Muhammad ibn Mūsā al-Khwārizmī (Arabic: محمد بن موسى الخوارزمي) was a
Persian[1] mathematician, astronomer, astrologer and geographer. He was born around 780 in Kh
wārizm[2] (now Khiva, Uzbekistan) and died around 850. He worked most of his life as a scholar in the House of Wisdom in Baghdad.
His Algebra was the first book on the systematic solution of linear and quadratic equations. Consequently he is considered to be the father of algebra,[3] a title he shares with Diophantus. Latin translations of hisArithmetic, on the Indian numerals, introduced the decimal positional number system to the Western world in the 12th century.[4] He revised and updated Ptolemy’s Geography as well as writing several works on astronomy and astrology.
His contributions not only made a great impact on mathematics, but on language as well. The word algebra is derived from al-jabr, one of the two operations used to solve quadratic equations, as described in his book. The words algorism and algorithm stem from algoritmi, the Latinization of his name.[5] His name is also the origin of the Spanish word guarismo[6] and of the Portuguese word algarismo, both meaning digit.
Biography
Few details about al-Khwārizmī’s life are known; it is not even certain where he was born. His name indicates he might have come from Khwarezm (Khiva) in the Khorasan province of the Abbasid empire (now Xorazm Province of Uzbekistan).
His kunya is given as either Abū ʿAbd Allāh (Arabic: أبو عبد الله) or Abū Jaʿfar (أبو جعفر in Arabic).[7]
The historian al-Tabari gave his name as Muhammad ibn Musa al-Khwārizmī al-Majousi al-Katarbali (Arabic: محمد بن موسى الخوارزميّ المجوسيّ القطربّليّ). The epithetal-Qutrubbulli indicates he might instead have came from Qutrubbull, a small town near Baghdad. Regarding al-Khwārizmī’s religion, Toomer writes:
Another epithet given to him by al-Ṭabarī, "al-Majūsī," would seem to indicate that he was an adherent of the old Zoroastrian religion. This would still have been possible at that time for a man of Iranian origin, but the pious preface to al-Khwārizmī’s Algebra shows that he was an orthodox Muslim, so al-Ṭabarī’s epithet could mean no more than that his forebears, and perhaps he in his youth, had been Zoroastrians.[8]
In Ibn al-Nadīm’s Kitāb al-Fihrist we find a short biography on al-Khwārizmī, together with a list of the books he wrote[citation needed]. Al-Khwārizmī accomplished most of his work in the period between 813 and 833. After the Islamic conquest of Persia, Baghdad became the centre of scientific studies and trade, and many merchants and scientists, from as far as China and India traveled to this city–as such apparently so did Al-Khwārizmī. He worked in Baghdad as a scholar at the House of Wisdom established by Caliph al-Maʾmūn, where he studied the sciences and mathematics, which included the translation of Greek and Sanskrit scientific manuscripts.
His major contributions to mathematics, astronomy, astrology, geography and cartography provided foundations for later and even more widespread innovation in algebra, trigonometry, and his other areas of interest. 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 (Arabic 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.
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 and Babylonian Astronomy, Indian numbers, and Greek sources.
Al-Khwārizmī 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".[9]
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 astrolabe and sundial.
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 (Segovia, 1145)[10] hence "algebra", and also by Gerard of Cremona. A unique Arabic copy is kept at Oxford and was translated in 1831 by F. Rosen. A Latin translation is kept is Cambridge.[11]
Al-Khwārizmī’s method of solving linear and quadratic equations worked by first reducing the equation to one of six standard forms (where b and c are positive integers)
- squares equal roots (ax2 = bx)
- squares equal number (ax2 = c)
- roots equal number (bx = c)
- squares and roots equal number (ax2 + bx = c)
- squares and number equal roots (ax2 + c = bx)
- roots and number equal squares (bx + c = ax2)
by dividing out the coefficient of the square and using the two operations al-ǧabr (Arabic: الجبر “restoring” or “completion”) and al-muqābala ("balancing"). Al-ǧabr is the process of removing negative units, roots and squares from the equation by adding the same quantity to each side. For example, x2 = 40x – 4x2 is reduced to 5x2 = 40x. Al-muqābala is the process of bringing quantities of the same type to the same side of the equation. For example, x2+14 = x+5 is reduced to x2+9 = x.
Several authors have published texts under the name of Kitāb al-ǧabr wa-l-muqābala, including Abū Ḥanīfa al-Dīnawarī, Abū Kāmil (Rasāla fi al-ǧabr wa-al-muqābala), Abū Muḥammad al-ʿAdlī, Abū Yūsuf al-Miṣṣīṣī, Ibn Turk, Sind ibn ʿAlī, Sahl ibn BiÅ¡r (author uncertain), and Å arafaddīn al-Ṭūsī.
ARITHMETIC
Al-Khwārizmī’s second major work was on the subject of arithmetic, which survived in a Latin translation but was lost in the original Arabic. The translation was most likely done in the 12th century by Adelard of Bath, who had also translated the astronomical tables in 1126.
The Latin manuscripts are untitled, but are commonly referred to by the first two words with which they start: Dixit algorizmi ("So said al-Khwārizmī"), or Algoritmi de numero Indorum ("al-Khwārizmī on the Hindu Art of Reckoning"), a name given to the work by Baldassarre Boncompagni in 1857. The original Arabic title was possibly Kitāb al-Jamʿ wa-l-tafrīq bi-ḥisāb al-Hind[12] ("The Book of Addition and Subtraction According to the Hindu Calculation")[13]
