# Why is the letter "x" used to denote unknown numbers in mathematics?

For thousands of years, the letter “x” has been used to denote unknown numbers in mathematical functions. So where did this character come from and when did it start being used?

We encounter the letter X in many areas of our lives. X is defaulted to be the letter used to refer to an unknown in mathematics or to refer to an unknown mysterious thing or event such as X file, X prize, X problem etc..

So why not any other character or drawing that defaults to “X”?

One theory accepted by scholars is that the language difference in the translation of the original Arabic mathematical documents gave birth to the letter “x” . Later, this principle continued to be popularized by the mathematician Descartes and became the common standard today. So what’s the story? Please find out.

Language differences in the translation of the original Arabic mathematical documents gave birth to the letter “x”

Algebra was born in the Middle East during the golden age of Islamic civilization (the Middle Ages from 750 to 1258 AD) and the first forms were compiled into mathematical works in the 9th century. During this golden age, Islamic canon law and civilization were spread to the Iberian peninsula (now the territory of Portugal, Spain,…) Teaching science subjects including Mathematics.

An Arabic math document from Islamic civilization ​

So what does that have to do with the “x” in math? According to some researchers, the “x” was born because Spanish scholars were unable to translate some sounds from Arabic. Accordingly, the word “unknown” in Arabic is “al-shalan”. This is the term used extensively in the early mathematical literature. Since there is no sound corresponding to “sh” in Spanish, the Spaniards used “sk” instead. This is a sound in Ancient Greek and is represented by the letter X ( “chi “).

The scientists theorized that the X continued to translate into Latin and was replaced by the more common x. This is similar to the origin of the word Xmas, where scholars use the shortened Greek X (chi) in place of the word “Christ” .

However, the above explanations are based on hypothesis and speculation without concrete evidence. Moreover, translators of mathematical works will often not focus on pronunciation, but only on conveying the meaning of words. Therefore, whether there is a “sh” sound or not has nothing to do with the letter “x” . However, many scholars including mathematicians still accept this argument.

In Webster’s 1909-1916 edition and some other dictionaries, a similar hypothesis is used to explain the origin of the letter “x” in mathematics. Although in Arabic the word “th”, the singular “shei” was translated into Latin as “xei” and later shortened to “x” .

Some argue that in Greek, the hidden word is written as “xenos” , starting with the letter x, so the abbreviation may also originate here. However, that is also a baseless argument.

In addition, experts also believe that the letter “X” is conventionalized by the famous mathematician Descartes.

René Descartes (1596-1650), the author of the famous mathematical work La Géométrie, used the letter x as an unknown number and widely applied to this day​

In the next era, the letter “x” continued to receive indirect support of the famous philosopher and mathematician, René Descartes (1596-1650). Although Descartes did not directly prescribe it, in his works and most famously La Géométrie (published in 1637), he used the first letters of the table (such as a, b, c, …) to indicate known values and the last letters of the table (such as x, y, z, …) to indicate unknown values (unknown numbers).

An edition of Descartes’ La Géométrie​

At this point, you will ask, why are y, z not as popular as the unknown “x” ? No one knows that. One story goes that it was Descartes’ printer of La Géométrie who suggested that the letter “x” was the least used and that it was also the letter for which he had the most number of inscriptions. The above story is still unsubstantiated, but in handwritten documents before La Géométrie was born, Descartes used “x” as an unknown. At the same time, Descartes is not too rigid, he uses all 3 letters x, y, z to represent both unknowns and known values. This further casts doubt on the accuracy of the “no sound in Arabic translation” hypothesis.

It is possible, therefore, that Descartes simply chose the letters at will for his convenience . In any case, it is certain that after La Géométrie was published, it became common practice to use the letters a, b, c for the known number and x,y,z for the hidden. and is accepted to this day.

References: Gizmodo, Muslimheritage, Exzuberant, Wiki​