Where does the word “algebra” come from? Its origin is linked to a single work and a single author, and it tells us a great deal about what solving an equation really means.
History — al-Khwārizmī and the birth of algebra
The word “algebra” derives directly from the title of a work written around AD 820 in Baghdad by Muḥammad ibn Mūsā al-Khwārizmī: al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala (“The Compendious Book on Calculation by Restoration and Reduction”). The term al-jabr (“restoration”) refers to the operation of transferring a subtracted term from one side of the equation to the other, changing its sign — exactly what we do today when applying the first principle of equivalence. Al-muqābala (“reduction”) is instead the cancellation of equal terms on the two sides.
al-Khwārizmī did not use symbols: all his equations were written in words. Yet he demonstrated systematically how to solve first- and second-degree equations, classifying them into six canonical types (to avoid negative coefficients, which were not yet accepted). The term “algorithm” too derives from the Latinisation of his name (Algoritmi) (Berggren, 2003, ch. 1).
Links
Topics: First-degree equations
Concepts: Equation · Principle of equivalence
People: al-Khwārizmī