Algebras: Old and new and their use (Q1910120)

In the author's opinion algebra has always been geometrically. It started with the work of Arabic mathematicians like al-Khwarizmi, Tabit ben Qurra and Omar Khayyam and it was born ``from the need to solve definite practical geometric and accounting problems''. In order to verify his assertion the author sketches some facts of the history of algebra. He follows the adoption of mathematical results from the Arabs since the 13th century and stresses the history of the theory of equations as well as the emergence of complex numbers. The article is closed by enumerating important inventions like \(n\)-dimensional vector spaces, matrices, groups and spinors.