Great Mathematicians 5: Al-Khwarizmi

Not heard of him? Born in 780 in what was then Persia, he became one of the learned men of the House of Wisdom in Baghdad. He lived to the age of 70 and, because of the breadth of his work in mathematics and the sciences, he must have been an amazing person to know.

The House of Wisdom acquired and translated scientific and philosophical treatises, mainly from Greek, as well as publishing original research. Al-Khwarizmi’s first major publication was The Compendious Book on Calculation by Completion and Balancing which discussed ways of solving what we would now call linear and quadratic equations and was the start of algebra (a word derived from its Arabic title once translated into Latin). The book works out several hundred simple quadratic equations by analysis as well as by geometrical example, and also has substantial sections on methods of dividing up inheritances and surveying plots of land. It is largely concerned with methods for solving practical computational problems rather than algebra as the term is now understood.

In the 12th century a Latin translation of his second great work, Algoritmi de numero Indorum (‘Al-Khwārizmī Concerning the Hindu Art of Reckoning’), led to the introduction of Hindu-Arabic numerals, and associated arithmetic, to the West, a major factor which allowed the development of trade and science because of a more efficient system of calculation. And, incidentally, we get the word ‘algorithm’ from the title.

As if these weren’t enough, he wrote a third major book on Geography whereby he improved on the work of Ptolemy by accurately plotting locations in the known world; he drew up a world map (supervising the work of 70 geographers); he participated in a project to measure the circumference of the Earth. He also constructed a set of astronomical tables, based on Hindu and Greek sources, including a table of sines of angles. Just imagine the amount of calculation, by hand, that had to go into such a volume!

In another project he developed a universal sundial which could be used anywhere on Earth, and from then on sundials were frequently placed on mosques to determine the time of prayer; and he invented a ‘shadow square’, an instrument which could be used to measure the height of an object. Thus his work was both practical and theoretical, and covered a wide variety of fields. But he will always be best remembered for becoming the father of modern algebra.

 


Previous blogs on Great Mathematicians:

Euclid
Ada Lovelace
Rene Descartes
John Napier

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