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Person: Al-Khwarizmi, Abu Ja'far Muhammad ibn Musa

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.

Mathematical Profile (Excerpt):

• 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.

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Tags relevant for this person:

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

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References

Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive