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Mathematician Muhammad Ibn Musa Al-Khwarizmi

Mathematician Muhammad Ibn Musa Al-Khwarizmi

Suppose a man frees two slaves in a state of sickness. One of them costs 300 dirhams and the other 500 dirhams. The slave, who was worth 300 dirhams dies in a short time and leaves only one daughter among his heirs. Then, the master of those slaves also dies and their heir is also their only daughter. The deceased slave leaves behind a property worth 400 dirhams. So now how much of everyone’s inheritance will come?

Muhammad Ibn Musa Al-Khwarizmi
Muhammad Ibn Musa Al-Khwarizmi

Work on  Al-jabar

This confusing question of mathematics is taken from a book written in the early ninth century AD. This issue actually provides guidance on the distribution of property among the heirs. This book is known worldwide as Kitab al-Jabr. The author of this book is the subject of our writing today and it was Muhammad Ibn Musa Al-Khwarizmi who mastered many subjects in the Middle Ages. I first heard his name in a history essay when I was in a school in Iraq.

He writes for the first time in this book on the subject of “algebra”, the word is taken directly from the title of this book and it has been given the status of a sub-field of mathematics. Khwarizmi was originally born around 780 AD and, as his name suggests, belonged to the province of Khwarizm in the Central Asian country of Uzbekistan. We have very little information about his life, but we do know that he came to Baghdad in the early ninth century. At that time, Baghdad was the capital of a vast Islamic empire ruled by the powerful Abbasid Caliphate

He worked for Caliph al-Mamun. Caliph Mamun, himself a fanatic of translating Greek books into Arabic, was one of the great figures in the history of scientific research and their importance.

Al-Khwarizmi worked at the Caliph’s Bait al-Hikmat, an institution that seemed to be a sham. It was the center of original research in translation and the scientific sciences, and gathered the great minds of an age known as the Golden Age of Arabic science.

The Arabic word is used here because most of the books were written in Arabic at that time because it was not only the official language of the empire but also the holy book of Muslims, the Qur’an, was revealed in that language.

philosophy, medicine, mathematics, optics, and astronomy. Among the great scientific achievements of this period, we will mention some of the achievements that were directly related to al-Khwarizmi.

In the second decade of the ninth century, Caliph al-Mamun established observatories in Baghdad to study astronomy. One or two years later, a critical examination of Greek astronomy began. During this time, several researchers under the auspices of Al-Khwarizmi made several observations on the sun and the moon.

These scientific books covered a variety of scientific disciplines, including During this time, a table of latitudes and longitudes of 22 stars at the same location was created. Al-Mamun, meanwhile, ordered the construction of another observatory on the slopes of Mount Qassion, overlooking the city of Damascus. The purpose of building the observatory was to gather more data in this regard. By the end of the work, Al-Khwarizmi and his colleagues had compiled statistics tables on the location of several stars.

The Greek astronomer Tonomi, in his famous book The Geography, recorded everything about geography around the world. It is said that the Arabic translation of his work aroused the interest of the Islamic world in geography.

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Al-Mamoun instructed his scholars to draw a new map of the world, as Tonomi’s maps did not include major Islamic cities such as Mecca or the capital, Baghdad. Mecca was not so important during the Tonomi period and Baghdad did not come into existence at that time.


Al-Khwarizmi and his colleagues decided to measure the distance between the two cities. In this regard, they measured and took statistics during the lunar eclipse.

The distance he drew between the two cities in this ancient period was less than two per cent wrong compared to the present day figures. He then tried to rediscover the letters of other important places which could determine the location of the focal point of these places. His maps, for example, show the Atlantic Ocean and the Indian Ocean as open waterways, not land-bound oceans, as Tonomi described in his book. Al-Khwarizmi’s book “Surat al-Ard” means he has the honor of being the first geographer of Islam. This book was completed in 833 AD. It is also the year of the death of Caliph al-Mamun. The book contained tables of latitudes and longitudes of 500 cities.

Al-Khwarizmi explained the geography of the Nile River and its course in a book
Al-Khwarizmi explained the geography of the Nile River and its course in a book

In this book, different places are divided into towns, rivers, mountains, seas and islands. In each table, these places were arranged from south to north.

However, all these achievements are blurred in the face of his achievements in the field of mathematics. Due to his essays on numbers and numerals, the decimal number system was introduced in the Muslim world. His book Al-Jum Wal-Tafriq B-Hind is of great importance in the sub-field of mathematics. This book was written around 825 AD, but there is no authentic Arabic translation and the title of the book is only an estimate. However, it was probably the first book written on the decimal system to be translated into Latin. It begins with the words written in Latin, “Al-Khwarizmi said …”

This book gives various instructions on arithmetic and hence the term algorithm which is actually the way to speak algorithm in Latin. In fact, this and earlier translations of Al-Khwarizmi’s work were criticized in Europe, a time when Europe was going through a dark period. That is why Khwarizmi’s work was considered ‘dangerous’ or ‘magical’. His greatest work was certainly his book on algebra. Al-Khwarizmi was a follower of the ancient Persian religion Zoroastrianism and we think he later converted to Islam.

