Muhammad ibn Musa al-Khwarizmi
(
Arabic: ) was a
Persian mathematician,
astronomer,
astrologer and
geographer. He was born around 780, in either
Khwarizm or
Baghdad, and died around 850.
He was the
author of
', the first book on the systematic solution of linear and quadratic equations. Consequently he is considered to be the father of algebra, a title he shares with Diophantus. The word algebra is derived from ', one of the two operations used to solve
quadratic equations, as described in his book.
Algoritmi de numero Indorum, the
Latin translation of his other major work on the
Indian numerals, introduced the
positional number system and the
number zero to the
Western world in the 12th century. The words
algorism and
algorithm stem from
Algoritmi, the
Latinization of his name. His name is also the origin of the
Spanish word
guarismo, meaning
digit.
Few details about al-Khwārizmī's life are known, it is not even certain where he was born. His name indicates he might have came from
Khwarizm (Khiva) in the
Khorasan province of the
Sassanid Persian Empire (now
Xorazm Province of
Uzbekistan).
His name is often given as either
' (Arabic: "Father of Abdullah, Muhammad, son of Moses, native of Khwārizm") or ' (Arabic: أبو جعفر محمد بن موسى الخوارزمي).
[possibly because it is mistaken with that of . M. Dunlop. . JRAS 1943 p. 248-250).]The
historian al-Tabari gave his name as Muhammad ibn Musa al-Khwārizmī al-Majousi al-Katarbali (Arabic: ). The
epithet al-Qutrubbulli indicates he might instead have came from
Qutrubbull, a small town near
Baghdad. Regarding al-Khwārizmī's religion,
G. Toomer writes "Another epithet given to him by al-Tabari, "al-Majusi", would seem to indicate that he was an adherent of the old Zoroastrian religion. ... the pious preface to al-Khwarizmi's "Algebra" shows that he was an orthodox
Muslim, so Al-Tabari's epithet could mean no more than that his forebears, and perhaps he in his youth, had been Zoroastrians."
In
Ibn al-Nadīm's
Kitāb al-Fihrist we find a short biography on al-Khwārizmī, together with a list the books he wrote. 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 , where he studied and translated Greek scientific manuscripts.
|
The frontispiece of Frederic Rosen's The Algebra of Mohammed ben Musa (1831) |
His major contributions to
Islamic 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 (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".
[Encyclopedia Britannica. al-Khwarizmi.]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
|
A page from al-Khwārizmī's Algebra |
' (Arabic: الكتاب المختصر في حساب الجبر والمقابلة "The Compendious Book on Calculation by Completion and Balancing") is a mathematical book written approximately 830 AD.
The book is considered to have defined algebra. The word algebra is derived from the name of one of the basic operations with equations (') described in this book. The book was translated in Latin as
Liber algebrae et almucabala by
Robert of Chester in
Segovia, 1145, hence "algebra", and also by
Gerard of Cremona.
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 (
x2 =
bx)
* squares equal number (
x2 =
c)
* roots equal number (
bx =
c)
* squares and roots equal number (
x2 +
bx =
c)
* squares and number equal roots (
x2 +
c =
bx)
* roots and number equal squares (
bx +
c =
x2)
by dividing out the cooeficient of the square and using the two operations
' (Arabic: الجبر "restoring" or "completion") and al-muqābala ("balancing"). 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 ', including .
Arithmetic
|
Page from a Latin translation, beginning with "Dixit algorizmi" |
Algoritmi de numero Indorum ("al-Khwārizmī on the Hindu Art of Reckoning") on 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 original Arabic title was possibly
'.
Geography
|
Hubert Daunicht's reconstruction of al-Khwārizmī's planisphere. |
|
A 15th century map based on Ptolomy's Geography for comparison. |
Al-Khwārizmī's third major work is his ' (Arabic: كتاب صورة الأرض "Book on the appearance of the Earth" or "The image of the Earth" translated as
Geography), which was finished in 833. It is a revised and completed version of
Ptolemy's
Geography, consisting of a list of 2402 coordinates of cities and other geographical features following a general introduction.
