The majority of countries in the world use Indian-Arabic numerals in the everyday life. The modern numeral system which uses digits 0,1,2,3,4,5,6,7,8,9 is called Indian-Arabic as it was probably originated in India and later spread to the West by the medieval scientists who wrote in Arabic. One of such scientists was Muḥammad ibn Musá al-Khwārizmiyy al-Majūsiyy al-Quṭrubbaliyy. He is often called “the genius of Arab mathematics”. So why did he gain such glory throughout the world?
There is almost no biographical information about this remarkable man so all the facts about him are quite conditional. From the extant fragmentary information, it is known that Muhammad al-Khorezmi was born on the outskirts of Bukhara in the village of Raml (territory of modern Uzbekistan) somewhere between 780 and 783 (Hovannisian & Sabagh, 1998). From the prefix al-Majūsiyy (magician) we can conclude that most likely his ancestors were the members of the highest caste of the ancient clergy, Zoroastrian Magi and priests.

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Starting from 809, the scientist worked in the court of Khorezm Shah al-mA’mun. In 819, he accompanied the enlightened ruler who by that time has already become the Caliph, and the both moved to Baghdad, the capital of the Arab Caliphate. He stayed there in the suburb Catabola till the rest of his life.

While in Bagdad, at the decree of Caliph al-mA’mun, the scientist takes over the reins of the famous “House of Wisdom”, later called “Academy of al-Mamun”.

The “House of Wisdom” was nothing else but the Academy of Sciences of that time. It was a workplace for many scientists from all over the world. This place was unique as in had an observatory and a large library of ancient manuscripts. Al-Khwarizmi wrote almost all his works in this place.

The scientist has created twenty scientific works, however, only seven of them have survived by this time. Most of the survived books are translations into Latin, less – comments to the scientific works of al-Biruni. Only a few of them are original manuscripts.

It is hard to estimate the contribution of this man to the development of science of middle-ages. The arithmetic “Book of the Indian account” had changed the ancient mathematics and science as a whole.

Unfortunately, the original manuscript is lost, there is a xii century preserved copy written in Latin. This work shows that Al-Khwarizmi was the first one who gave a systematic presentation of arithmetic as a science, based on the decimal numeral system.

The manuscript translation begins with the words: “Dixit Algorizmi” – “Said Algorismi”, and the author’s name very soon becomes a household word. At first, the word “Algorizm”, referred to arithmetic, but then to any system of computation that is subject to a specific rule. This is how the word “algorithm” came into our lives.

In his book “The Brief Book About Calculation of Algebra and Almukabula”, Al-Khwarizmi presented the basic types of equations and ways of their solution. The European scientists used the term “al-Jabr” in Latin script to give definition to subdivision on science that solves linear and quadratic equations (Berggren, 1986). This subdivision has later transformed into what we now call algebra.

An interesting fact is that all al – Khwarizmi’s works in the field of geography are closely associated with works on astronomy and mathematics. He is known as the first author of the mathematical geography essay. The scientist has first described the inhabited lands of the earth in the Arabic language. This work also included the detailed and highly accurate maps of settlements with lakes, seas and oceans. The high accuracy of his works in geography is directly connected with the painstaking calculations of the terrestrial Meridian.

Here is the story that happened with the word “sine”. The geometric meaning of sine is half the chord length which is subtending the arc. Al-Khwarizmi called it beautifully and accurately: “a bowstring”; in Arabic, it sounds “jiba”. But the Arabic alphabet has only consonants. People who were not very fluent in Arabic literacy often confused vowels. The same happened with the translator of al-Khwarizmi’s book into Latin. Instead of “jiba” – “bowstring” – he read “jayb” – “bay”. In Latin, “bay” means “sinus” (Boyer & Merzbach, 1991). Since then, European mathematicians use this concept, without worrying about its original meaning

The last mention of al-Khwarizmi refers to 847 when the Caliph Al-Wathiq died. Al-Khwarizmi is mentioned among the people who were present at his passing. It is considered that al-Khwarizmi died in 850.

Contribution to world science
Al-Khwarizmi has made an invaluable contribution to the civilization, majorly through the development of geography, mathematics and astronomy. Here is the list of his major contributions to the world of science:

He introduced the decimal positional number system with numbers 0,1,2,3,4,5,6,7,8,9 and contributed to its spread throughout the world.
He was the one who created the science of algebra.
He developed the method or presenting the information through the clear structure and following certain rules. It is now known as the algorithm.
He was the first person to use polar coordinates.
Al-Khwarizmi considered the movement of five planets, the moon and the sun, eclipses, trigonometry and mathematical geography in his astronomical works.
He has developed the concept of sine.
The merit of al-Khwarizmi in the history of astronomy is compiling trigonometric and astronomical tables (“Zij al-Khwarizmi”), which was the basis of medieval research in this area both in the East and in Western Europe.

    References
  • Berggren, J. (1986). Episodes in the mathematics of medieval Islam (1st ed., p. 7). New York-Berlin: Springer.
  • Boyer, C. & Merzbach, U. (1991). A history of mathematics (1st ed., p. 252). New York: John Wiley.
  • Hovannisian, R. & Sabagh, G. (1998). The Persian presence in the Islamic world (1st ed., pp. 126–127). Cambridge: Cambridge University Press.