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Abū ‘Abd Allāh Muḥammad ibn Mūsā al-Khwārizmī (Arabic: أبو عبد الله محمد بن موسى الخوارزمي) was a Muslim mathematician, astronomer, astrologer, geographer and author. Few details are known about his life but he was born around 780, and died around 850.
The word algebra is derived from al-jabr, one of the two methods used to solve quadratic equations, as described in his book al-Kitāb al-mukhtaṣar fī hīsāb al-jabr wa’l-muqābala and consequently he is considered to be the father of algebra. The words algorism and algorithm are derived from the Latinization of his name, Algoritmi.
Biography
It is not certain where al-Khwarizmi was born. His name indicates he might have came from Khwarizm in the Khorasan province of Persia (now Khiva, Uzbekistan), however the historian al-Tabari gave him the epithet al-Qutrubbulli, indicating he might instead have came from Qutrubbull, a small town near Baghdad. Al-Tabari also gave him the epithet al-Majusi, meaning that al-Khwarizmi was a Zoroastrian. The preface to his Algebra suggests that he was an orthodox Muslim, however.
He accomplished most of his work in the period between 813 and 833. Mathematical historian Gandz gives this opinion of Khwarizmi's algebra:
- "Khwarizmi's algebra is regarded as the foundation and cornerstone of the sciences. 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." (1)
and Mohammad Khan, says:
- "In the foremost rank of mathematicians of all time stands Khwarizmi. He composed the oldest works on arithmetic and algebra. They were the principal source of mathematical knowledge for centuries to come in the East and the West. The work on arithmetic first introduced the Hindu numbers to Europe, as the very name algorism signifies; and the work on algebra ... gave the name to this important branch of mathematics in the European world..."(2)
There is a widely held view that, after a brilliant period for mathematics when the Greeks laid the foundations for modern mathematics, there was a period of stagnation before the Europeans took over where the Greeks left off at the beginning of the sixteenth century. The common perception of the period of 1000 years or so between the ancient Greeks and the European Renaissance is that little happened in the world of mathematics except that some Arabic translations of Greek texts were made which preserved the Greek learning so that it was available to the Europeans at the beginning of the sixteenth century.
That such views should be generally held is of no surprise. Many leading historians of mathematics have contributed to the perception by either omitting any mention of Persian mathematics in the historical development of the subject or with statements such as that made by Duhem in :-
... Arabic science only reproduced the teachings received from Greek science.
The regions from which the "Arab mathematicians" came was centred on Iran/Iraq but varied with military conquest during the period. At its greatest extent it stretched to the west through Turkey and North Africa to include most of Spain, and to the east as far as the borders of China.
The background to the mathematical developments which began in Baghdad around 800 is not well understood. Certainly there was an important influence which came from the Hindu mathematicians whose earlier development of the decimal system and numerals was important. There began a remarkable period of mathematical progress with al-Khwarizmi's work and the translations of Greek texts.
This period begins under the Caliph Harun al-Rashid, the fifth Caliph of the Abbasid dynasty, whose reign began in 786. He encouraged scholarship and the first translations of Greek texts into Arabic, such as Euclid's Elements by al-Hajjaj, were made during al-Rashid's reign. The next Caliph, al-Ma'mun, encouraged learning even more strongly than his father al-Rashid, and he set up the House of Wisdom in Baghdad which became the centre for both the work of translating and of research. Al-Kindi (born 801) and the three Banu Musa brothers worked there, as did the famous translator Hunayn ibn Ishaq.
It should be emphasised that the translations into Arabic at this time were made by scientists and mathematicians such as those named above, not by language experts ignorant of mathematics, and the need for the translations was stimulated by the most advanced research of the time. It is important to realise that the translating was not done for its own sake, but was done as part of the current research effort.
Contributions
He made major contributions to the fields of algebra, trigonometry, astronomy/astrology, geography and cartography. His systematic and logical approach to solving linear and quadratic equations gave shape to the discipline of algebra, a word that is derived from the name of his 830 book on the subject, al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala (الكتاب المختصر في حساب الجبر والمقابلة) or: "The Compendious Book on Calculation by Completion and Balancing". The book was first translated into Latin in the twelfth century.
Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as "algebraic objects". It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before. As Rashed writes in (see also ):-
Al-Khwarizmi's successors undertook a systematic application of arithmetic to algebra, algebra to arithmetic, both to trigonometry, algebra to the Euclidean theory of numbers, algebra to geometry, and geometry to algebra. This was how the creation of polynomial algebra, combinatorial analysis, numerical analysis, the numerical solution of equations, the new elementary theory of numbers, and the geometric construction of equations arose.
His book On the Calculation with Hindu Numerals written about 825, was principally responsible for the diffusion of the Indian system of numeration in the Middle-East and then Europe. This book also translated into Latin in the twelfth century, as Algoritmi de numero Indorum. From the name of the author, rendered in Latin as algoritmi, originated the term algorithm.
Some of his contributions were based on earlier Persian Astronomy Indian numbers and Greek sources.
Al-Khwarizmi systematized and corrected Ptolemy's data in geography as regards to Africa and the Middle east. Another major book was his Kitab surat al-ard ("The Image of the Earth"; translated as Geography), which presented the coordinates of localities in the known world based, ultimately, on those in the Geography of Ptolemy but with improved values for the length of the Mediterranean Sea and the location of cities in Asia and Africa.
He also assisted in the construction of a world map for the caliph al-Ma'mun and participated in a project to determine the circumference of the Earth, supervising the work of 70 geographers to create the map of the then "known world".(3)
When his work was copied and transferred to Europe through Latin translations, it had a profound impact on the advancement of basic mathematics in Europe. He also wrote on mechanical devices like the clock, astrolabe, and sundial. His other contributions include tables of trigonometric functions, refinements in the geometric representation of conic sections, and aspects of the calculus of two errors.
al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala
Main article: al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābalaal-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala (Arabic: كتاب المختصر في حساب الجبر والمقابلة “The Compendious Book on Calculation by Completion and Balancing”) is a mathematical book written approximately 820 AD by the Persian mathematician Al-Khawarizmi.
The book extended the work of Indian mathematician Brahmagupta and Greek mathematician Diophantus on algebraic equations. The book is considered to have defined algebra. The word algebra is derived from the name of one of the basic operations with equations (al-jabr) described in this book. The book was translated in Latin as Liber algebrae et almucabala by Robert of Chester in 1145 , hence "algebra".
The al-jabr operation is subtracting a quantity from one side of the equation and adding it to another. al-muqābala means subtraction of the same quantity from both sides.
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Algoritmi de numero Indorum
Main article: Algoritmi de numero IndorumAlgoritmi de numero Indorum ("al-Khwarizmi on the Hindu Art of Reckoning") on Arithmetic, which survived in a Latin translation but was lost in the original Arabic.
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Kitāb al-zīğ
Kitāb al-zīğ (Arabic: كتاب الزيج "Book on the tables")
Kitāb ṣūrat al-arḍ
Kitāb ṣūrat al-arḍ (Arabic: كتاب صورة الأرض "The image of the earth" translated as Geography)
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Other works
Other works by al-hwarizmi include Istikhraj Tarikh al-Yahud (about the Jewish calendar), Kitab al-Tarikh (literally, the book of history) and Kitab al-Rukhmat (about sun-dials). The last two have been lost.
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See also
Notes
- “Father of Abdullah, Mohammed, son of Moses, native of Khwārizm”
- His name is often given as Abū Ğa‘far Muḥammad ibn Mūsā al-Khwārizmī (Arabic: أبو جعفر محمد بن موسى الخوارزمي). Many alternative translations of his name exist: Abu .
- Arabic: الجبر — “restoring” or “completion”
- Arabic: الكتاب المختصر في حساب الجبر والمقابلة — “The Compendious Book on Calculation by Completion and Balancing”
- O'Connor, John J.; Robertson, Edmund F., "Abraham bar Hiyya Ha-Nasi", MacTutor History of Mathematics Archive, University of St Andrews
References
- al-Khwarizmi at Encyclopædia Britannica. 2006.
- O'Connor, John J.; Robertson, Edmund F., "Abu Ja'far Muhammad ibn Musa Al-Khwarizmi", MacTutor History of Mathematics Archive, University of St Andrews
- John J. O'Connor and Edmund F. Robertson. Arabic mathematics: forgotten brilliance? at the MacTutor archive.
- S Gandz, The sources of al-Khwarizmi's algebra, Osiris, i (1936), 263-77.
- A A al'Daffa, The Muslim contribution to mathematics (London, 1978).