[http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Cartography.html]There is only one surviving copy of
, which is kept at the
Strasbourg University Library. A Latin translation is kept at the
Biblioteca Nacional de España in
Madrid. The complete title translates as
Book of the appearance of the Earth, with its cities, mountains, seas, all the islands and rivers, written by Abu Ja'far Muhammad ibn Musa al-Khwārizmī, according to the geographical treatise written by Ptolemy the Claudian.
[In al-Khwārizmī's opinion, "the Claudian" indicated that Ptolemy was a descendent of the emperor Claudius.]The book opens with the list of
latitudes and
longitudes, in order of "
weather zones", that is to say in blocks of latitudes and, in each weather zone, by order of longitude. As
Paul Gallez points out, this excellent system allows us to deduce many latitudes and longitudes where the only document in our possession is in such a bad condition as to make it practically illegible.
Neither the Arabic copy nor the Latin translation include the map of the world itself, however
Hubert Daunicht was able to reconstruct the missing map from the list of coordinates. Daunicht read the latitudes and longitudes of the coastal points in the manuscript, or deduces them from the context where they were not legible. He transferred the points onto
graph paper and connected them with straight lines, obtaining an approximation of the coastline as it was on the original map. He then does the same for the rivers and towns.
One of the corrections which al-Khwārizmī made in Ptolemy's work is the reduction of the latitude of the
Mediterranean from 62° to 52° when, in actual fact, it should be only 42°. The Arab opts for the same zero meridian as Ptolemy, that of the
Canaries. The amount of inhabited land extends over 180°.
The majority of the placenames used by al-Khwārizmī match those of Ptolemy,
Martellus and
Behaim. The general shape of the coastline is the same between
Taprobane and
Cattigara. The Atlantic coast of the Dragon's Tail, which does not exist in Ptolemy's map, is traced in very little detail on al-Khwārizmī's map, but is clear and precise on the
Martellus map and on the later Behaim version.
Astronomy
("
astronomical tables") is a work consisting of approximately 37 chapters on calendrical and astronomical calculations and 116 tables with calendrical, astronomical and astrological data, as well as a table a
sine values.
The original Arabic version (written around 820) is lost, but four manuscripts of a Latin translation have survived and are kept at the Bibliothèque publique (Chartres), the Bibliothèque Mazarine (Paris), the Bibliotheca Nacional (Madrid) and the Bodleian Library (Oxford). The Latin translation is assumed to have been done by
Adelard of Bath and completed
January 26,
1126. It is based on a version of by the Spanish astronomer .
Other works
Al-Khwārizmī has written several other works including
' on the Jewish calendar, as well as books on using and constructing the astrolabe. Ibn al-Nadim in his ' (an index of Arabic books) also mentions
' (the book on sundials) and ' (the book of
history) but the two have been lost.
*
Al-Khwarizmi (crater) — A crater on the far side of the moon named after al-Khwārizmī.
*
Khwarizmi International Award# Britannica,
al-Khwarizmi# #
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...# #: I. Rekonstruktion der Karte, Interpretation der Karte: Südasien. II. Die ost- und südostasiatische Inselwelt und die Meere. III. Der Süden des festländischen Ostasiens. IV. 1. Der Norden des festländischen Ostasiens und Nord- und Mittelasien. 2. Der Norden des festländischen Ostasiens und Nord- und Mittelasien# #: This is a new edition of the complete medieval Latin translation of the Arithmetic of al-Khwarizmi (previous editions are all incomplete). This work is lost in Arabic.# |url=http://links.jstor.org/sici?sici=0369-7827%28193601%291%3A1%3C263%3ATSOAA%3E2.0.CO%3B2-3}}#
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.# |url=http://links.jstor.org/sici?sici=0369-7827%281938%291%3A5%3C319%3ATAOIAR%3E2.0.CO%3B2-2}}# Jan P. Hogendijk.
al-Khwarzimi. Pythagoras 38 (1998) no. 2, pp. 4-5.# Barnabas Hughes.
