The "lost" Islamic library that created modern mathematics

Centuries ago, a prestigious Islamic library brought "Arabic numerals" to the world. Although this library disappeared long ago, the revolution it brought about in terms of mathematics and numbers changed our world.

The name "House of Wisdom", which was carried by a library established during the Abbasid Caliphate era, seems imaginative, especially since there is no trace now of this ancient library that was destroyed in the thirteenth century AD, which makes it impossible for us to determine its exact location. or shape and design.

However, the ambiguity surrounding this library does not negate that it was a major intellectual beacon in Baghdad during the golden age of Islamic civilization, and that it also represented the cradle of concepts related to mathematics, such as mathematical conversion, zero, as well as our "Arabic" numbers used today. .

In the beginning, the "House of Wisdom" library was established as a place to preserve the collection of books belonging to the caliph Harun al-Rashid in the late eighth century AD, and then, about 30 years later, it turned into a scientific edifice that everyone could visit. At that time, it seemed that this edifice was attracting scholars from all over the world to Baghdad, thanks to the vibrant atmosphere of scientific and intellectual curiosity that prevailed there, as well as the freedom of expression that the city enjoyed. Within its borders, Muslim, Christian and Jewish scholars were allowed to conduct their research without discrimination.

With an enormous archive that was comparable in size to its current counterparts in the British Library in London, or the National Library in Paris; The House of Wisdom eventually became an unparalleled center for the study of the sciences in general and the humanities in particular, including mathematics, astronomy, medicine, chemistry, geography, philosophy, literature and the arts, along with such dubious subjects as alchemy and astrology.

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Apart from imagining the shape of this great edifice, requiring one to give free rein to one's imagination, it is certain that the "House of Wisdom" was heralding a cultural renaissance that would completely change the course of mathematics. This library was destroyed during the Mongol siege of Baghdad in 1258. According to legends circulating in this regard, a large number of manuscripts that were contained in it were thrown into the Tigris River, which led to its waters turning black because of the ink. Despite this, the discoveries witnessed in the corridors of this library included important mathematical concepts, which were then celebrated by the Islamic nation, then Europe, and eventually the entire world.

Jim Al-Khalili, a physicist at the University of Surrey in Britain, says: "We should not focus our attention on the minute details of the place or time in which the 'House of Wisdom' library was built.. The most important thing is the history of scientific ideas themselves, and how they developed. these ideas."

Tracking the legacy of that library in the field of mathematics requires some time travel, but in a way, like "back to the future". For hundreds of years, until the decline of the Italian Renaissance, there was one name synonymous with mathematics in Europe, and that is Leonardo Pisano, who was given this name in relation to his city of Pisa, and was known after his death as Fibonacci. This man was born in Pisa in the year 1170, and received his basic education in the Algerian coastal city of Bejaia. And when he was in his early twenties, he visited other countries in the Middle East, and he fascinated us with ideas related to mathematics, which then moved from India west through Persia. When he returned to Italy, Fibonacci published Liber Apache, one of the first Western books on the Indo-Arab numeral system.

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When the book first appeared in 1202, the Indo-Arabic numerals were known to a limited number of intellectuals, and European merchants and scholars were still clinging to Roman numerals, which made multiplication and division very tedious. Hence, the Fibonacci book showed how to use numbers in calculations, through methods that can be applied to practical matters such as determining the profit margin, interest rate, currency exchange rate, weight conversion, and so on.

In the first chapter of this encyclopedic work, the Italian mathematician wrote, saying that those who want to know "the art of arithmetic, its accuracy and creativity, must learn how to count on the fingers of their hands," referring to the numbers from one to nine that children learn. At school. Fibonacci went on to say in his book, "With these nine numbers and the 0 sign called zero, any number can be written whatever it is." And so mathematics suddenly became available to everyone, in a form that everyone could benefit from.

Fibonacci's genius was not only in his creative abilities as a mathematician, but also in his keen understanding of mathematical concepts known to Muslim scholars for centuries, such as arithmetic equations, the decimal system, and ink science. In fact, Liber Apache relied almost entirely on concepts developed by the ninth-century Arab mathematician Al-Khwarizmi. The "revolutionary thesis" that this man formulated - for the first time - provided a systematic method for solving quadratic equations. Thanks to his achievements in this regard, Al-Khwarizmi is often referred to as the “founder of the science of algebra.” Indeed, this science is known in the English language by its same Arabic name, and also by the same spelling (Al-Jabr). In 821, he was chosen to be an astronomer and assigned the responsibility of running the House of Wisdom.

Jim Al-Khalili explains that Al-Khwarizmi's findings in mathematics led to the definition of the decimal number system in the Islamic world. It also helped others, including Leonardo Pisano, "transmit that knowledge to various parts of Europe".

Fibonacci therefore owes a great deal to Al-Khwarizmi, with regard to his legacy of transformations in modern mathematics. This means that an ancient library such as the "House of Wisdom" brought together two men separated by a period of time of nearly four centuries, which makes us say that Fibonacci; The most famous mathematician of the Middle Ages, he was standing almost on the shoulders of Al-Khwarizmi, another of the pioneers of this science; He achieved his achievements on that path, within one of the most prominent scientific edifices of the golden age of Islamic civilization.

