia on Dec 3, 2006 and is still available for anyone interested. I am honored to be called a Professor (but I am not one, at least not yet and did not call myself one :) ), but in reality I am just another Doctor of Philosophy. Anyhow, the above response shows that the honorable Professor, after delving more into his research , became aware of the fact that Al-Khwarizmi like many others mathematicians who contributed to the Islamic Golden age were of Iranian background.

Professor Frye

Source: The Golden age of Persia by Richard N. Frye, Professor of Iranian, Harvard university Weidenfeld and Nicolson, London 1975 Professor Richard (Emeritus) was a Professor of Iranian and Middle Eastern studies at Harvard University.

pages 161-162:

“ The contributions of Iranians to Islamic mathematics is overwhelming. Undoubtedly Iran acted as a middleman for the transmission of a great deal of mathematical knowledge from India, and it is not easy to determine the source of many ideas, but Iranians were active and did contribute much. The centre of scientific activity was, as expected, Baghdad. The caliph al-Ma'mun collected a great number of mathematicians and astronomers at his court, almost all

of them from eastern Iran. Perhaps the most famous of the mathematicians was Muhammad b. Musa al-Khwarazmi (d. c. 850) who wrote on algebra, and it is possible that this word comes from his book al-Jabr just as the word algorism, the decimal system of computation, most probably comes from his own name. To record even the names of scientists of Iranian origin who flourished in the time of al-Ma'mun would occupy much space, and their contributions to learning and science were extensive. The Banu Musa, three brothers, were instrumental in translating Greek and Pahlavi manuscripts on scientific subjects into Arabic. Abu Ma'shar of Balkh was more an astrologer than a mathematician but many of his works were translated into Latin and were well known in Europe where he was called Albumasar. The mathematical tradition was continued in Iran by Abu `Abdallah Muhammad al-Mahani (d. c. 884) from the famous shrine town near Kirman, and Abu'l-`Abbas al-Nairizi (d. c. 922) from the town near Perspolis. More famous than these two was Abu'l-Wafa' al-Buzjani (d. 997), from a town in Kuhistan, eastern Iran, who made significant contributions to trigonometry, especially in studies on the tangent ... and the famous `Umar Khaiyam (d. 515/1122) who is better known in the west as a poet. He was, however, a great mathematician and also an astronomer. He reformed the old Persian solar calendar which had continued in use in Iran beside the Muslim lunar calendar. This new calendar, called the Jalali, was more accurate than the Gregorian calendar. The name of Abu Raihan al-Biruni (d. 1048), from Khwarazm, must be mentioned since he was one of the greatest scientists in world history. His encyclopedic knowledge is evident from his many and varied writings which have survived. His works include treatises on geography, geology, mathematics, astronomy and history, which include a great deal of information on philosophy and religion. To describe the contributions of al-Biruni and other Iranians to the body of mathematical knowledge in the Muslim world would far exceed the scope of the present volume.

”

Ibn Khaldun

From the same book by Professor Frye:

“ page 150: The famous Ibn Khaldun, living in the fourteenth century in north Africa, wrote the following:

It is a remarkable fact that, with few exceptions, most Muslim scholars both in the religious and intellectual sciences have been non-Arabs ... Thus the founders of grammar were Sibawaih and, after him, al-Farisi and az-Zajjaj. All of whom were of Persian descent. They were brought up in the Arabic language and acquired knowledge of it through their upbringing and through contact with Arabs. They invented the rules [of grammar] and made it into a discipline for later generations. Most of the hadith scholars, who preserved traditions of the Prophet for the Muslims also were Persians, or Persian in language and breeding because the discipline was widely cultivated in Iraq and regions beyond. Furthermore, all the great jurists were Persians, as is well-known. The same applies to speculative theologians and to most of the Qu'ran commentators. Only the Persians engaged in the task of preserving knowledge and writing systematic scholarly works. Thus the truth of the statement of the Prophet becomes apparent, ``If learning were suspended at the highest parts of heaven the Persians would attain it. ... The intellectual sciences were also the preserve of the Persians, left alone by the Arabs, who did not cultivate them. They were cultivated by arabicized Persians, as was the case with all the crafts, as we stated at the beginning. This situation continued in the cities as long as the Persians and Persian countries, Iraq, Khurasan and Transoxiana, retained their sedantary culture.

”

Regional background

The region of Chorasmia before its Turkification was an Iranian speaking region with a long developed civilization. A comprehensive article on Chorasmia can be found in here. Both Encyclopedia Iranica and Encyclopedia of Islam entry on Chorasmia are very well done. Another important article is about the Al-e-Afrigh dynasty. They were native Iranian Chorasmian rulers of the area until the Ghaznavid period. See here for the actual article: [8]

I have also noted some facts about the Iranian Chorasmian language and culture in [9].

In Athar al-Baqqiyah (Chronology of Nations), the Persian-Chorasmian writer Biruni in his chronology of the ancient nations states states:

“ Original Arabic

و أما أهل خوارزم، و إن کانوا غصنا ً من دوحة الفُرس

Translation: And the people of Khwarizm, they are a branch of the Persian tree.

