Did you know . . .?

The word "algebra" comes to us from a Latin translation of the title of an important mathematical treatise by the ninth-century Arabic author al-Khwarizmi. A translation of al-Khwarizmi's name itself gives us the word "algorithm."

(Illustration source: http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Al-Khwarizmi.html)

Abu Jafar Muhammad ibn Musa al-Khwarizmi lived in Baghdad in the early ninth century. Baghdad at that time was a cultural crossroads, and, under the patronage of the Abbassid caliphs, the so-called House of Wisdom at Baghdad produced a Golden Age of Arabic science and mathematics. In Baghdad, scholars encountered and built upon the ideas of ancient Greek and Indian mathematicians.
(Illustration source: http://www.silk-road.com/maps/images/Arabmap.jpg)

There, al-Khwarizmi encountered the Indian numeral system (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and he wrote a treatise on what we call Arabic numerals. It was translated into Latin in the twelfth century as Algoritmi de numero Indorum (that is, Al-Khwarizmi on the Hindu Art of Reckoning) and was crucial in the introduction of Arabic numerals to medieval Europe. It may well represent the first use of zero as a positional place holder. From that title, we have the word "algorithm."

Al-Khwarizmi's most important work, however, was probably the treatise called al-Kitab al-mukhtasar fi hisab al-jabr w'al-muqabala or The Compendious Book on Calculation by Completion [or Restoring] and Balancing. This book is an explanation of the solution to quadratic and linear equations of six varieties. Al-jabr refers to the process of moving a subtracted quantity to the other side of an equation; al-muqabala involves subtracting equal quantities from both sides of an equation. Hisab al-jabr w'al-muqabala was translated into Latin in 1140 as Liber algebrae et almucabala, from which we have the word "algebra" for the whole process.

But don't expect al-Khwarizmi's al-jabr to look anything like our algebra. Al-Kwharizmi's book is written entirely in prose, with none of the symbols we use today.

Here is an example:

If the instance be, 'ten and thing to be multiplied by thing less ten,' then this is the same as 'if it were said thing and ten by thing less ten. You say, therefore, thing multiplied by thing is a square positive; and ten by thing is ten things positive; and minus ten by thing is ten things negative. You now remove the positive by the negative, then there only remains a square. Minus ten multiplied by ten is a hundred, to be subtracted from the square. This, therefore, altogether, is a square less a hundred dirhems. (Quotation source: http://www.millersv.edu/~deidam/m301/arab04.htm)

For a translation in mathematical terms, click here.

Here begins the algorismus.
This new art is called the algorismus, in which
out of these twice five figures

0 9 8 7 6 5 4 3 2 1,
of the Indians we derive such benefit

--Medieval Latin Carmen de Algorismo (Quotation source: http://www.peak.org/~jeremy/calculators/alKwarizmi.html)

That fondness for science...has encouraged me to a compose a short work on Hisab al-jabr w'al muqabala , confining it to what is easiest and most useful in arithmetic, such as men constantly require in cases of inheritance, legacies, partition, law-suits [all based on the Qur'an], ...the measuring of lands, the digging of canals, and geometrical computations.

--al-Khwarizmi (Quotation source: http://www.millersv.edu/~deidam/m301/arab04.htm)

When I consider what people generally want in calculating, I found that it always is a number.

--al-Khwarizmi (Quotation source: http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Al-Khwarizmi.html)

Fun links:

Illustration of a page from al-Khwarizmi's Kitab al-Jabr wal-Muqabala: http://www.superluminal.com/cookbook/gallery_alkhwarizmi_kitab.html

Discussion of a fun book about algebra: http://www.sciencenews.org/20000115/mathtrek.asp

Math cartoons: http://www.csun.edu/~hcmth014/comicfiles/allcomics.html (Be sure to check out al-Zebra!)

The world of Trotter math (lots of fun links): http://www.geocities.com/ttrotter3/

For more information:

http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Al-Khwarizmi.html

http://members.aol.com/bbyars1/algebra.html

http://www.millersv.edu/~deidam/m301/arab04.htm

http://members.tripod.com/~wzzz/KHAWARIZ.html

http://users.erols.com/zenithco/khawariz.html

http://www.aug.edu/dvskel/MichSP93.htm

On Arabic mathematics: http://www-groups.dcs.st-andrews.ac.uk/~history/HistTopics/Arabic_mathematics.html

On the development of algebra: http://www.lib.virginia.edu/science/parshall/algebra.html

Al-Khwarizmi, Arabic numerals, and algorithms: http://www.peak.org/~jeremy/calculators/alKwarizmi.html

By Laura Smoller, UALR Department of History.

May 2001.