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The origin of x in maths
I’m still wrestling with the fallout from marking exams. Despite this, I found time to watch a short TED video posted recently that features Terry Moore explaining why x is used as an unknown in mathematics. Watch the video – only 4 minutes – or jump to the spoilers below if you want to know more.
The main idea is that the we use x because the Spanish used
(chi) as the first sound of the Arabic word for “something” because they couldn’t say the correct “sh” sound. I recollect a similar argument made somewhere else with slightly different details, though, sadly, I cannot remember them precisely, nor their location. I was unable to track down references at the time to verify this argument and so dismissed it as a Just So Story. Since it has resurfaced it would be interesting to see evidence. Does anyone know of any?
My reason for asking is that I’ve spent the last few years learning about Greek mathematics and I am interested in how it has been transmitted to us via the Arabic scholars and scientists. So far I’ve only read the popular accounts, Science and Islam: A History by Ehsan Masood and Pathfinders: The Golden Age of Arabic Science by Jim Al-Khalili. The latter is good but spends the first few chapters explaining the history of Islam and various empires. Furthermore, one of the first bits, maybe the first bit, of science to be explained in depth is Eratosthenes’ measurement of the Earth, i.e., a high point of Hellenistic science. Obviously providing a context is important in a book but I still feel as though I don’t know much about the science from the Arabic world between the end of the Greek era and the beginning of the Renaissance. Currently I’m not sure where to look next for more information so suggestions for new leads are welcome.
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Hi, There is an interesting book for You . Le soleil d Allah brille sur l Occident , written by the great german historian Sigrid Hunke . I don t know if it is translated in english, but you’ll find a lot of knowledge about this great civilisation that is Islam and the Arabo-persian. Especially in science . And thanks a lot for your wisdom about mathematician’s thinking . Your book is a guide for my studies. Greeting from an arabic who was born in France !
This talk contains some misinformation.
The link between the algebraic “x” and Arabic _shay’un_ (‘thing’) is fascinating, but Moore’s version of it is more complex than it needs to be. The Latin (not Greek) letter “x” was used freely in the manuscripts of Old Spanish (say, 10th to 15th century), and expert opinion is pretty unanimous that its pronunciation was practically equivalent to English “sh”, and likewise equivalent to Arabic ش (shīn). There was no need to import a Greek letter, and no problem for medieval Spanish-speakers to pronounce the “correct” sound.
The statement that “Spanish doesn’t have that ‘sh’ sound” is correct with regard to Modern Spanish, but Old Spanish did have such a sound, and it matched Arabic shīn in many loanwords. Since the Middle Ages, that sound, and its spelling, have evolved into what we now have in, for example, the modern name “Javier” (formerly “Xavier”). The Aztecs were sometimes known as “Meshika”, and their country, Mexico, has kept the old spelling with X.
The link between the algebraic “x” and “thing” is, however, supported by the Wikipedia article “History of algebra”, which refers to something called “rhetorical algebra” (in ancient Babylonia), in which statements were given in words rather than symbols, and an example is “the thing plus one equals two”.
Arabic _shay’un_, without its grammatical ending, would be _shay_, and likely spelled _xay_ if it appeared in Old Spanish, but I have not yet found it in the handful of Old Spanish dictionaries and glossaries that I’ve consulted.
P.S.: The fact that René Descartes introduced the use of “x” in algebra is well-documented. The idea that it came from Arabic through Spanish is not. Medieval Arabic culture contributed important things to today’s mathematics, but not this one.