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(M-2) Al-Khorezmi and the dawn of Algebra

The word "algebra" comes from a phrase (in bold below) in the title of an Arab book "Kitab al muhtasar fi hisab al gabr w'al muqubalah." This has been translated as "A compact introduction (book) to calculation using rules of completion and reduction," but Solomon Gandz has suggested "al gabr" comes from Babylonian "gabru" meaning solution of an equation, and that "muqubalah" (q reads like k) was its equivalent in Arabic. The book covered simple equations like the one in the preceding section, also quadratic ones involving x2, as well as other areas such as geometry and the division of inheritances.

Its author, Mukhammad ibn Musa Al-Khorezmi (lived about 780-850) was the chief mathematician in the "House of Wisdom", an academy of sciences established in Baghdad by the Caliph Al Ma'mun, son of Harun Al Rashid of "Arabian Nights" fame. The "House of Wisdom" was involved in Al Ma'mun's expedition to measure the size of the Earth, which Al-Khorezmi afterwards estimated to have a circumference of 21000 Arab miles. (We are not sure how big the Arab mile was, the actual figure is about 25000 of our miles; more about such estimates, here).

Al-Khorezmi's family (and possibly he as well) apparently came from the oasis of Khorazem, at the southern end of the Aral Sea, in what is now Uzbekistan. He is also credited with helping establish among the Arabs the Indian numbering system, using decimal notation and the zero. Previous systems of writing numbers used letters, like the Roman numeral systems or the cruder ones of the Greeks and Hebrews. When Al-Khorezmi's book on the new system reached Europe, the Europeans called its use "algorism" or "algorithm," a corruption of the author's name. Today "algorithm" means method of calculation, and the rise of computers has led to extensive work on developing efficient computer algorithms.

More about Al-Khorezmi's work, here.


This material is taken from a long and charming article about Al-Khorezmi, his work and his times, by Heinz Zemanek of Vienna, Austria. In September 1979, in what was (give or take a year or two) the 1200th anniversary of Al-Khorezmi's birth, mathematicians marked the occasion by convening at the site of the Khorazem oasis a conference "Algorithms in Modern Mathematics and Computer Science." Dr. Zemanek's article opens the bound proceedings of that conference, edited by A.P. Ershov and D.E. Knuth and published in 1981 by Springer Verlag as volume 122 of "Lecture Notes in Computer Science."

Further Exploration

Another great Moslem contributor to the development of algebra was Omar Khayyam (1044-1123), author of the famous "Rubaiyat" poems, masterfully translated in 1839 into English by Edward Fitzgerald. Acording to the above source, Khayyam ("tentmaker," his "takhallus" or poetical name) authored Maqalat fial-Jabr wa al-Muqabila which (among other things) used conics to obtain solutions of cubic equations.
  For a general inventory of web sites on the history of mathematics look here.

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Author and Curator:   Dr. David P. Stern
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Last updated 1 December 2003

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