The Role of Muslims in the Formation and Development of Sciences (Part 32)
Abu Bakr Al-Karkhi
Another skilled thinker and scholar who made significant contributions in the fields of mathematics and experimental sciences was Imam Abu Bakr Al-Karkhi. He played a fundamental role in the sciences of arithmetic and algebra, which are important branches of mathematics.
Getting to Know Him
He is “Abu Bakr Muhammad ibn Al-Hasib al-Karkhi,” who was born in “Karkh,” a suburb of Baghdad. The exact date of his birth is not known, but he died in Baghdad in 421 AH (1020 AD). His extensive scientific output took place in Baghdad during a period when the city was known as a thriving scientific center in the late 4th century AH and early 5th century AH (late 10th century and early 11th century AD).
Al-Karkhi paid special attention to the sciences of arithmetic and algebra, writing a book on arithmetic in which he did not use conventional numbers but rather utilized the arithmetic of sentences (using letters of the alphabet to represent numbers). This method was prevalent among Arab and Muslim scholars for a long time, as they assigned specific numbers to each letter of the alphabet. His book, “Al-Fakhri in Algebra,” is based on “Al-Jabr wa Al-Muqabelah” by Muhammad ibn Musa al-Khwarizmi (164-235 AH) and “Al-Kamil in Algebra” by Abu Kamil al-Misri (236-318 AH). Al-Karkhi followed the analytical method in algebra established by his predecessors, al-Khwarizmi and Abu Kamil al-Misri. Consequently, “Al-Fakhri in Algebra” contains innovative ideas that had not been addressed before him, showcasing the originality of al-Karkhi’s thought.
Abu Bakr Al-Karkhi intended to repay part of the favor that his friend, the minister Abu Ghalib Muhammad ibn Khalaf, known as Fakhr al-Mulk, had shown him. Fakhr al-Mulk was the minister of Sultan Baha al-Dawlah ibn ‘Azd al-Dawlah Buyid. Thus, he titled his book “Al-Fakhri in Algebra” in honor of his close friend Abu Ghalib. This work can rightfully be considered a source of pride for the Arab and Islamic nations, as it embodies originality, depth, and innovation in the field of algebra. Therefore, Abu Bakr Al-Karkhi’s “Al-Fakhri in Algebra” can be seen as a true measure of scientific progress and intellectual creativity in the field of algebra within Arab and Islamic culture.
Al-Karkhi spent a significant portion of his life in mountainous regions, which contributed to his proficiency in geometry. This expertise is evident in his famous book “Hall Al-Hafr Aba’ar,” which remains one of the important sources and references in applied geometry.
Among the mathematical ideas that al-Karkhi used or invented in his works are the following: 1. A number whose square is added to itself results in a square, and whose square is subtracted from itself also results in a square. 2. Two numbers whose cubes sum to the square of a third number. 3. Development of a general law for solving quadratic equations. 4. Improvement of the famous law for finding the approximate root of numbers whose roots cannot be calculated. 5. Derivation of a new law for finding the square root. 6. Invention of methods for adding and subtracting irrational numbers. 7. Modification of Heron’s Law (150 AD) for finding the area of a triangle based on its sides. 8. Systematic study of algebraic quantities with different bases. 9. Detailed exploration of numerical, geometric, and comparative sequences.
Unfortunately, most of Al-Karkhi’s scientific works have been lost, and only a few have survived. Moreover, many contemporary Western scientists have attributed some of his inventions to themselves. For example, the theory stating that the sum of two cubic numbers can never be another cubic number is often wrongly attributed to the French scientist Pierre Fermat (1601-1766 AD). This claim is inaccurate, as the foundational theory is indeed present in al-Karkhi’s works—Fermat made some modifications in its proof.
Al-Karkhi was an Arab and Muslim scholar who detested copying and translating texts; instead, he focused on compiling, analyzing, and explaining the works of others. He left no subject unexplored or undeveloped. He was an experienced scholar and a systematic encyclopedia. Hence, when he wrote about a subject, he explained it clearly and simply for the reader.
By 
