Math Tutor – Algebra – X Marks the Spot: A Closer Look at Everyone’s Favorite Variable

The Purpose of X

Algebra is the type of mathematics in which equations are used to define relationships between things that vary. In an equation, a variable is used to represent the unknown quantity. These variables can represent tangible things, such as the number of apples that can fit in a bin based on the container’s dimensions. They can also be used to answer mathematical questions, such as what number can be multiplied by seven to get 21; that equation would be written as 7x = 21.

Any letter or symbol can act as the variable in an algebraic equation, yet x is most commonly used. In textbooks, classrooms and throughout the world, x has become the standard-bearer. While its role is firmly entrenched, its origins are more ambiguous.

From the Roots of Algebra

There are differing accounts of the origin of the variable x. The oldest and most credible story traces its roots back to the early days of algebra in the Middle East. Muhammad Al-Khwarizmi, who lived from approximately 780 to 850, was a prominent mathematician in the House of Wisdom in Baghdad. He quite literally wrote the book on algebra, Kitab al-Jabr wal-Muqabala, which roughly translates to ‘the book of calculation by completion and reduction.’ The term ‘algebra’ originates with ‘al-jabr,’ from Al-Khwarizmi’s book title.

Though Al-Khwarizmi’s book on algebra was written in prose, it laid the foundation for solving algebraic equations. Since these equations involve variables, the origin of x has been linked to the Arabic language. In Arabic, the word for an unknown thing or object is ‘shei.’ Translated into Greek, the word becomes ‘xei.’ It has been hypothesized that the shortening of this word to x explains the origin of the popular variable.

An Unclear Unknown

There is still debate about the origins of x as a variable. While it may have come from the Middle East, it may also have begun in Greece. The Greek word for unknown, stranger or foreigner is ‘xenos.’ Abbreviating ‘xenos’ to x is a possible alternate history. There are other theories as well. Though they may only be conjecture, they offer an insight into the practical nature of using x.

For example, one theory posits that x was originally used as a variable as a result of the difficulty with using ancient writing implements. Algebra began in an era before pencils or ballpoint pens. When people wrote by dipping feathers into ink, it was easiest and cleanest to use a symbol like x. While this theory may sound plausible, like the many others, it may never be known precisely how x came to be algebra’s favorite variable.



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Stuart Raffeld

B. A. Operations Research & Statistics, California State University, Long Beach, Teaching Assistant undergraduate Mathematics. B.S. Mathematics, California State University, Long Beach. Mathematics University of California, Irvine, Teaching Assistant undergraduate Mathematics. Completed course work for MS Degree with 4.0 GPA. M.S. Mathematics, Kingsbridge University. Transcript available upon request. 1988-Present: Mathematics tutoring--One on one tutoring for SES students through YP institute and Academic advantage. Tutored students with low learning skills as well as very bright students. Tutored groups of four students in math classes from basic mathematics through calculus. Mathematics teaching for EFN, Inc., a private school.

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