Robert of Chester's Latin translation of al-Khwarizmi's al-Jabr: A new critical edition. In Latin. F. Steiner Verlag Wiesbaden (1989). ISBN 3515045899.# King, D. A. Al-Khwarizmi and New Trends in Mathematical Astronomy in the Ninth Century.
New York University: Hagop Kevorkian Center for Near Eastern Studies: Occasional Papers on the Near East 2 (1983).#: Description and analysis of seven recently discovered minor works related to al-Khwarizmi.# Donald E. Knuth,
Algorithms in Modern Mathematics and Computer Science. Springer-Verlag. 1979. ISBN 0387111573.# Donald E. Knuth,
The Art of Computer Programming: Fundamental Algorithms 3rd edition. Addison-Wesley. 1997. ISBN 0-201-89683-4.# Historisk-filosofiske Skrifter. Bind 4, nr. 2.#: Based on the medieval Latin translation by Adelard of Bath. The Arabic original is lost. See the review by G.J. Toomer in
Centaurus 10 (1964), pp. 202-212.# Jeffrey A. Oaks.
Was al-Khwarizmi an applied algebraist?. The University of Indianapolis.# # # John J. O'Connor and Edmund F. Robertson.
Arabic mathematics: forgotten brilliance? at the MacTutor archive.# R. Rashed,
The development of Arabic mathematics: between arithmetic and algebra, London, 1994.# #:Arabic text of the Algebra of al-Khwarizmi, with English translation. Various medieval Latin translations of the Algebra of al-Khwarizmi have also been published.# Julius Ruska.
Zur ältesten arabischen Algebra und Rechenkunst. ISBN 3533038173.# Fuat Sezgin.
Geschichte des arabischen Schrifttums. 1974, E. J. Brill, Leiden, the Netherlands.# Sezgin, F., ed.,
Islamic Mathematics and Astronomy, Frankfurt: Institut für Geschichte der arabisch-islamischen Wissenschaften, 1997-9.#:This is a collection of (mostly) reprints, consisting of 112 volumes to date. Practically all the literature on Islamic mathematics published before 1960 will be reprinted in these volumes. The volumes are compiled thematically, for example vols. 1-4 are about Al-Khwarizmi, vols. 14-20 on Euclid in the Arabic tradition, vols. 21-22 on Tabit ibn Qurra, vol. 23 on Abu Kamil, vols. 24-25 on Ibn Yunis, vols. 32-36 on al-Biruni, etc.# Suter, H. [Ed.]: Die astronomischen Tafeln des Muhammed ibn Mûsâ al-Khwârizmî in der Bearbeitung des Maslama ibn Ahmed al-Madjrîtî und der latein. Übersetzung des Athelhard von Bath auf Grund der Vorarbeiten von A. Bjørnbo und R. Besthorn in Kopenhagen. Hrsg. und komm. Kopenhagen 1914. 288 pp. Repr. 1997 (Islamic Mathematics and Astronomy. 7). ISBN 3-8298-4008-X.# Gillispie, Charles C. ed.
The Dictionary of Scientific Biography, 16 vols. 2 supps. New York: Charles Scribner's Sons, 1970-1990. S.v. "Al-Khwarizmi, Abu Ja'far Muhammad ibn Musa" by Gerald Toomer.# Van Dalen, B. Al-Khwarizmi's Astronomical Tables Revisited: Analysis of the Equation of Time.#: Published in "Casulleras, J, Samsó, J., eds.,
From Baghdad to Barcelona: Studies in the Islamic Exact Sciences in Honour of Prof. Juan Vernet. 2 vols. Barcelona: Universitat de Barcelona 1996.", pp. 195-252. With survey of all work done on the tables of al-Khwarizmi.# Nito Verdera.
South America on ancient, medieval and Renaissance maps.
