Algebra, restoration, and strength

It’s well-known that the word algebra comes from Arabic, but pursuing the origin in more detail reveals some interesting connections. The term comes from Persian mathematician Muhammad ibn Musa al-Khwarizmi, who made numerous contributions to mathematics during the Golden Age of Islamic Golden Age of the 9th and 10th centuries, and whose surname gives us the word algorithm.

The word comes from the title of a mathematical treatise by al-Khwarizmi entitled ٱلْكِتَاب ٱلْمُخْتَصَر فِي حِسَاب ٱلْجَبْر وَٱلْمُقَابَلَة‎ (al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah), or The Compendious Book on Calculation by Restoration and Balancing. The root jabar meant “to restore” or “to set a bone”, and still has that sense in modern Arabic.

al-Khwarizmi meant restoration in the following sense. Consider the equation $$x - 1 = 3.$$ In order to resolve this equation, one can move the $-1$ from the left to the right side by adding $ +1 $ to both sides, thus “restoring” the natural order of the equation.

The same root exists in Hebrew for words having to do with strength (setting a broken bone means restoring its strength, after all). Thus we have the words גבר (gever) man (particularly connoting a strong man) and גיבור (gibur) hero. There’s another word for man, איש (ish) referring to men or people more generally. The biblical name גבריאל (Gabriel) has the same origin, literally meaning God is my strength.