His bokk Aljabra starts with بسم اللہ الرحمٰن الرحیم (In the name of God, Most Gracious, Most Merciful) Even today, most books written by Muslim writers begin with this phrase. However, al-Khwarizmi may have written this in keeping with tradition because he did not want to offend a Muslim caliph who had his full support. In this book, al-Khwarizmi combined obscure mathematical rules that only a few people knew about. He then drafted the rules into guidelines for solving everyday problems, such as inheritance, trade and agriculture.

It is also important to commend the Muslim mathematicians who came after al-Khwarizmi, who also publicized his work and presented evidence of its authenticity after the impact of his work on Europe.

His book was translated twice into Latin in the 12th century. Once by Robert Ochester of Great Britain and once by Gerard of Cremona, Italy.

His work was also known to Fabanachi, arguably the greatest mathematician of the Middle Ages. He also cites al-Khwarizmi’s work in his famous book, Labor Abachi.

Here we need to be careful that we do not attribute the credit for inventing a branch of mathematics to Al-Khwarizmi, simply because the name we use for it today, ‘Algebra’, is the name of Al-Khwarizmi’s book.

For example, there is evidence that Greek and Babylonian mathematicians were solving algebraic equations long before al-Khwarizmi. In addition, the great Greek mathematician Diafent and the Hindu mathematician Brahmagupta have also worked in this regard before him. Couldn’t the title of this sub-section have been attributed to his books? Not close to me This is because al-Khwarizi was of the opinion that his book was a guide according to which data could be changed through algebra. However, their purpose was bigger than that. He explained that the purpose of his book is to explain what is easiest and most useful in arithmetic, such as the need to deal with the judicial system in the process of distributing inheritance to men, trade, division of property.

Also transactions between them where land measurement, canal digging, geometric computing, and other such issues require mathematics. The book Algebra is divided into two parts. As a theoretical physicist, the first part contains very interesting material for me because here algorithms formulate the rules of algebra. And use different algorithms to solve queries and different equations. With each acquisition there is pictorial evidence of their answer.

The second part of the book is about the use of their methods by which they find solutions to everyday problems as mentioned above. However, this book is very different from the books we find today on algebra. Instead of flipping through the pages of his book with symbols and equations, he put it all in plain language.

This, of course, meant that what could have been said in two lines through the symbols of algebra was explained in a two-page explanation. If I were to tell you that long before Al-Khwarizmi, Diafants and Hindu mathematicians were explaining their equations with basic symbols, that Al-Khwarizmi and his algebra could not go beyond quadratic equations, that Diafents solved more complex problems. Searched, and Al-Khwarizmi’s methods of solving algebraic questions were also old, such as the method of solving ‘Computing the Square’, then the arguments in favor of them become obsolete.

I have also heard the argument that al-Khwarizmi’s popularity is due to the fact that his book popularized algebra because he made it so widely understood that many people could use it. However, this is a weak argument. We can also say that the reason for the fame of the famous modern scientist Stephen Hawkings is his book ‘A Brief History of Time’ and not his important research in cosmology and his theories about black holes. Contrary to all this, it does not matter who used the symbols, or whether there was any geometric evidence, how complex these equations were, and whether their writing reached the general public.

However, what Al-Khwarizmi did for the first time and what makes him look unique is a small thing but very important. That is, algorithms, instead of solving specific questions, have come up with common sense rules by which they can be solved, as well as solving equations in a phased manner, that is, through algorithms.

Al-Khwarizmi thus ensured that algebra could be viewed as a separate subject, not a technique for changing statistics.

It’s just that on the one hand you give specific examples and leave it up to the readers to conclude that this is the stage where they can solve other problems while on the other hand Al-Khwarizmi did this stage. Explained in common sense language. They later explain it, of course, with specific numbers, but the steps they take to solve it are considered common sense.

Although al-Khwarizmi explained algebra using words instead of symbols, which diaphragms had done before him.   Al-Khwarizmi’s algebra is very close to the algebra used today.

Al-Khwarizmi died in 858, but his place belongs to the mathematician who introduced the subdivision of mathematics in the presence of arithmetic and geometry.


George Sarton, the great scientist of the world of science, is famous for writing a multi-volume book, The Introduction to Science. In this book, he divides the history of science into several parts. Each part covers half a century, which is named after the most important scientist of that period.

It covers the period from 800 to 850 AD under the title “Al-Khwarizmi Period”.










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