Algebra

Published: 2002

Muhammad Ibn Musa Al-Khwarizmi, the father of Algebra, was a mathematician and astronomer. Caliph Al-Mamun summoned him to Baghdad and appointed him court astronomer.

Muhammad Ibn Musa Al-Khwarizmi, author of the Book of Calculations, Restoration, and Reduction (Hisab Al-Jabr wal Mugabalah). Algebra (Al-Jabr) derived its name from the title of his work.

He added zero to the Hindu 1-9 numbers, helping create the science of algebra, the base of technology and industry; every machine, device, and computer design is grounded in algebra and algorithms (al-Khawarizmi).
Al-Khwarizmi left his name in the history of mathematics through the term algorism (the old name for arithmetic). Al-Khwarizmi wrote his algebra book to serve people’s practical needs in inheritance, legacies, partition, lawsuits, and commerce. In the twelfth century, Gerard of Cremona and Robert of Chester translated Al-Khwarizmi’s Algebra into Latin.

Mathematicians used it worldwide until the sixteenth century. Traditional systems had used different letters of the alphabet to represent numbers or cumbersome Roman numerals. The new system was far superior, allowing people to multiply and divide easily and check their work. The merchant Leonardo Fibonacci of Pisa, who had learned about Arabic numerals in Tunis, wrote a treatise rejecting the abacus in favor of the Arab method of reckoning. As a result, the Arabic numeral system quickly caught on in Central Italy.

In addition to his treatise on numerals, al-Khwarizmi also wrote a revolutionary book on resolving quadratic equations. These were given either as geometric demonstrations or as numerical proofs in an entirely new mode of expression.

The book was soon translated into Latin, and the word in its title, al-Jaber, or transposition, gave the entire process its name in European languages, Algebra. Today, it is understood as an arithmetic generalization in which symbols, usually letters of the alphabet such as A, B, and C, represent numbers. Al-Khwarizmi used the Arabic word for “thing” (shay) to refer to the unknown quantity. When al-Khwarizmi’s work was translated into Spanish, the Arabic word shay was transcribed as xay, since the letter x was pronounced sh in Spain. In time, this word was abbreviated as x, the universal Algebraic symbol for the unknown.

Robert of Chester’s translation of al-Khwarizmi’s treatise on Algebra opens with the words Dixit Algorithmic, meaning “Algorithmic says.” In time, the mathematician’s epithet of his Central Asian origin, al-Khwarizmi, came to the West to denote the new reckoning process with Arabic numerals, algorithms, and then the entire step-by-step process of solving mathematical problems: algorithm. In the 9th century, Muslim scholars, including Abu al Wafaa, turned Algebra into a science.

They created the zero and the decimal point. Abu al Wafaa was the first to demonstrate the sine theorem for a spherical triangle: sin(a+b) = sin a cos b – cos a sin b. The word ‘sine’ is the exact translation of the Arabic word Jayb.