# What Is Algebra?

But when we come to the end of our arithmetic we do not content ourselves with guesses; we proceed to algebra -- that is to say, to dealing logically with the fact of our own ignorance. ... Instead of guessing whether we are to call it nine, or seven, or a hundred and twenty, or a thousand and fifty, let us agree to call it The Arabs had some cousins who lived not far off from Arabia and who called themselves Hebrews. A taste for Algebra seems to have run in the family. Three Algebras grew up among the Hebrews. I should think they are the grandest and most useful that ever were heard of or dreamed of on earth. Mary Everest Boole |

*Algebra* is a branch of mathematics that deals with properties of operations and the structures these operations are defined on. *Elementary Algebra* that follows the study of arithmetic is mostly preoccupied with operations on sets of whole and rational numbers and solving first and second order equations. What puts elementary algebra a step ahead of elementary arithmetic is a systematic use of letters to denote generic numbers.

Mastering of elementary algebra which is often hailed as a necessary preparatory step for the study of Calculus, is as often an insurmountable block in many a career. However, the symbolism that is first introduced in elementary algebra permeates all of mathematics. This symbolism is the alphabet of the mathematical language.

The word "algebra" is a shortened misspelled transliteration of an Arabic title *al-jebr w'al-muqabalah* (circa 825) by the Persian mathematician known as al-Khowarismi [Words, p. 21]. The *al-jebr* part means "reunion of broken parts", the second part *al-muqabalah* translates as "to place in front of, to balance, to oppose, to set equal." Together they describe symbol manipulations common in algebra: combining like terms, moving a term to the other side of an equation, etc.

In its English usage in the 14^{th} century, *algeber* meant "bone-setting," close to its original meaning. By the 16^{th} century, the form *algebra* appeared in its mathematical meaning. Robert Recorde (c. 1510-1558), the inventor of the symbol "=" of equality, was the first to use the term in this sense. He, however, still spelled it as *algeber*. The misspellers proved to be more numerous, and the current spelling *algebra* took roots.

Thus the original meaning of *algebra* refers to what we today call *elementary algebra* which is mostly occupied with solving simple equations. More generally, the term *algebra* encompasses nowadays many other fields of mathematics: geometric algebra, abstract algebra, boolean algebra,

### References

- S. Schwartzman,
*The Words of Mathematics*, MAA, 1994

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