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Around CE he was appointed as the astronomer and head of the library of the House of Wisdom in Baghdad. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square , for which he provided geometric justifications. The term algebra itself comes from the title of his book specifically the word al-jabr meaning "completion" or "rejoining".

In the 12th century, Latin translations of his textbook on arithmetic Algorithmo de Numero Indorum which codified the various Indian numerals , introduced the decimal positional number system to the Western world.

In addition to his best-known works, he revised Ptolemy 's Geography , listing the longitudes and latitudes of various cities and localities. The epithet al-Qutrubbulli could indicate he might instead have come from Qutrubbul Qatrabbul , [24] a viticulture district near Baghdad. However, Rashed [25] suggests:. Recently, G. His systematic approach to solving linear and quadratic equations led to algebra , a word derived from the title of his book on the subject, "The Compendious Book on Calculation by Completion and Balancing".

On the Calculation with Hindu Numerals written about , was principally responsible for spreading the Hindu—Arabic numeral system throughout the Middle East and Europe. It was translated into Latin as Algoritmi de numero Indorum. Some of his work was based on Persian and Babylonian astronomy, Indian numbers, and Greek mathematics. Another major book was Kitab surat al-ard "The Image of the Earth"; translated as Geography , presenting the coordinates of places based on those in the Geography of Ptolemy but with improved values for the Mediterranean Sea , Asia, and Africa.

He also wrote on mechanical devices like the astrolabe and sundial. He assisted a project to determine the circumference of the Earth and in making a world map for al-Ma'mun , the caliph, overseeing 70 geographers. When, in the 12th century, his works spread to Europe through Latin translations, it had a profound impact on the advance of mathematics in Europe. The book was written with the encouragement of Caliph al-Ma'mun as a popular work on calculation and is replete with examples and applications to a wide range of problems in trade, surveying and legal inheritance.

The book was translated in Latin as Liber algebrae et almucabala by Robert of Chester Segovia , hence "algebra", and also by Gerard of Cremona. A unique Arabic copy is kept at Oxford and was translated in by F. A Latin translation is kept in Cambridge. It provided an exhaustive account of solving polynomial equations up to the second degree, [32] and discussed the fundamental methods of "reduction" and "balancing", referring to the transposition of terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation.

Al-jabr is the process of removing negative units, roots and squares from the equation by adding the same quantity to each side. The above discussion uses modern mathematical notation for the types of problems that the book discusses. For example, for one problem he writes, from an translation. If some one says: "You divide ten into two parts: multiply the one by itself; it will be equal to the other taken eighty-one times.

Separate the twenty things from a hundred and a square, and add them to eighty-one. It will then be a hundred plus a square, which is equal to a hundred and one roots. Halve the roots; the moiety is fifty and a half. Multiply this by itself, it is two thousand five hundred and fifty and a quarter.

Subtract from this one hundred; the remainder is two thousand four hundred and fifty and a quarter. Extract the root from this; it is forty-nine and a half. Subtract this from the moiety of the roots, which is fifty and a half. There remains one, and this is one of the two parts. O'Conner and E.

Robertson wrote in the MacTutor History of Mathematics archive :. Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra.

It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed rational numbers , irrational numbers , geometrical magnitudes, etc. 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. Al-Khwarizmi's text can be seen to be distinct not only from the Babylonian tablets , but also from Diophantus ' Arithmetica. It no longer concerns a series of problems to be solved , but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study.

On the other hand, the idea of an equation for its own sake appears from the beginning and, one could say, in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems. According to Swiss-American historian of mathematics, Florian Cajori , Al-Khwarizmi's algebra was different from the work of Indian mathematicians , for Indians had no rules like the ''restoration'' and ''reduction''.

It is true that in two respects the work of al-Khowarizmi 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-Khowarizmi is thoroughly rhetorical, with none of the syncopation found in the Greek Arithmetica or in Brahmagupta's 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.

Nevertheless, the Al-jabr comes closer to the elementary algebra of today than the works of either Diophantus or Brahmagupta, because the book is not concerned with difficult problems in indeterminant analysis but with a straight forward and elementary exposition of the solution of equations, especially that of second degree.

The Arabs in general loved a good clear argument from premise to conclusion, as well as systematic organization — respects in which neither Diophantus nor the Hindus excelled. Called takht in Arabic Latin: tabula , a board covered with a thin layer of dust or sand was employed for calculations, on which figures could be written with a stylus and easily erased and replaced when necessary.

Al-Khwarizmi's algorithms were used for almost three centuries, until replaced by Al-Uqlidisi 's algorithms that could be carried out with pen and paper. As part of 12th century wave of Arabic science flowing into Europe via translations, these texts proved to be revolutionary in Europe.

