Episode 5 – Algebra, Algorithm and al-Khwarizmi

Islamic Golden Age (2017)

By Eamon Gearon

Film Review

Although the Egyptians were the first to develop a base 10 system of numerical notation in 1900 BC, though the Umayyad caliphate adopted the base 10 place value system the Chinese invented in the 11th century BC.*

Under the Abbasid caliphate House of Wisdom employed Persian and Eastern Jewish mathematicians. Al-Khwarizmi (780-850 AD) was a Baghdad-based scholar specializing in mathematics, astronomy and geography.

According to Gearon, Babylonian, Greek and Indian mathematicians had all solved algebraic equations, but al-Kwarizmi was the first to lay out algorithms (ie a series of steps) for solving them in his Compendious Book on Calculation by Completion and Balancing. In the second half of the book, the equations are written out in Arabic (rather than numerals) to open the topic to non-mathematicians. Al-jabr is the Arabic word for completion and algebra the Latin translation of of al-jabr. Algorithm is the Latin translation of al-Kwarizmi.

The book’s translation into Latin in the 11th century by Gerard of Cramona and Robert of Chester introduce algebra to Europe.

Al-Khwarizmi also updated Ptolemy’s book on geography, which reached Europe in translation around 1400 and significantly influenced Columbus.

Al-Kwarizmi was born in Uzbekistan at a time when serious scholars were expected to have expertise in math, chemistry, medicine, philosophy, literature, theology and Koranic studies.

The Arab world adopted the Indian numerals we use today between the first and fourth century AD. In 825 al-Kwarizmi wrote a book outlining the advantages of Indian, numerals and decimals. Pope Sylvester II was responsible for introducing them to Europe. He read and spoke Arabic owing to studies he completed in Andalusia.

Fibonacci (1170-1250), who first encountered Indian (Arabic) numerals in North Africa, helped popularize them with his Book of the Abacus. Three hundred years later the Persian mathematician (and poet) Omar Khayyam expanded on al-Kwarizmi’s work by demonstrating the use of intersecting conic sections to solve cubic equations.

*The Sumerians invented a base 60 numerical system, subsequently adopted by the Babylonians.

https://www.kanopy.com/en/pukeariki/watch/video/5756987/5756997