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| Muḥammad ibn Mūsā al-Khwārizmī |
Al-Khwarizmi's discussion was confined to the equations of the first and second degrees. His work mainly focused on time, astronomy, calculating exact positions of the Sun, Moon and the other planets. He also worked on calculating the tables of sines, cosec and tangents, astrological tables, reason behind eclipse and their calculations, periodic visibility of the moon.
As written by E. F. Robertson and J. J. O'Conner in their book, MacTutor History of Mathematics archive "One of the most significant advances made by Arabic mathematics began with the mathematical study and research of al-Khwarizmi, namely the beginning of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move in real senseand much differ from the concept of mathematics adopted by Greeks. They (Greeks) mainly worked on geometry.
Al-Khwarizmi research was a unifying theory which allowed geometrical magnitudes, irrational numbers, rational numbers, etc., putting them under a single category of "algebraic objects". His work gave mathematics a new look if compared to that which had existed before, and became a tool for future development of maths." They further wrote "Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before."
Al-Khwarizmi supervised the work of seventy geographers and they successfully created a map of the then “known world”. When his work became popular in Europe through Latin translations, his popularity made a permanent mark on the development of science in the Western world.
Al-Khwarizmi also influenced the proper use of the term "algorithm". His name (al-Khwarizmi) was Latinized as "algorism" and later used to refer to the art of counting and calculating. Al-Khwarizmi also worked on astronomical tables and later wrote a book on the same subject. Some of his books were translated into Latin in the l2th century by Gerard and Adelard. A book on algebra, Al-Maqala fi Hisab-al Jabr wa-al-Muqabalah and a treatises on Arithmetic Kitab al-Jam'a wal-Tafreeq bil Hisab al-Hind are available only from Latin translations. It was this later translation which introduced the new science to the West "unknown till then." These books were used until the sixteenth century as the main mathematical books in European universities. The astronomical tables which he prepared were also translated into Chinese and many other European languages.
