Wednesday, November 12, 2014

Why We Use "X" as the Unknown in Math

"For hundreds of years, x has been the go-to symbol for the unknown quantity in mathematical equations. So who started this practice?" according to Melissa, writes for the website TodayIFoundOut.com.

 Photo: Gizmodo

Algebra was born in the Middle East, during the Golden Age of medieval Islamic civilization (750 to 1258 AD), and its early form can be seen in the work of Muhammad Al-Khwarizmi and his 9th century book, Kitab al-jabr wal-muqabala (al-jabr later morphing into algebra in English). During this heyday, Muslim rule and culture had expanded onto the Iberian Peninsula, where the Moors encouraged scholarship in the sciences and math.

So what does this have to do with the letter "x" in math? In a recent TED talk, the director of The Radius Foundation, Terry Moore, posited that the the use of "x" in this way began with the inability of Spanish scholars to translate certain Arabic sounds, including the letter sheen (or shin). According to Moore, the word for "unknown thing" in Arabic is al-shalan, and it appeared many times in early mathematical works. (For example, you might see "three unknown things equals 15," with the "unknown thing" then being 5.)

But since Spanish scholars had no corresponding sound for "sh," they went with the "ck" sound, which in classical Greek is written with the chi symbol, X. Moore theorizes, as many others before him have done, that when this was later translated into Latin, the chi (X) was replaced with the more common Latin x. This is similar to how Xmas, meaning Christmas, came about from the common practice of religious scholars using the Greek letter chi (X) as a shorthand for "Christ."

The principle problem with Moore's explanation is that there is no direct documented evidence to support it. More speculatively, people translating the works would not care about phonetics, but the meaning of the words. So whether they had a "sh" or not one would think would be irrelevant. Despite the lack of direct evidence and flaws in the argument, it nonetheless remains a very popular origin theory, even among many academics. (Do a quick Google search and you'll find many a PhD in mathematics parroting this theory.)

The 1909-1916 edition of Webster's Dictionary, among others, also puts forth a similar theory, although stating that the Arabic word for the singular "thing," "shei," was translated into the Greek "xei," and later shortened to x. Dr. Ali Khounsary also notes that the Greek word for unknown, xenos, also begins with x, and the convention could simply have been born of an abbreviation. But here, again, we have a lack of any direct documented evidence to support these theories.

As for a documented theory, we turn to the great philosopher and mathematician, René Descartes (1596-1650). It's entirely possible Descartes did not come up with the practice of using "x" for an unknown, perhaps borrowing it from someone else, but at least as far as documented evidence that has survived to today goes, he seems to be the creator of the practice, as noted by the OED and the phenomenal work by Florian Cajori, A History of Mathematical Notations (1929). At the least, Descartes’ helped popularize the practice.