In this TED Talk, the speaker says that the use of X for unknown quantities was the result of Spanish people taking the Arabic word shay (meaning "thing"), which was used by Arabs to denote unknown quantities, and representing it by the Greek letter kay (χ) since they didn't have the "sh" sound.

But this article asserts that its unlikely to be true. What's the more trustworthy opinion?

1 Answer 1


Most likely no. X is one of many symbols used for unknowns throughout the history of mathematics, and comes from a notation in the 1600's that used several other letters alongside X. Some Arab mathematicians used the Arabic word for 'thing' to represent an unknown, however it was several hundred years between that and X becoming popular, with many other unrelated symbols in between.

Florian Cajori's History of Mathematical Notation, which can be read here, goes into detail about early symbolism used for unknowns in page 395*:

Brahmagupta and Rhsskara did not confine the symbolism for the unknown to a single sign, but used the names of colors to designate different unknowns. The Arab Abu Kami (about 900 A.D.), modifying the Hindu practice of using the names of colors, designated the unknowns by different coins, while later al-Karkhe (following perhaps Greek source) called one unknown "thing", a second "measure" or 'part', but had no contracted sign for them. Later still al-Qalasbdf used a sign for unknown.

So, at least some Arab mathematicians were using 'thing' and other signs for unknowns, however, according to Cajori, there is no evidence to suggest that 'thing' became X through Greek letters:

There is nothing to support the hypothesis on the origin of x due to Wertheim namely, that the Cartesian x is simply the notation of the Italian Cataldi who represented the first power of the unknown by a crossed "one," thus X. Nor is there historical evidence to support the statement found in Noah Webster's Dictionary, under the letter x, to the effect that "x was used as an abbreviation of Ar. shei a thing, something, which, in the Middle Ages, was used to designate the unknown, and was then prevailingly transcribed as xei."

X became a popular symbol for unknowns in the 1600's, as a result of its use in René Descartes' notation:

The use of z, y, x . . . . to represent unknowns is due to Rene Descartes, in his La geometrie(1637). Without comment, he introduces the use of the first letters of the alphabet to signify known quantities and the use of the last letters to signify unknown quantities... In equations, in the third book of the Geometrie, x predominates. In manuscripts written in the interval 1629-40, the unknown z occurs only once. In the other places x and y occur.

Cajori does not know for sure why X was more popular than z and y, but he does offer some theories, such as that X was simply a more common letter at the time and thus easier to print:

Enestrom, on the other hand, inclines to the view that the predominance of x over y and z is due to typographical reasons, type for x being more plentiful because of the more frequent occurrence of the letter x, to y and z, in the French and Latin language.

Regardless of why X became the most popular symbol, it's clear that there were several hundred years between the Arab use of 'thing' as an unknown and the European use of X. In between, a wide variety of other notation was used, implying that any connection is unlikely at best:

Luca Pacioli remarks that the older textbooks usually speak of the first and the second cosa for the unknowns, that the newer writers prefer cosa for the unknown, and quantita for the others. Pacioli abbreviates those co. and fla. Vieta's convention of letting vowels stand for unknowns and consonants for knowns was favored by Albert Girard, and also by W. Oughtred in parts of his Algebra, but not throughout. Near the beginning Oughtred used Q for the unknown. The use of N (numem) for x in the treatment of numerical equations, and of Q, C, etc., for the second and third powers of x, is found in Xylander's edition of Diophantus of 1575, in Vieta's De emendatione aequationum of 1615, in Bachet's edition of Diophantus of 1621, in Camillo Glorioso in 1627. In numerical equations Oughtred uses 1 for x, but the small letters q, c, qq, qc, etc., for the higher powers of x. Sometimes Oughtred employs also the corresponding capital letters.

*The book itself is organized by paragraphs, not pages. I reference the page in the PDF of the book for easier reference, but what I quote is in paragraphs 339-341.

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