المؤتمر الأول للاكاديمية الدولية لتاريخ العلوم اليونان- اثينا- 12-15 ايلول/سبتمبر 2019 العلم في الثقافات والحضارات المختلفة العلم في الحضارة العربية الاسلامية البروفيسور الدكتور محمود الحمزة

 

The 1-st conference of the International Academy of the History of Science

Athens, Greece, 12-15 September, 2019

“Science in different cultures and civilizations”

 

About mathematics in the Arab-Islamic civilization

Prof. Mahmoud al-Hamza

Moscow

 

World culture went through several stages, and it reached, at different times, the development of mankind, certain successes. Arab-Islamic civilization has strengthened in world history as an integral part of world culture. Ancient civilizations like Babylonian, Egyptian, Chinese, Indian and Greek made significant contributions to the accumulation of new scientific knowledge and cultural heritage. Of course, Greek science stands out here, and especially mathematics and philosophy. The famous works of Greek scholars and philosophers, translated into Arabic since the 8th century, have created a solid foundation for Arab scholars in the assimilation of this knowledge, their commentary and the advancement of new scientific theories and ideas.

The Arab scientific heritage, together with the translated works of Greek scholars, became the property of European scholars beginning in the 12th century. (translated in Latin). All this confirms the globality and unity of science, the creation of which was attended by different peoples in the East and in the West.

In this work, I focused on the main achievements of the development of mathematics during the period of Islamic civilization, based on the idea that Arabic mathematics is an integral part of mathematical science.

The main features of Arabic mathematics in the period of 8-16 centuries, which was written in Arabic – as the main language of science of that time – are as follows:

– Arabic science was formed on the basis of ancient sciences, through translation into Arabic, which was the language of modern science of that time. Some important features of Arab science can be noted as: 1- the global character of Arab science (a new feature in world science), 2- new mathematical thinking and 3- the use of the experimental approach as a method of proof (Rashed).

– Representatives of different nations and religions participated in the creation of Arab science, and this is the power of science and its universality.

– Arab scientists proceeded from the fact that it is necessary to critically study the heritage of previous scientists and continue these studies and correct inaccuracies or create new directions in science.

– Arab science, as a whole, developed as a continuation of ancient science and, according to the prominent historians of science, significant progress has been made in various fields of science, and especially mathematics and astronomy.

– It is necessary to recall the Arabic term Al-Jabr (Algebra), which was introduced for the first time by the great mathematician of the Middle Ages, Mohammad bin Musa Al-Khorezmi (8th century) in his book “The Art of al-Jabr and al-Mukabala” where this the term and then began to designate the whole mathematical science (algebra) in all languages ​​of the world. Another important mathematical term is “Algorithm”, which was produced on behalf of Al-Khorezmi when translated into Latin.

– One of the main successes of Arab mathematicians in the Middle Ages was the arithmetization of algebra, which the Greeks predominantly geometric.

– In the 10th century, combinatorics was first used to compile an Arabic dictionary (Al-Farahidi).

– Al-Biruni and others found a numerical solution to the cubic equations.

– It is known that decimal fractions were first used by ibn al-Samawal (12th century), although for a long time it was believed that al-Qashi was the first to introduce decimal fractions.

– Ibn Al-Samawal also knew the decomposition of binomial (binomial) to the nth degree (now known as Newton binomial), and in his manuscript was written the triangle of coefficients of binomial decomposition (now known as Pascal’s triangle)

– O. al-Khayyam et al. Used geometric methods (using conical section methods) in solving cubic equations.

– Ibn Kurra and Ibn al-Haytham calculated the area and volume by methods close to modern integration methods.

– In the works of Sharaf al-Din al-Tusi, approaches were applied similar to the concept of the derivative in the study of polynomials and for finding the maximum and minimum points (research by R. Rashed)

– Algebraic symbolism was invented and used to describe algebraic equations. This was with Ibn al-Yasimin (12th century). Although some historians believed that Al-Kalasadi (15th century) was the first in this matter.

– In the mathematics of the western part of the Islamic world (Morocco and Andalusia) scientific results were obtained on the topic “rules of two false positions”, which they called the “rule of the scales” and got some parallel to this rule with the structure of physical scales. On the other hand, we note the connection of this rule of weights with algebraic linear equations.

– The trigonometric methods with which scientists operated as part of astronomy were transformed into an independent science.

– Special attention was paid to the development of spherical trigonometry.

– Arab mathematicians made significant progress in defining the concept of a real number, Ibn al-Baghdadi (12th century) examined the tenth book of Euclid and commented on it, where he made the transition from the concept of number as geometric to number as arithmetic and, thus, clearly and mathematically operated with irrational numbers (which were considered by Euclid as geometric quantities). Ibn al-Baghdadi also gave an abstract definition of number, close to the modern philosophical definition (B. Russell). Finally, a hypothesis was put forward on the density of uncountable numbers on a line (which was rigorously formulated several centuries later).

– Important attempts were made to study the fifth postulates of Euclid (axiom of parallel), especially in the writings of Nasir al-Din al-Tusi (13th century), whose work was translated into Russian by Kazim Bek Zade for the great Russian mathematician, the creator’s hyperbolic version of non-Euclidean geometry in the first half of the 19th century).

In this work, we also studied the main reasons for the decline of Arab science (which developed successfully in the Middle Ages of the 8-14 centuries) and examined an important scientific, historical and philosophical question: why did not Arab science, which was several centuries old, turn into a classical science, created later in Europe.

The problem of freedom of scientific search and its manifestation in the Middle Ages and in the present was also studied in this work. Especially about the connection between science and religion.

This work included the main results obtained in my studies on the history of Arabic mathematics in the Middle Ages, and which were published in various journals and were presented at various international conferences during my work at the Institute of the History of Science and Technology named after S. Vavilova , RAS in Moscow (2002-2016) and still.

The work also pays special attention to the role of Russian historians of Arab science, such as A. Yushkevich, B. Rosenfeld, G. Matvievskaya and M. Rozhanskaya (with the latter I had the honor to collaborate for 12 years), who made a huge contribution to the study of scientific Arabic manuscripts and gave an objective scientific assessment of Arab science in general and Arab mathematics in particular.