The Role of Muslims in the Formation and Development of Sciences (Part 33)
Abul-Futuh Omar Khayyam
He was “Abul-Futuh Omar ibn Ibrahim Khayyam Nishapuri,” who lived between 436 and 517 AH (1044 to 1123 AD). As a child, he worked in the profession of making and selling tents, which is why he received the title “Khayyam.” From an early age, Omar Khayyam dedicated most of his time to the pursuit of science and knowledge, ultimately settling in Baghdad in 466 AH (1074 AD).
Omar Khayyam became renowned in many scientific fields, including mathematics, astronomy, language, jurisprudence, history, and literature. Although he gained great fame for his quatrains, which have been translated into various languages in verse and prose and can be found in libraries worldwide, he also made significant achievements, particularly in the field of algebra. He innovated geometric methods for solving cubic equations that had not been previously addressed.
Additionally, he played a crucial role in generalizing theories related to limits and powers, which is why he is often regarded as the originator of binomial theory. The quatrains of Omar Khayyam captured the attention of many Western scholars, earning praise both philosophically and literarily for their specific themes about life and its pleasures, encouraging people to enjoy the fleeting nature of existence. However, some historians believe these quatrains were mistakenly attributed to Omar Khayyam, suggesting they may have been written by others or associated with him due to his fame in mathematics and astronomy.
When examining the life of Omar Khayyam, a distinctly different person emerges from the “Khayyam of the quatrains,” who is often depicted as indulgent in worldly pleasures and seemingly lost on the path to guidance. In various translations of his life, Khayyam appears as a great and distinguished scholar who enriched science and contributed significantly to humanity.
Historians across different fields agree that Omar Khayyam was one of the greatest Arab and Muslim poets in both Arabic and Persian; however, there is little reference to his connection with the quatrains. Recent studies indicate that many of these quatrains do not genuinely belong to Omar Khayyam but rather to other poets. The Russian researcher Zhukovsky has identified 82 quatrains along with their original authors, although a few remain whose identities are still undetermined.
Omar Khayyam achieved remarkable results in solving cubic equations, a major advancement recognized as one of the most outstanding achievements not only among Arab and Muslim scientists but also globally, even to this day. He did not confine himself to the development of algebra alone; he was also particularly interested in incorporating algebra into trigonometry. Consequently, he solved many complex problems in trigonometry using algebraic equations of the third and fourth degrees.
Khayyam also paid considerable attention to astronomy. In 471 AH (equivalent to 1078 AD), he calculated the length of the solar year with remarkable accuracy: 365 days, 5 hours, 49 minutes, and 5.75 seconds. His precise observations led to an error of only one day in five thousand years, whereas the Gregorian calendar currently used worldwide has an error of one day in 3,330 years.
Khayyam’s interests extended wide. He conducted a thorough study of the principle of the equilibrium of liquids, which was a critical topic of his time, solving numerous complex problems that had stumped Arab and Muslim scientists in this vital field.
Omar Khayyam considered geometry a fundamental area in the study of any branch of mathematics. For this reason, he focused heavily on the study of Euclidean geometry, which Arab and Muslim scientists had explained and interpreted. He also paid special attention to the “parallel hypothesis” (the fifth postulate of Euclid), which Thabit ibn Qurra (221-288 AH) and Hasan ibn Haytham (354-430 AH) had attempted to prove. Khayyam provided a new and unique proof in this domain, although this hypothesis still remains unproven to this day.
Khayyam can thus be regarded as one of the founders of a school of algebra. He studied algebraic equations of the first, second, third, and fourth degrees with remarkable precision, depth, and originality. Notably, he was the first to theorize that third-degree algebraic equations have two roots and to present mathematical methods for calculating square and cube roots. This legacy is evident in the book “Jami’ al-Hisab Be Al-takht Wal-Torab” by Nasir al-Din al-Tusi (597-672 AH), which incorporated the ideas of Omar Khayyam.
Khayyam conducted a scientific investigation into algebra and made significant innovations, particularly in cubic equations, where he identified geometric roots, though he primarily approached numerical solutions for positive roots.
