The Role of Muslims in the Formation and Development of Sciences (Part 25)
Achievements of Muslim Scientists in the Science of Algebra
The Islamic lands were the center of scientific activities from the 2nd century AH to the 7th century AH (the 8th century AD to the 13th century AD). The most important scientific activities during this time were carried out in the “Bayt Al-Hekmah,” which was founded by Caliph Al-Ma’mun in Baghdad. In this center, Imam Al-Khwarizmi’s influence on mathematical thought surpassed that of any other mathematician in the Middle Ages. In the year 21 AH (825 AD), he discovered geometric and algebraic methods for solving first and second-degree equations with one or two unknowns.
Initially, Imam Al-Khwarizmi’s main motivation for inventing the science of algebra was related to the science of inheritance (known as the science of obligations). He presented algebraic methods to facilitate this branch of knowledge, which was difficult for some people. For this purpose, he wrote a famous book titled “Hesab Al-Jabr Wa Al-Moqabelah.”
Imam Al-Khwarizmi transformed numbers from their specific values into symbols that could replace different values. His book “Hesab Al-Jabr Wa Al-Moqabelah” is considered the first cornerstone of the science of algebra because he clearly understood that algebra should be completely separated from arithmetic, which had dominated mathematical sciences throughout the ages.
What is the meaning of “Jabr” and “Moqabelah”?
Muhammad ibn Musa Al-Khwarizmi defined “Jabr” as the transfer of a value from one side of an equation to the other by changing the signs; that is, he converted negative signs to positive and vice versa. “Moqabelah” means simplifying the resulting algebraic value by eliminating similar terms with opposite signs and combining terms with the same signs.
Another scholar with a strong influence in the field of algebra was Abul-Hasan Ali Qalsadi Al-Andalusia (813-891 AH/1410-1486 AD), who was a pioneer in using mathematical symbols. This is clearly evident in his book Kashf al-Mahjoob fi ‘Ilm al-Ghabar. Unfortunately, many Western scholars and their contemporary Arab followers mistakenly believe that “François Witte” (1540-1603 AD), a French mathematician, was the inventor of mathematical symbols and signs (+ , – , : , …). This overlooks the role of Muslim scholars in this field, as Qalsadi presented algebraic symbols in a very clear manner before Witte in his book Kashf al-Mahjoob fi ‘Ilm al-Ghabar.
One of the greatest achievements of Muslim mathematicians is the method of solving cubic equations by Omar Khayyam (436-517 AH). He solved these equations using conic sections. When Omar Khayyam examined cubic equations using parallel sections and circles, it became clear that he was discussing horizontal coordinates (sine coordinates) to interpret the coordinates of a point. Thus, Omar Khayyam actually laid the foundation stone of analytic geometry; a geometry that would later be attributed to the French scientist René Descartes (1596-1650 AD) and which is still taught in universities in Arab and Islamic nations today.
There is no doubt that René Descartes developed analytic geometry and established its principles, but this should not overshadow Omar Khayyam’s role as the original contributor to this science.
Muhammad ibn Musa al-Khwarizmi was also aware of imaginary numbers, which he referred to as “impossible states.” However, Western scholars claim that the first person to consider the concept of imaginary numbers was the Swiss mathematician Leonhard Euler (1707-1783 AD). Al-Khwarizmi clearly stated this in his book Hisab Al-Jabr wa Al-Muqabla: “Know that if you take half the value of the square root and multiply it by itself, and the result is less than the number that corresponds with the square root, then the problem will be impossible.”
Additionally, Arab and Muslim mathematicians were also interested in binomial theory (Za’at Al-Hadin). Abu Bakr al-Karkhi (d. 421 AH) presented a mathematical method for expanding the binomial equation, considering the squares of 1, 2, 3, 4, and 5. Then, Omar Khayyam confirmed this theory and extended it to positive integer squares. However, it was Ghiyath al-Din Jamshid Kashi (died 829 AH) who fully developed the binomial theory.
The Role of Arab and Muslim Scientists in Arithmetic
When Arab and Muslim scientists began their studies in arithmetic, they inherited knowledge from previous civilizations such as India, Greece, Persia, and others. They reached two fundamental levels in this field:
1. Dust Arithmetic: In this method, pen and paper were needed to perform calculations.
2. Air Arithmetic: In this method, calculations were performed mentally without requiring pen and paper. This type of arithmetic was particularly useful for merchants, travelers, and ordinary people who needed to perform financial calculations mentally.
Initially, Arab and Muslim scientists followed the Greek methods for the four basic operations (addition, subtraction, multiplication, and division), but they soon found these methods inefficient. For this reason, they made numerous improvements in this field, which are still recognized in modern mathematics today.
Muslim scientists introduced a new and straightforward method for performing addition, in which the digits kept in a separate row were placed above the sum. In the case of subtraction—which they called “Tafriq” (Tafraqa)—they initially used a method in which the number to be subtracted was positioned below the original number, and then the remainder was written down.
However, this method did not last long, and Arab and Muslim scientists developed a new approach in which the original number was written on top, the reduced number below it, and then the remainder. This is the method that continues to be used in mathematical calculations today.
