Origins of Aljebra : Hindu or Islamic? Iqbal Sahib Aljabr works were original, and was free of Sassanid, Hellenistic or Vedic influences. I will disagree with you, it was the result of Islam and Mamun House of Wisdom. Prof.Tariq Qureshy Irfan Bokhari Origins of Aljebra - I have answered this last year Out of womb of Babylonian algebra, Egyptian algebra, Greek geometric algebra, Euclid of Alexandria, Chinese algebra and Diophantine algebra and Modus Indorum from Hind comes the algebra of today. There are three main schools of thought on the origin of Arabic algebra: one emphasizes Hindu influence, another stresses the Mesopotamian, or Syriac-Persian, tradition, and the third points to Greek inspiration. The truth is probably approached if we combine the three theories. In The Arabic Hegemony Boyer highlights that The first century of the Muslim empire had been devoid of scientific achievement. This period (from about 650 to 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 other parts of the world had faded. Had it not been for the sudden cultural awakening in Islam during the second half of the eighth century, considerably more of ancient science and mathematics would have been lost. It was during the caliphate of al-Mamun (809–833), however, that the Arabs fully indulged their passion for translation. Al-Mamun established at Baghdad a House of Wisdom (Bait al-hikma) comparable to the ancient Museum at Alexandria. Among the faculty members was a mathematician and astronomer, Mohammed ibn-Musa al-Khwarizmi, whose name, like that of Euclid, later was to become a household word in Western Europe. The scholar, who died sometime before 850, wrote more than half a dozen astronomical and mathematical works, of which the earliest were probably based on the Sindhad derived from India This algebra came along with the Hindu Number system to Arabia and then migrated to Europe. Muslims have not come out of emptiness; they incorporate values of spirit and civilisations of that of Pharaohs, Hellenistic, Vedic and Zoroaster; it is a combination of all these that helped a great era of renaissance that was nipped in the bud. During this time, observatories were set up, and the House was an unrivalled center for the study of humanities and for science in medieval Islam, including mathematics, astronomy, medicine, alchemy and chemistry, zoology and geography and cartography. Drawing on Persian, Vedicand Greek texts—including those of Pythagoras, Plato, Aristotle, Hippocrates, Euclid, Plotinus, Galen, Sushruta, Charaka, Aryabhata and Brahmagupta—the scholars accumulated a great collection of world knowledge, and built on it through their own discoveries. Baghdad was known as the world’s richest city and center for intellectual development of the time, and had a population of over a million, the largest in its time. Inclusion not exclusion was the name of the game. Extroversion not introversion was the strategy. The spirit of Greek science, literature and philosophy fell into the hands of Muslims. With the conquest of Persia, the treasure chest of knowledge of old twin civilisations—Byzantines and the Sassanids—had fallen in the hands of the Arab armies. Instead of burning them, they made these treasures the mainstay of their governance. In the spring of 633 CE, a grandson of Khosrau called Yezdegerd, ascended the throne, and in that same year the first Arab squadrons made their first raids into Persian territory. The caliph is said to have had a dream in which Aristotle appeared, and as a consequence al-Mamun determined to have Arabic versions made of all the Greek works that he could lay his hands on, including Ptolemys Almagest and a complete version of Euclids Elements. From the Byzantine Empire, with which the Arabs maintained an uneasy peace, Greek manuscripts were obtained through peace treaties. The word algebra is derived from the Arabic word Al-Jabr, and this comes from the treatise written in 820 by the medieval Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī, entitled, in Arabic Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, which can be translated as The Compendious Book on Calculation by Completion and Balancing. , In China and India Brahmagupta (fl. 628) is referred , who lived in Central India somewhat more than a century after Aryabhata in the trigonometry of his best-known work, the Brahmasphuta Siddhanta, here we find general solutions of quadratic equations, including two roots even in cases in which one of them is negative. In The Arabic Hegemony it is quoted : It is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the translation above. The word al-jabr presumably meant something like restoration or completion and seems to refer to the transposition of subtracted terms to the other side of an equation, which is evident in the treatise; the word muqabalahis said to refer to reduction or balancing—that is, the cancellation of like terms on opposite sides of the equation. The earliest known Indian mathematical documents are dated to around the middle of the first millennium