The character “x” has symbolized unknown variables in mathematical functions for thousands of years. So where did this character come from and when did it start being used?
We encounter the letter X in many areas of life. X is commonly used to represent an unknown value in mathematics or to denote something mysterious, such as case X, award X, issue X, etc.
But why is it specifically the letter “X” and not any other character or symbol?
One widely accepted hypothesis among scholars is that the letter “x” originated from language differences during the translation of foundational Arabic mathematical documents. This principle was later popularized by mathematician Descartes and has since become a standard convention. So, what’s the truth behind this story? Let’s find out.
Language differences in translating foundational Arabic mathematical documents gave rise to the letter “x”
Hypothesis: No Corresponding Sound
Algebra emerged in the Middle East during the golden age of Islamic civilization (from 750 to 1258 AD), with the earliest mathematical works compiled in the 9th century. During this flourishing period, Islamic teachings and civilization spread to the Iberian Peninsula (now Portugal and Spain). Here, Muslims began teaching various sciences, including mathematics.
An Arabic mathematical document from the Islamic civilization
So, what does this have to do with the letter “x” in mathematics? According to some researchers, the letter “x” was created because Spanish scholars could not translate certain sounds from Arabic. The term “unknown” in Arabic is “al-shalan.” This term appeared frequently in the earliest mathematical documents. As there was no corresponding sound in Spanish for “sh,” Spanish scholars replaced it with “sk.” This sound comes from ancient Greek and is represented by the character X (the letter “chi.”)
Scientists hypothesize that the character X was then translated into Latin and replaced by the more common letter x. This is similar to the origin of the term Xmas, where scholars used the letter X (chi) in Greek as an abbreviation for “Christ.”
However, these explanations are based on hypotheses and speculation without concrete evidence. Furthermore, translators of mathematical works typically focused on conveying meaning rather than pronunciation. Thus, whether there is an “sh” sound or not does not necessarily relate to the letter “x.” Nevertheless, many scholars, including mathematicians, accept this argument.
The 1909-1916 version of the Webster Dictionary, along with other dictionaries, uses a similar hypothesis to explain the origin of the letter “x” in mathematics. Although in Arabic, the word “thing,” “shei” in the singular was translated into Latin as “xei” and later shortened to “x.”
Some opinions suggest that in Greek, the term for unknown is “xenos,” which starts with the letter x, so the abbreviation may stem from there. However, that argument also lacks concrete evidence.
Additionally, experts believe the letter “X” was established by the renowned mathematician Descartes.
Descartes’ Random Choice?
René Descartes (1596-1650), author of the famous mathematical work La Géométrie, used the letter x as a variable, applying it widely to this day
In the following era, the character “x” continued to receive indirect support from the famous philosopher and mathematician René Descartes (1596-1650). While Descartes did not explicitly set the standard, in his works, especially La Géométrie (published in 1637), he used letters from the beginning of the alphabet (like a, b, c,…) to represent known values and letters from the end (like x, y, z,…) for unknown values (variables).
A published edition of Descartes’ La Géométrie
At this point, you may wonder why y and z aren’t as popular as the variable “x”? No one knows for sure. A tale suggests that the printer of La Géométrie proposed that the character “x” was used the least, and that’s also the letter he had the most engravings of. This story has yet to be substantiated, but in handwritten documents prior to La Géométrie, Descartes had used “x” as a variable. Furthermore, Descartes was not too rigid; he used the three letters x, y, z to represent both variables and known values. This further casts doubt on the accuracy of the hypothesis regarding the “absence of sound when translating from Arabic.”
Therefore, it is possible that Descartes simply chose letters for his own convenience. Nevertheless, one thing is certain: after the publication of La Géométrie, using letters a, b, c to denote known numbers and x, y, z for variables became a convention accepted to this day.
References: Gizmodo, Muslimheritage, Exzuberant, Wiki
