Mathematical Stories 4 – An historical and international endeavour

In the late eighth and early ninth centuries there lived a Persian mathematician called Muhammad ibn Musa al-Khwarizmi. Al-Khwarizmi was an official mathematician and astronomer for the Abbasid Caliphate and was the head of the library at the House of Wisdom in Baghdad – an academy in the original sense, a centre of scholarship and learning which followed in the footsteps of the Library of Alexandria a millennium earlier.

It is al-Khwarizmi who popularised the Hindu numeral system in the Arab world, the same system that came to Europe via Arab merchants and determines how we write our numbers today. It is also al-Khwarizmi who provided the world with one of the first major works on solving equations: The Compendious Book on Calculation by Completion and Balancing, a book which contains the word al-Jabr to describe this process of completion and balancing, from which we get algebra. The equations in The Compendious Book are all linear or quadratic and all have positive roots (since negative numbers seem not to appear in Islamic mathematics of the time) and al-Khwarizmi provides systematic, or algorithmic, ways of solving such equations. In fact, the word algorithm is directly derived from his name, via its original Latin transliteration Algoritmi, as is the Spanish word for ‘digit’: guarismo.

Al-Khwarizmi is often termed the father of algebra for these reasons but, as with most of mathematics, algebra cannot be traced to one root (forgive the pun). It is the culmination of centuries of mathematical thought, encompassing the ideas of the ancient Egyptians and Babylonians, who solved equations using numerical methods such as interpolation; the Greeks, who thought geometrically; the Chinese, who were experts in numerical patterns and infinite series; the Indians, who were rigorous in number systems and linear and quadratic equations; and the Arabs, who went on to solve much more complex equations and introduced much of the notation we use today for numbers, including fractions.

One of the things that fascinates me most about mathematics is how it is composed of strands that weave together through history, around the world, and across disciplines – think about the many visual, geometric and abstract ways of solving an equation; or the fact that Andrew Wiles needed to prove a thoroughly modern theorem to do with elliptic curves which originated in Japan in order to prove the infamous Fermat’s Last Theorem, stated in France three hundred years ago; or the fact that imaginary numbers, a construct of seventeenth and eighteenth century European mathematicians, are required to gain a full understanding of trigonometric functions, which emerged more than two thousand years ago in Greece. It may be rather cliché to say (and exceeding a pun, sorry!) but as a whole, mathematics is certainly greater than the sum of its parts.

Some of the text here forms part of a book I have written for Oxford University Press, called “How to Enhance Your Maths Subject Knowledge: Number and Algebra for Secondary Teachers” . The book is a subject knowledge workbook and guide,  aimed at anyone new to teaching mathematics, which should be available at the start of July and which you can order here or here.

This post follows from three earlier ones, which you can find here:

Mathematical Stories

Mathematical Stories 2 (or Shakespeare never saw a decimal point)

Mathematics Stories 3 – Irrationality and Infinity