The First Mathematical Book in the Golden Horde State: A Masterpiece of Computational Mathematics (“et-Tuhfe fî ilmi’l-hisâb”) (1) - Ihsan Fazlioglu (Золотоордынское обозрение)
The author of this article represents the first example of the scientific activity in the Golden Horde, which began before Janibeg khan and during the reign of his father, Uzbek khan. The composition entitled “Masterpieces in Computational Science” (“et-Tuhfe fî ilmi’l-hisâb”), written in the Golden Horde on a mathematical topic, occupies a special place because of the information contained therein. This treatise, the contents of which will be described below, shows us the following: scientific activity in the Golden Horde, which began with the adoption of Islam, brought results in a short time and laid the foundations for the “breakthrough” during the reign of Janibeg khan. In the future, the author plans to explore and learn the value of the text for the mathematical sciences from a historical point of view: the computational book “et-Tuhfe fî ilmi’l-hisâb”, whose author is unknown, was handed to the Crimean Governor and right hand’s bey, Ebul-Muzaffer Giyaseddin Tuluktemir bey, during the reign of Uzbek khan (1313–1342). After mentioning the distinguishing features of the work, the author will focus on the definition of numbers, which is attributed to Muhammad b. Musa Al-Khwarizmi, and which, at the moment, is not recorded in any other sources. The author will test ability to understand the evidence used in the calculation, surveying, and algebra, and will consider definitions regarding the theory of numbers. Subsequently, the author will analyze the formula of approximate values of square and cube roots of irrational numbers, proposed by Mohammed al-Khwarizmi, Abdulkadir al-Baghdadi, and a teacher of the author, Saduruddin al-Farazi. In the first chapter, “Scientific and Philosophical Life in the Golden Horde State” (discussed in detail in this article), the author presents a brief description of the political, economic, and social life in the ulus of Jochi, to proceed to the consideration of the progress of scientific life developed in close connection with Islamic culture since the time of the formation of the Golden Horde. The author presents the writing under consideration in the context of this broad topic, briefly describing its contents. The purpose of this paper is to define scientific environment, which made possible the writing of the “et-Tuhfe fî ilmi’l-hisâb”.