The article is devoted to the scientific and methodological analysis of one of the mathematical treatises of al-Khorezmi. In fact, this treatise by al-Khwarizmi, the original Arabic title of which sounds like “Kitab al-mukhtasar fi-hisab al-jabr wa al-muqabala” (“A short book of calculus al-jabr and al-alqabala”), is the pearl of world mathematics. Because this is the first textbook written for an algebra course in the whole world. In general, the contribution of Muslim peoples, including scientists from Central Asian countries, to the formation and development of mathematics in the 9th-16th centuries is enormous. The author of the mentioned treatise, al-Khorezmi, is a prominent representative of Central Asian mathematics of the 9th century (more precisely, he was born in the city of Khorezm, part of the territory of modern Uzbekistan). In this regard, in Soviet times there was a tendency to call all scientists in Central Asia Arab scientists. Unfortunately, this tendency still occurs in Western European scientific literature, which is based predominantly on a Eurocentric point of view. These points determine the relevance of the topic of the article from the point of view of the requirements of today, and it is necessary to remove the history of mathematics from such “whitewashing” and supplement it with new definitions in accordance with modern requirements. This is important not only for today, but also for the future. When writing the article, scientific research methods such as theoretical and historical-comparative analysis, systematization and structuring were used. The materials of the article can be used in the dissemination of the subject "History of Mathematics" for students studying in the educational programs "6В01501 – Mathematics", "6В01502 – Mathematics and Physics", "6В01503 – Mathematics and computer sciences” in pedagogical higher educational institutions.