”

Biruni was a native of the region living approximately 200 years after Khwarizmi. Which shows that the inhabitants of Khwarizm were still speaking the Old Iranian Chorasmian language. He has recorded some of the names, months and festivals in the Old Iranian Chorasmian language. There are also some other manuscripts in the Old Chorasmian language.

I also quote the late eminent linguist Professor David Mackenzie on the old Iranian Chorasmian Language:

“ The earliest examples have been left by the great Chorasmian scholar Abu Rayhan Biruni. In his works on chronology and astronomy (ca. 390-418/1000-28) he recorded such calendrical and astronomical terms as some of the tradi­tional names of days, months, feasts, and signs of the zodiac. ”

.

The historian Tabari (a generation after Khwarizmi)

The earliest evidence at hand about Al-Khwarizmi is from Tabari (born around 839 A.D.) who lived one generation after Al-Khawarizmi. Tabari mentions his name in passage(accessed from www.al-waraq.com):

وذكر أنه لما اعتلّ علته التي مات فيها وسقى بطنه أمر بإحضار المنجمّين، فأحضروا؛ وكان ممن حضر الحسن بن سهل، أخو الفضل بن سهل، والفضل بن إسحاق الهاشميّ وإسماعيل بن نوبخت ومحمد بن موسى الخوارزميّ المجوسيّ القطربّليّ وسند صاحب محمد بن الهيثم وعامة من ينظر في النجوم، فنظروا في علّته ونجمه ومولده، فقالوا: يعيش دهراً طويلاً، وقدّ روا له خمسين سنة مستقبلة؛ فلم يلبث إلا عشرة أيام حتى مات

The full name given by Tabari is: Muhammad ibn Musa Al-Khawarazmi Al-Majoosi Al-Qutrubbuli (Qutrub was a district near Baghdad). The significance of this passage is the title Al-Majoosi (Zoroastrian) given here to him by Tabari. This would be a clear indicator of his Iranian background. In the preface of his Algebra (if effectively written by himself) shows him a pious Muslim. If we take the preface, then Tabari’s designation could mean also that his ancestors, and perhaps Khwarizmi in his youth, had been Zoroastrian. It would also connect it with Biruni statements about the Zoroastrians of Chorasmia, specially during the time of Qotayba b. Moslem in 93/712 A.D..(See his Athar).

Note Tabari is the oldest source on al-Khwarizmi we probably posses and given that they lived in the same time, it would probably be the most accurate.

Ibn Nadeem

Ibn-Nadeem ( 930-990 A.D) an important biographer of Muslim scholars in his Al-Fihrist mentions:

الخوارزمي واسمه محمد بن موسى وأصله من خوارزم وكان منقطعاً إلى خزانة الحكمة للمأمون وهو من أصحاب علوم الهيئة وكان الناس قبل الرصد وبعده يعولون على زيجيه الأول والثاني ويعرفان بالسند هند وله من الكتب كتاب الزلزيج نسختين أولى وثانية كتاب الرخامة كتاب العمل بالاسطرلابات كتاب عمل الإسطرلاب كتاب التاريخ سند .

The important passage here translates to "His Asl( origin, root, background) is from Khawarazm(Chorasmia))".

This again shows the Iranian background of Khwrizmi who was from Chorasmia and of course his name is a testament to that.

Khwarizmi and his use of the Persian calendar

A well known fact is Abu al-Qasim Muslamah ibn Ahmand known as al-Majriti worked on the table of Khwarizmi and changed its dates from the Persian to the Solar calendar.

This shows that Al-Khawarzmi used Persian dates and calendar in his astronomical tables. The general Iranian calendars (Iran proper, Zoroastrian, Chorasmian and Sogdian) had a specific name for each day of the month and a specific name for each month. So over all, a unique combination (with ordering) of around 12*30 names shows up in these calendars. The reason for the conversion to Hijri calendar might be because of its wider usage and its simplicity (only 12 names of the month and the number of day is required).

Conclusion

Al-Khawarazmi was of an Iranian background and his origin lies in the advanced civilization of Chorasmia. We should also mention that Baghdad was a very cosmopolitan city (note its name is actually Persian) and many Iranian scientists as well Arabs were working together to create the great Islamic cultural renaissances which occurred during the Abbassids under Nawbakht, Barmakids, Harun ar-Rashid and other notable figures. Al-Khawarazmi is from Khawarazm (Chorasmia) (Ibn Nadeem and as his name indicates), Biruni another native Chorasmian mentions that the people of Khawarazm are a branch Persians, there is sufficient evidence on the Iranian dialect spoken in the Zoroastrian Chorasmia (Iranica article) and a title Al-Majoosi (Zoroastrian) by Tabari (indicating his ancestry). Also we have the fact that he used Persian dates in his table instead of Arabic and Hijrah dates and was at ease with this. His astronomical table was used by the Muslim world and up to the revision of his table by Al-Majiriti, it was based on a Persian calendar. The role of Zoroastrian and Indian astrology and astronomy in the Islamic era is well known. Al-Khwarizmi was one of the first to bring Zoroastrian/Indian astrology/astronomy into the Islamic world.