It gradually replaced the previous abacus-based methods used in Europe. Four Latin texts providing adaptions of Al-Khwarizmi's methods have survived, even though none of them is believed to be a literal translation: [39]. Dixit Algorizmi 'Thus spake Al-Khwarizmi' is the starting phrase of a manuscript in the University of Cambridge library, which is generally referred to by its title Algoritmi de Numero Indorum.

It is attributed to the Adelard of Bath , who had also translated the astronomical tables in It is perhaps the closest to Al-Khwarizmi's own writings.

Al-Khwarizmi's work on arithmetic was responsible for introducing the Arabic numerals , based on the Hindu—Arabic numeral system developed in Indian mathematics , to the Western world. This is the first of many Arabic Zijes based on the Indian astronomical methods known as the sindhind. This work marked the turning point in Islamic astronomy.

Hitherto, Muslim astronomers had adopted a primarily research approach to the field, translating works of others and learning already discovered knowledge. The original Arabic version written c. It is a major reworking of Ptolemy 's 2nd-century Geography , consisting of a list of coordinates of cities and other geographical features following a general introduction. As Paul Gallez [ dubious — discuss ] points out, this excellent system allows the deduction of many latitudes and longitudes where the only extant document 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. He "also depicted the Atlantic and Indian Oceans as open bodies of water , not land-locked seas as Ptolemy had done. It describes the Metonic cycle , a year intercalation cycle; the rules for determining on what day of the week the first day of the month Tishrei shall fall; calculates the interval between the Anno Mundi or Jewish year and the Seleucid era ; and gives rules for determining the mean longitude of the sun and the moon using the Hebrew calendar.

No direct manuscript survives; however, a copy had reached Nusaybin by the 11th century, where its metropolitan bishop , Mar Elyas bar Shinaya, found it. Elias's chronicle quotes it from "the death of the Prophet" through to AH, at which point Elias's text itself hits a lacuna. Other papers, such as one on the determination of the direction of Mecca , are on the spherical astronomy. He also wrote two books on using and constructing astrolabes. From Wikipedia, the free encyclopedia.

Khwarezm [1]. Further information: Latin translations of the 12th century , Mathematics in medieval Islam , and Science in the medieval Islamic world. Further information: Astronomy in the medieval Islamic world.

Saidan states that it should be understood as arithmetic done "in the Indian way", with Hindu-Arabic numerals, rather than as simply "Indian arithmetic". The Arab mathematicians incorporated their own innovations in their texts. The Voyage and the Messenger: Iran and Philosophy. North Atlantic Books. Pickover Sterling Publishing Company, Inc. Iranian Studies. Take, for example, someone like Muhammad b. Musa al-Khwarizmi fl.

From Al-Jabr to Algebra. Mathematics in School, 27 4 , 14— Polynomials and equations in Arabic algebra.

Archive for History of Exact Sciences, 63 2 , — 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; the word muqabalah is said to refer to "reduction" or "balancing" — that is, the cancellation of like terms on opposite sides of the equation. A History of Mathematics , p. Princeton University Press. In a sense, al-Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because al-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.

Archived from the original PDF on The first true algebra text which is still extant is the work on al-jabr and al-muqabala by Mohammad ibn Musa al-Khwarizmi, written in Baghdad around

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## Muhammad ibn Musa al-Khwarizmi

The Persian scholar built on the work of the Indian mathematician to create this modern-age force. A thousand years ago, this land had a very famous resident, Abu Abdullah Muhammad ibn Musa Al-Khwarizmi, a scholar, mathematician and an astronomer of repute. If I were to pick one word, which people use routinely and nod knowledgeably when used, but do not have the faintest idea of what it means, it will be this one. Everything around us—traffic, maps, information, news, social networks, weather forecasting, shopping—seems to be governed by the all-powerful yet mysterious algorithms.

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## Al-Khwārizmī

Latinized versions of his name and of his most famous book title live on in the terms algorithm and algebra. In fact, the words algorithm and algebra come from his name and the title of one of his works, respectively. He wrote a book on algebra from whose title the word algebra is derived, and he wrote a book on calculation that introduced to Europe the Hindu-Arabic numerals and how to do arithmetic with them. His mathematical books introduced the ideas of algebra and Hindu-Arabic numerals to Western mathematicians during the Middle Ages. His scientific works concerned geography and astronomy. The House of Wisdom acquired and translated scientific and philosophic treatises , particularly Greek, as well as publishing original research. Algebra is a compilation of rules, together with demonstrations, for finding solutions of linear and quadratic equations based on intuitive geometric arguments, rather than the abstract notation now associated with the subject.

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## Opinion | Al-Khwarizmi’s algorithms and the Brahmagupta connection

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## Algoritmi Numero Indorum

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