Why is the letter X used to represent the unknown?

The letter ‘X’ has taken on a new meaning in recent days, with the rebranding of the social media giant formerly known as Twitter. 

For centuries, however, humans have used the letter to represent an unknown quantity; as a variable in mathematics, to describe confidential “X-files”, or even to mark the spot on (imaginary, revisionist) treasure maps. The unpredictable nature of Twitter under Elon Musk continues that trend. 

Rene Descartes letter x
Engraving of René Descartes, circa 1834. Descartes lived From 1596 Until 1650.

The use of ‘X’ to represent an unknown is believed to date back to the work of French philosopher and mathematician René Descartes. It is said that while working towards his 1637 treatise, La Géométrie, he decided to use the final three letters in the alphabet – X, Y, Z – to represent unknown variables.

Because they were more commonly used in the French language, the Ys and Zs kept running out of ink when Descartes set the type on his printer. X became his primary variable, with the mystery around the letter intensified further by how unusual it was in French. 

x-ray letter x
Circa 1940, a doctor holds up an x-ray of a patient’s chest. (Photo by FPG/Getty Images)

While this may seem confined to solving mathematical equations, by 1895 the decision of Descartes was shaping other technology that is commonplace today. 

German physicist Wilhelm Röntgen is credited with the discovery of a new kind of radiation. He made the breakthrough accidentally (like the first song ever recorded) while serving as a Professor of Physics in Wurzburg, Bavaria. While experimenting, he realized that certain rays of light could pass through substances while leaving behind a shadow of solid objects. Not knowing what these rays were called, he crowned them “X-rays” – now a crucial piece of medical technology.

Descartes is not universally considered the first proponent of X as the unknown. Another theory, posited in a TED talk by Terry Moore, director of the Radius Foundation, gives X a different origin.

letter x unknown quantity

He believes that it dates back to early 11th and 12th century Spanish translations of Arabic scholars, who invented algebra. According to Moore, “al-shalan” translates to “unknown thing” in Arabic, and was often used in early Arabic calculations. 

Moore proposes that because Spanish translators had to corresponding “sh” sound, they opted for “ck” instead. In classical Greek, the “ck” sound is represented by the chi symbol – X. When the work was in turn translated into a common European language, they replaced the Greek chi with the Latin X. 

It’s an interesting theory, but there is no known historical evidence for Moore’s claims. 

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