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The term algebra comes from the arabic term àl-jàbrà that means "to force", "to restore". Over centuries mathematicians, in east and west, celebrate by this term mathematical disciplines.

What is the mathematical intuition behind this term ("to force", "to restore") and modern derivatives such as in abstract algebra and algebraic geometry?

Append found the following information: In Arabic, al- is the definite article "the." The first noun in the title is jebr "reunion of broken parts," from the verb jabara "to reunite, to consolidate." The second noun is from the verb qabala, with meanings that include "to place in front of, to balance, to oppose, to set equal." Together the two nouns describe some of the manipulations so common in algebra: combining like terms, transposing a term to the opposite side of an equation, setting two quantities equal, etc. Because the original Arabic title was so long, and because it was in Arabic, Europeans soon shortened it. The result was algeber or something phonetically similar, which then took on the meanings of both nouns and eventually acquired its modern sense...

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  • $\begingroup$ I am confused about what is being asked. Are you asking about the arabic word, or about modern abstract algebra and algebraic geometry, or both, or is there supposed to be some connection between these? $\endgroup$
    – Jonas Meyer
    Aug 7, 2013 at 7:45
  • $\begingroup$ The question shall be clear as the answers came well, it is about the mathematical intuition behind these terms of to force and to restore wherever/whenever we apply the term algebra - e.g. algebra, abstract algebra, algebraic geometry... what/how do we force or restore in the mathematical context? $\endgroup$
    – al-Hwarizmi
    Aug 7, 2013 at 8:07
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    $\begingroup$ There seems to be a presumption that the literal meaning of the original word has bearing on how it is applied in modern mathematics, which is what confuses me. Thank you for elaborating. $\endgroup$
    – Jonas Meyer
    Aug 7, 2013 at 8:09
  • $\begingroup$ What's the particular problem or theorem you want to prove? We probably could say that algebra helps us to force some theorems, and oftentimes enables us to restore simpler forms. $\endgroup$
    – Doug Spoonwood
    Aug 7, 2013 at 14:07
  • $\begingroup$ @DougSpoonwood the question is not about a theorem. It refers clealry to terminology (tag) and math history (tag) and History and development of mathematics (topic). $\endgroup$
    – al-Hwarizmi
    Aug 8, 2013 at 18:04

2 Answers 2

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"The word “algebra”—al jebr in Arabic—was first used by Mohammed of Kharizm, who taught mathematics in Baghdad during the ninth century. The word may be roughly translated as “reunion,” and describes his method for collecting the terms of an equation in order to solve it. It is an amusing fact that the word “algebra” was first used in Europe in quite another context. In Spain barbers were called algebristas, or bonesetters (they reunited broken bones), because medieval barbers did bonesetting and bloodletting as a sideline to their usual business. The origin of the word clearly reflects the actual context of algebra at that time, for it was mainly concerned with ways of solving equations. In fact, Omar Khayyam, who is best remembered for his brilliant verses on wine, song, love, and friendship which are collected in the Rubaiyat—but who was also a great mathematician—explicitly defined algebra as the science of solving equations."

(it's from the book - "A Book of Abstact Algebra" by Charles C. Pinter).

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  • $\begingroup$ Excellent! Thanks! $\endgroup$
    – al-Hwarizmi
    Aug 7, 2013 at 14:22
  • $\begingroup$ don't mention it :D $\endgroup$
    – Eli Elizirov
    Aug 8, 2013 at 7:12
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    $\begingroup$ @EliElizirov: His name is Mohammad Al-Kharazmi and he was an Persian person who was teaching Algebra via Arabic language. Also, Omar Khayyam was another Persian one. :-) $\endgroup$
    – Mikasa
    Aug 9, 2013 at 21:18
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From Wikipedia (or rather, its citation of "The Arabic Hegemony" by Carl Boyer):

The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation.

Other uses of the word algebra or its root simply stem from this original use (just like things involving the word geometry no longer actually have to be about measuring the earth).

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