The Algebra of Mohammed Ben Musa

Mohammed Ben Musa (Abu Abdullah Mohammad Ibn Musa al-Khawarizmi) (c. 790-840) – mathematician, astronomer and geographer – is generally considered the “Father of Algebra.” Not only did he initiate the subject of algebra in a systematic form but he also developed it to the extent of giving analytical solutions of linear and quadratic equations, which established him as the founder of Algebra. The name algebra was derived from his famous book Al-Jabrwa-al-Muqabilah. His arithmetic synthesized Greek and Hindu knowledge and also contained his own contribution of fundamental importance to mathematics and science. He explained the use of zero, a numeral of fundamental importance developed by the Arabs; he developed the decimal system so that the overall system of numerals, algorithm is named after him. In addition to introducing the Indian system of numerals (now generally known as Arabic numerals), he developed at length several arithmetical procedures, including operations on fractions. It was through his work that the system of numerals was first introduced to Arabs and later to Europe, through its translations in European languages. He developed in detail trigonometric tables containing the sine functions, and also perfected the geometric representation of conic sections and developed the calculus of two errors, which practically led him to the concept of differentiation. He is also reported to have collaborated in the degree measurements ordered by Mamun al-Rashid were aimed at measuring of volume and circumference of the earth. The development of astronomical tables by him was a significant contribution to the science of astronomy, on which he also wrote a book. The contribution of Mohammed Ben Musa to geography is also outstanding, in that not only did he revise Ptolemy’s views on geography, but also corrected them in detail as well as his map of the world. His other contributions include original work related to clocks, sun-dials and astrolabes.