One of al-Khwarizmi’s greatest contributions was to provide a comprehensive guide to the numbering system which originated in India about 500 CE. It is this system, later called the Arabic system because it came to Europe from al-Khwarizmi, that became the basis for our modern numbers. It was first introduced to the Arabic-speaking world by al-Kindi, but it was al-Khwarizmi who brought it into the mainstream with his book on Indian numerals, in which he describes the system clearly.
The system, as explained by al-Khwarizimi, uses only ten digits from 0 to 9 to give every single number from zero up to the biggest number imaginable. The value given to each digit varies simply according to its position. So the 1 in the number ‘100’ is 10 times the 1 in the number ‘10’ and 100 times the 1 in the number ‘1’. An absolutely crucial element of this system was the concept of zero.
The system, as explained by al-Khwarizimi, uses only ten digits from 0 to 9 to give every single number from zero up to the biggest number imaginable. The value given to each digit varies simply according to its position. So the 1 in the number ‘100’ is 10 times the 1 in the number ‘10’ and 100 times the 1 in the number ‘1’. An absolutely crucial element of this system was the concept of zero.
This was a significant advance on previous numbering systems, which were often cumbersome with any large numbers. The Roman system, for instance, needs seven digits to give a number as small as, for example, 38: XXXVIII. Arabic numbering can give even very large numbers quite compactly. Seven digits in Arabic numerals can, of course, be anything up to 10 million. What’s more, by standardising units, Arabic numerals made multiplication, division and every other form of mathematical calculation simpler.
This system quickly caught on, and has since spread around the world to become a truly global ‘language’. Along with the numbers, English also gained another word, ‘algorithm’, for a logical step-by-step mathematical process, based on the spelling of al-Khwarizmi’s name in the Latin title of his book, Algoritmi de numero Indorum. The new numbers took some time to embed themselves in the Islamic world, however, as many people continued with their highly effective and fast method of finger-reckoning.
