The mathematics practised and taught in the Arabo-Islamic world covered a great variety of subjects. From the 9th century onward, several texts were devoted to the "science of restoration and comparison" (‘ilm al-jabr wa al-muqābala). This science, whose first word gave rise to the term "algebra", was not yet a discipline but rather an "art", with its own specific rules and methods and its own body of typical problems. In classifications of the sciences, algebra was often regarded as a sub-branch of the science of computation (‘ilm al-ḥisāb), and its objects could be numbers, quantities or concrete objects involved in a calculation.
Al-Zanjānī and the algebraic tradition ------------------------------------------
Among the works written in the 13th century was the book Balance of the Equation in the Science of Algebra and al-Muqābala. Written by the Persian mathematician al-Zanjānī, this ten-chapter treatise is devoted to algebraic computation. Little is known for certain about al-Zanjānī's life. A native of the Zanjān region, he is said by bio-bibliographers to have travelled and spent part of his life working in Tabriz with the celebrated mathematician and philosopher Naṣir al-Dīn al-Ṭūsī. Al-Zanjānī's name is associated with a very diverse body of work, encompassing both literary and scientific texts. Some sources attribute these writings to a single person, while others suggest that there were two scholars, perhaps a father and son.
Al-Zanjānī is credited with an arithmetic book entitled The Support of Arithmeticians, transmitted as a companion volume to Balance of the Equation, two other arithmetic texts (an epistle and a treatise on "mental calculation", see the article), a geometry book and a book on the construction of the astrolabe. It is important to remember that, in this context, arithmetic encompassed a highly diverse range of approaches to computation and number theory. Master calculators such as al-Zanjānī made precisely this diversity the key to developing algebra: they studied numbers and operations to identify arithmetic methods that could be adapted to algebra, and vice versa. This approach was already typical of the earliest algebraic texts by al-Khwārizmī and Abū Kāmil. Around the year 1000, the mathematician al-Karajī ushered in a new phase of this tradition by addressing:
• elementary arithmetic and algebraic operations, the extraction of square roots and certain arithmetic theorems;