**Al'Khwarizmi** was an Islamic mathematician who wrote on Hindu-Arabic numerals. The word *algorithm* derives from his name. His algebra treatise *Hisab al-jabr w'al-muqabala* gives us the word *algebra* and can be considered as the first book to be written on algebra.

- 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.
- Al-Tabari's words should read: "Muhammad ibn Musa al-Khwarizmi and al-Majusi al-Qutrubbulli ...", (and that there are two people al-Khwarizmi and al-Majusi al-Qutrubbulli): the letter "wa" was omitted in the early copy.
- This would not be worth mentioning if a series of conclusions about al-Khwarizmi's personality, occasionally even the origins of his knowledge, had not been drawn.
- This is not the last disagreement that we shall meet in describing the life and work of al-Khwarizmi.
- However before we look at the few facts about his life that are known for certain, we should take a moment to set the scene for the cultural and scientific background in which al-Khwarizmi worked.
- Harun al-Rashid became the fifth Caliph of the Abbasid dynasty on 14 September 786, about the time that al-Khwarizmi was born.
- Al-Khwarizmi and his colleagues the Banu Musa were scholars at the House of Wisdom in Baghdad.
- Certainly al-Khwarizmi worked under the patronage of Al-Mamun and he dedicated two of his texts to the Caliph.
- The algebra treatise Hisab al-jabr w'al-muqabala was the most famous and important of all of al-Khwarizmi's works.
- Having introduced the natural numbers, al-Khwarizmi introduces the main topic of this first section of his book, namely the solution of equations.
- However, although we shall use the now familiar algebraic notation in this article to help the reader understand the notions, Al-Khwarizmi's mathematics is done entirely in words with no symbols being used.
- Al-Khwarizmi then shows how to solve the six standard types of equations.
- The question, which seems not to have an easy answer, is whether al-Khwarizmi was familiar with Euclid's Elements.
- In al-Rashid's reign, while al-Khwarizmi was still young, al-Hajjaj had translated Euclid's Elements into Arabic and al-Hajjaj was one of al-Khwarizmi's colleagues in the House of Wisdom.
- Al-Khwarizmi has neither definitions, nor axioms, nor postulates, nor any demonstration of the Euclidean kind.
- Al-Khwarizmi continues his study of algebra in Hisab al-jabr w'al-muqabala by examining how the laws of arithmetic extend to an arithmetic for his algebraic objects.
- Al-Khwarizmi's scientific achievements were at best mediocre.
- The next part of al-Khwarizmi's Algebra consists of applications and worked examples.
- Al-Khwarizmi also wrote a treatise on Hindu-Arabic numerals.
- The Arabic text is lost but a Latin translation, Algoritmi de numero Indorum in English Al-Khwarizmi on the Hindu Art of Reckoning gave rise to the word algorithm deriving from his name in the title.
- The first use of zero as a place holder in positional base notation was probably due to al-Khwarizmi in this work.
- al-Khwarizmi's work was the first to expound it systematically.
- Another important work by al-Khwarizmi was his work Sindhind zij on astronomy.
- There are two versions of al-Khwarizmi's work which he wrote in Arabic but both are lost.
- The main topics covered by al-Khwarizmi in the Sindhind zij are calendars; calculating true positions of the sun, moon and planets, tables of sines and tangents; spherical astronomy; astrological tables; parallax and eclipse calculations; and visibility of the moon.
- Al-Khwarizmi wrote a major work on geography which give latitudes and longitudes for 2402 localities as a basis for a world map.
- In particular it is clear that where more local knowledge was available to al-Khwarizmi such as the regions of Islam, Africa and the Far East then his work is considerably more accurate than that of Ptolemy, but for Europe al-Khwarizmi seems to have used Ptolemy's data.
- A number of minor works were written by al-Khwarizmi on topics such as the astrolabe, on which he wrote two works, on the sundial, and on the Jewish calendar.
- We have already discussed the varying views of the importance of al-Khwarizmi's algebra which was his most important contribution to mathematics.

Born about 780, possibly Baghdad (now in Iraq). Died about 850.

View full biography at MacTutor

Algebra, Ancient Arab, Ancient Babylonian, Ancient Indian, Astronomy, Origin Iraq, Number Theory, Special Numbers And Numerals

Parts: 1

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive