The Second Father of Algebra: Muḥammad ibn Mūsā al-Khwārizmī

History of Science again examines an Eastern scientist; this week’s installment focuses on a Middle Eastern mathematician, al-Khwarizmi. The exact dates of his birth and death are unknown, but it is estimated that he lived from 780 to 850. He lived most of his life in Baghdad, the capital of the Abbasid caliphate at the time. In 813, a new caliph by the name of al-Ma’mun came to power. Much like his father, al-Ma’mun strived to further intellectual pursuits. He founded the “House of Wisdom”, an academy where works of early philosophers and scientists were translated and studied. Al-Khwarizmi became a scholar at this academy, publishing multiple treatises during the rule of al-Ma’mun (813-833). The most famous of these treatises is Hisab al-jabr w’al-muqabala, his treatise on algebra. Al-Khwarizmi provides a very practical take on algebra in the text. He begins by defining natural numbers (counting numbers) in an original, useful way. From there, he proposes how to solve linear and quadratic equations. All of his work lacks any typical algebraic notation seen today; instead, the example problems he provides are all written out in Arabic. The rest of the text provides information on finding the area and volume of geometric figures, a collection and summary of the works of others.

Al-Khwarizmi’s impact on the field of mathematics is still visible today. The English word ‘algebra’ is derived from a Latinized version of al-jabr, a portion of the name of his treatise on algebra and an Arabic word meaning ‘completion’ or ‘restoration’. The English word ‘algorithm’ is derived from a corrupted form of al-Khwarizmi’s name attached to another of his works, a treatise on the Hindu-Arabic number system. While the original text is lost, the Latin translation, Algoritmi de numero Indorum, allows us to understand al-Khwarizmi’s impact on the number system used today. Previously, Indian mathematicians had already developed numbers one through nine, as well as their symbols. While these mathematicians grasped the concept of zero, Al-Khwarizmi formally recognized zero as a number as well as its use symbolically. Although this idea seems fundamental to the math students of today, the use of zero as a number was pioneering and proved immensely useful in the field of mathematics.

Al-Khwarizmi produced texts on other subjects as well, but his treatises on algebra and Arabic numerals were the most influential of his works. His algebra text was so useful that translations of Hisab al-jabr w’al-muqabala were used in European universities until the 1500s! Any math textbook, stock ticker, or even food label today is a testament to the global influence of his number system. Diophantus may be traditionally known as the “Father of Algebra” for his Arithmetica text, but al-Khwarizmi deserves a large share of the title for his treatise on algebra. Although his work was done during the Dark Ages, al-Khwarizmi added greatly to scientific knowledge and set the foundation for modern mathematics.

Vijay Venkatesan is a freshman from Baker College at Rice University.

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