Question’s in the title. I have a few WAGs:
It has some significance due to its resemblance to the letter Chi in the Greek alphabet.
There are very few English words that start with “x” (in general, I think it’s the rarest letter), so it is unlikely to be confused as an initial for something.
It’s the coolest-looking letter, so mathematicians chose it to complement their swagger.
I stand to be corrected, but ‘z’, ‘j’, and ‘q’ are all less frequent (in English, at least).
In his 1637 work La Géometrie, Descartes introduced the convention of using the first letters of the alphabet (a, b, c) for known quantities and the last letters (x, y, z) for unknown quantities. (This isn’t the strictly first instance; Descartes had in fact used x as an unknown quantity in some earlier works, even before fixing this convention. But the usage of x does appear to begin with Descartes)
Wikipedia says:
“Another key event in the further development of algebra was the general algebraic solution of the cubic and quartic equations, developed in the mid-16th century. The idea of a determinant was developed by Japanese mathematician Kowa Seki in the 17th century, followed by Gottfried Leibniz ten years later, for the purpose of solving systems of simultaneous linear equations using matrices. Gabriel Cramer also did some work on matrices and determinants in the 18th century.
The symbol x commonly denotes an unknown variable. Even though any letter can be used, x is the most common choice. This usage can be traced back to the Arabic word šay’ شيء = “thing,” used in Arabic algebra texts such as the Al-Jabr, and was taken into Old Spanish with the pronunciation “šei,” which was written xei, and was soon habitually abbreviated to x. (The Spanish pronunciation of “x” has changed since). Some sources say that this x is an abbreviation of Latin causa, which was a translation of Arabic شيء. This started the habit of using letters to represent quantities in algebra. In mathematics, an “italicized x” () is often used to avoid potential confusion with the multiplication symbol.”
I find that a dubious hypothesis. At any rate, my source is “A History of Mathematical Notation” by Cajori, via this site and others.
The x is not italicized to avoid confusion with times. All variables are in italics and all constants are supposedly in roman. But more recently, this convention appears to have become that single characters in equations, even the constant e, are always in italics, while multicharacter identifiers, such as sin, Hom, log, are in roman. That way, you can distinguish sin from sin, since mathematicians almost invariably use juxtaposition to denote multiplication.
I would have assumed that X being used for an unknown quality came from use outside mathematics. An X is a fairly good way of marking a point while making it large enough to be seen, and thus is used on maps. It wouldn’t take much from X marking the spot to X representing whatever was found there, something that is different on every map just like x represents a different number in each equation.
Here is a cite for the alternative explanation (from PBS):
Yeah, some people say it, but some other people, myself included, find it dubious. Where is the evidence? At any rate, the Oxford English Dictionary says
Rigamarole was referring to initial letters. There might not be very many English words starting with Z, J, or Q, but there are almost none starting with X.
Why do you ask?
I am in the process of reading thisbook in which the author backs up Descartes as the originator of "x/y/z"as unknowns.
But he also includes an anecdote that credits Descartes’ printer with the choice of X as the first choice. The story goes that the printer asked which of last letters in the alphabet he should use, and Descartes said he didn’t care. As a result the printer used X as he was running out of letters and X was the most infrequently used.