Mathematics is an exact science that is commonly defined as ‘the way to study patterns and structures’. The verb ‘to cipher’ for example comes from the Arabic ‘sifr’ that translates to ‘zero’ or ‘empty’. The figures ten and the number zero in particular have Arab roots. Many Muslim scholars have built the foundations of mathematical systems that have demonstrated the great usefulness of these figures.
Muhammad Ibn Musa Al-Khwarizmi
Almost every Muslim scientist has devoted a part of his time to mathematical research. After all, it was the way to provide insight and tools to move on to another scientific field.
Al-Khwarizmi – for many this name will not ring a bell – is without a doubt one of the most prominent mathematicians in history. Al-Khwarizmi was an Arab mathematician who lived from about 780 till 850. His name refers to his birthplace ‘Khwarizm’. Currently it is known as ‘Khiva’, a city in Uzbekistan on the border with Turkmenistan. Sadly, only limited information is available about his social life.
He worked in the ‘House of Wisdom’, which was founded in the city of Baghdad by the Muslim caliph al-Mamun. His work mainly consisted of translating scientific manuscripts of the ancient Greeks, Hebrews and Romans from the Byzantine Empire into Arabic. Furthermore Al-Khwarizmi primarily specialised in astronomy and mathematics.
On the European continent, Al-Khwarizmi’s name was assimilated to ‘Algorismi’ from which the name of ‘algorithm’ was derived. Algorithms later became useful in the creation of computer software. Computers require algorithms to count in the binary system. Today, we can no longer imagine a world without computers. Al-Khwarizmi has had a significant share in this technological ingenuity from which our digital society profits today.
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Al-Khwarizmi’s contributions to mathematics, geography, astronomy and cartography established the basis for innovation in algebra and trigonometry. Since these contributions are too numerous to cover them completely here, I am forced to refer in general terms to some of his most famous books.
He wrote a book about algorithms titled ‘Kitab Al-Jam wal-tafriq bi hisab al-hind’ of which – because of the book burning during the Mongol invasion – only a Latin translation is left, namely; ‘Algoritmi de numero indorum’.
In this book he describes the position system from the Hindus based on symbols for the numbers 1 until 9, and also for the number 0. The first use of the number 0 in the position system is possibly a contribution from al-Khwarizmi himself.
He also wrote a geography book called ‘Kitab surat al-ard’, which has been translated into French to ‘Configuration de la Terre’, or today simply known as ‘geography’. In this book he discusses and calculates the longitude and latitude of about 2400 sites to form the basis for a world map. In this scientific discipline he improved the famous work of Ptolemy. The maps of Al-Khwarizmi however were much more accurate than those of Ptolemy, so much that they are even the ones most consistent with the world map which we use today.
The contributions of Al-Khwarizmi to trigonometry are shown in detail in his book ‘Zīj al-Sindhind’. In this book there are listings of trigonometric tables for the ‘Sind’ and the ‘Hind’, better known as ‘Sinus’ and ‘Cosinus’ which now form the basis of almost all trigonometric formulas. In this book he uses trigonometric astronomical tables made to interpret the movement of the sun, the moon and the then-known planets (Mercury, Venus, Mars, Jupiter, Saturn).
The most famous of his writings, however, is ‘Hisab al-jabr w’al muqabala’. Al-Jabr means ‘restoration’ and the West took this term as ‘al-gabr’ from which the word ‘algebra’ is derived. It is in fact the first book on algebra.
In this book Al-Khwarizmi demonstrated how to apply arithmetical methods in order to simplify everyday matters such as inheritance, the measuring of farmlands, trading, the digging of canals, geometrical calculations and so on.
Doing this he soon came to what we call ‘quadratic equations’. Much of his book is devoted to solving such complex equations. The word ‘al-jabr’ literally means ‘the bringing together of broken bones’ and is on its turn derived from the verb ‘djabara’ which means ‘to reunite’. The etymological meaning of algebra hence illustrates the underlying purpose of this field, namely the solution of linear and quadratic equations with only one unknown factor, and the solving of ‘brackets’ observing ‘the order of operations’.
The complicated part of his extensive book is that he defines everything with words while he hardly ever uses symbols for his variables, which makes his book very difficult to read for mathematicians nowadays. However, this has everything to do with the fact that there was no “scientific language” at hand yet. To support his evidence, he used geometrical methods to help his readers form a mental imagine.