BCE (around the 6th century BCE). Āryabhaṭīya or Āryabhaṭīyaṃ, a Sanskrit astronomical treatise, is the magnum opus and only surviving work of the 5th century Indian mathematician, Āryabhaṭa. Aryabhatta is the first mathematician to solve equations using methods that are acceptable to modern scholarship. In it he gave the rules, other were Brahma Sphuta Siddhanta - Brahmagupta (fl. 628) was an Indian mathematician who authored Brahma Sphuta Siddhanta. In his work Brahmagupta solves the general quadratic equation for both positive and negative roots, and Bhāskara II (1114–c. 1185) was the leading mathematician of the 12th century. In Algebra, he gave the general solution of the Pell equation. The Mathematics of the Hindus He gave more elegant rules for the sum of the squares and cubes of an initial segment of the positive integers. The sixth part of the product of three quantities consisting of the number of terms, the number of terms plus one, and twice the number of terms plus one is the sum of the squares. The square of the sum of the series is the sum of the cubes. In The Arabic Hegemony Boyer further highlights that al-Khwarizmis work had a serious deficiency that had to be removed before it could serve its purpose effectively in the modern world: a symbolic notation had to be developed to replace the rhetorical form. This step the Arabs never took, except for the replacement of number words by number signs. Thabit was the founder of a school of translators, especially from Greek and Syriac, and to him we owe an immense debt for translations into Arabic of works by Euclid, Archimedes, Apollonius, Ptolemy, and Eutocius. Al-Khwarizmi writes: We have said enough so far as numbers are concerned, about the six types of equations. Now, however, it is necessary that we should demonstrate geometrically the truth of the same problems which we have explained in numbers. The ring of this passage is obviously Greek rather than Babylonian or Indian. There are, therefore, three main schools of thought on the origin of Arabic algebra: one emphasizes Hindu influence, another stresses the Mesopotamian, or Syriac-Persian, tradition, and the third points to Greek inspiration. The truth is probably approached if we combine the three theories. So who is finally the father of Algebra? Boyer in The Arabic Hegemony says that Diophantus sometimes is called the father of algebra, but this title more appropriately belongs to Abu Abdullah bin mirsmi al-Khwarizmi. It is true that in two respects the work of al-Khwarizmi represented a retrogression from that of Diophantus.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 rhetorical, with none of the syncopation found in the Greek Arithmetica or in Brahmaguptas 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 scholars made use of syncopation or of negative numbers. Even J Gandz and Saloman in The sources of al-Khwarizmis algebra, wrote that In a sense, Khwarizmi is more entitled to be called the father of algebra than Diophantus because Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers. It is most heart rending to see that Muslim Arabs who took over the introductory effort done by the Greeks and Hindus in algebra produced the ultimate algebraist Khowarizmi (9th century - his name is commemorated in the word algorithm; his major work was entitled jabr walmugabalah (restoration and balancing) and from the first word in this title we now have the word algebra), Ibn-Rushd (Averroës), Ibn-Hayan (Geber), Ibn-Haytham (Al Hazen), and others, have had no prizes in science or medicine since death of rationalism. From 735 to 1300 the field of literature, sciences and philosophy was definitely dominated by the regions under the influence of Islam. Islam encouraged science and learning because nomads of the Arab peninsula as conquerors were not bogged down with dogma; their minds were like fresh slates, liberated from dogma of their systems, the conquered reared a new breed of thinkers; Al-Razi, poet Al-Maarri surfaced as new rationalists. A vacuum of knowledge or lack of free thought could not have produced so many in the age of darkness. It was the marriage of civilisations that made populace culturally and knowledge wise so rich. All these philosophers owed their past to rich Hellenistic-Zoroastrian-Vedic affluence of three religions. It was later infusion of this crossbred multifaceted knowledge into Western Europe that stimulated the Renaissance and the scientific revolution. Recent world events belie the image cast on Islams rich intellectual history; this rich intellectual history credits its origins to intercourse of ideas between three great civilisations – the Hellenistic, the Zoroastrians and the civilisation of collective religions. The invading desert Arabs, free from intellectual fixations and unspoiled with predetermined ideas, incorporated essential truths. Today the same people are bogged down cleansing and tearing each other apart. Learn or Leave Iqbal Latif Quotes
Posted on: Sat, 14 Jun 2014 18:02:19 +0000
Trending Topics
Recently Viewed Topics
© 2015