The "House of Wisdom" library has acquired a legendary status, which contradicts in some way the meager historical records that we have left about it, because historians tend to exaggerate the scope within which this library operated and the functions it performed, due to the lack of sufficient information in this regard.

In this context, Al-Khalili says: "Some say that the 'House of Wisdom' was not as luxurious as many people imagine it to be. But the association of this library with men like Al-Khwarizmi and what he did in the sciences of mathematics, astronomy and geography, is evidence for me." Incidentally, it was more like a real scientific academy than just a repository for translated books.

But the matter was not limited to the connection of that library with eminent personalities such as Al-Khwarizmi. The scholars and translators who worked in it, in turn, made strenuous efforts to ensure that their works reached the reach of readers. John Barrow-Green, Professor of Mathematics History at the Open University in the United Kingdom, says that the “House of Wisdom” library is of fundamental importance, given that it witnessed the translations carried out by Arab scholars of Greek concepts related to mathematics, which formed “the cornerstone of our understanding of this science.” ". In this sense, that ancient library represented a window on the ancient Greek numeral system, as much as it was at the same time a bastion of scientific innovation.

Long before the discovery of the decimal number system we currently use, the binary number system with which our computers are programmed, as well as before the discovery of Roman numerals, or the arithmetic systems used by the inhabitants of ancient Mesopotamia, humans used primitive methods to perform calculations. Although we may now find these methods inaccurate or outdated, we remain able to draw lessons from them regarding human relations and the historical and cultural contexts that emerged from them.

These ancient methods reinforce, for example, the idea of ​​abstraction, and explain the concept of the difference in the value of a number according to the box in which it is placed, and whether it is placed in the tens, hundreds, or thousands box, for example. All of this helps us to better understand how numbers work. Barrow-Green says that these various methods show us "that the Western method (of arithmetic) was not the only one, and that there is real value in understanding different arithmetic methods."

Among the methods that prevailed in this regard in the past, referring to the available number of something, by drawing this thing for times equal to that number. For example, when the old merchant wanted to indicate that he had two sheep, he could draw on the clay a picture of two sheep. But that would have been impractical, if he wanted to talk about 20 sheep, for example. This ancient method of calculation continued, in some form, through Roman numerals, even though Al-Khwarizmi developed his own system in this regard, which relied on the placement of the number and its digit, to indicate the quantity it expresses. Like the monuments and towering edifices in which they are carved, Roman numerals outlived the empire under which they were born. No one knows for sure whether this happened by chance, or by virtue of an emotional connection, or if there was some function to those numbers.

As this year marks the 850th anniversary of Fibonacci's birth, threats to what remains of the legacy of Roman numerals lie ahead. In the United Kingdom, for example, the traditional clocks, which were placed in the classrooms, known as "analog clocks", were dispensed with and replaced by digital clocks that facilitate the recognition of the time through them. This step was taken for fear that students would not be able to recognize In some parts of the world, authorities no longer use Roman numerals on road signs or official documents, and Hollywood has stopped using them to write the titles of different parts of films.

Lucy Rycroft-Smith, head of the Cambridge Mathematics website, says: “Our Western colonial heritage inevitably influences the nature of the (historical) stories we tell, and the identity of the culture we identify with. It also determines what kind of knowledge we have. We give it the character of continuity and eternity, by including it in the curricula of formal education.”

Rycroft-Smith, a former mathematics teacher, is studying the differences between approaches taught around the world. While regions such as Wales, Scotland and Ireland do not include knowledge of Roman numerals among the goals of their educational systems, and in the United States there are no uniform requirements in this regard, the education system applied in England stipulates that students must be able to read these numbers from zero to 100.

For this reason, many of us may not find any special meaning for a Roman numeral such as MMXX, but in any case it means 2020, which is the year we currently live in. On the other hand, we may have to acknowledge Fibonacci's credit for mathematics, in connection with his invention of the famous numerical pattern known by his name, which is called the "Fibonacci sequence", which is an iterative sequence, starting with the number 1, and each number in it is equal to the sum of the two numbers preceding it .

There is no doubt that this "Fibonacci sequence" is noteworthy in every sense of the word, as it appears to us with surprising frequency in the nature that surrounds us, starting with the shape of seashells, passing through the appearance of mutated leaves - one of which is known as "tentilage" - and existing In some species of climbing plants, down to the number of windings around the head of the sunflower plant, as well as the shape of animal horns, and the arrangement of the buds on the stems of the plants. This sequence has invaded the digital world as well, as you can find it in computer science, as well as it has found its way, to include multiple aspects of popular culture, such as literature, cinema, visual arts, and architecture. One can even sense its presence in the "chorus" of the words of a particular song, or the note of an orchestral group.

However, it is remarkable that the most enduring contribution of "Leonardo Pisano" in the field of mathematics, which is related to his transfer of the Indo-Arabic number system to Western culture, is rarely included in the curricula of children in schools. And the Italian mathematician accomplished this, through a journey that began in an ancient library that appeared about a thousand years ago, when most parts of Western Christendom were shrouded in intellectual darkness. It is a story that should lead to undermining our vision of mathematics, as a science in which Europe played the central role on the one hand, and should shed light - on the other hand - on the scientific achievements of the Islamic world. This story is also suitable, in order to form a basis through which we can confirm that the knowledge that man reached about numbers and mathematics many centuries ago is of continuing importance.