# On the origin of $$x$$

Recently I had the opportunity to watch Why the $$x$$ is Unknown TED talk from Terry Moore but I soon realized after talking to a colleague that the explanation Terry gives is much too simplified.  Since there are cultural aspects to this question I’ve asked my colleague Carmen for her opinion.  Have a listen in.

Carmen,

In case you have not seen it, have a look at Terry Moore’s lecture on the origins of the mathematical $$x$$ and tell me what you think.  Briefly, Terry argues that the $$x$$ is unknown because you cannot say ‘SH’ in Spanish.

The argument goes something like this.  Terry points out that the Persians, Arabs and Turks worked all this out in the first and second century of the common era (CE) and that the arabic texts containing the mathematical wisdom made their way to Spain in the 11th and 12th centuries. One of the difficulties in translating this material was that many of the sounds in Arabic cannot be easily handled by the Spanish voice box. For example, the ‘SH’ sound and in particular the word referring to ‘an unknown thing – al-shalan’ which as you can imagine is rife in these texts. According to Terry, the solution was to borrow the ‘CK’ sound from classical Greek by using the chi symbol $$\chi$$. When the material was translated from Spanish into Latin (the common European language) the $$\chi$$ became the Latin $$x$$.

My basic problem with this reasoning is that the translators don’t need to translate the sound ‘SH’ in arabic. They are translating concepts and not sounds. If the term al-shalan is the concept ‘a unknown thing’ then why not use the Spanish phrase ‘una cosa desconocida’? Also there was a huge upheaval in Christianity at this time from what I can gather. Have a look here and notice that the medallion at the top of the page has that $$\chi$$ symbol.  Can you give me some insight?!?

Sean,

When you first sent me the link to this video I was expecting a much more robust explanation of the use of $$x$$.  My preliminary thoughts were that we were about to discover another connection between your discipline and mine.  Instead, I felt as though the speaker had not only oversimplified the reasoning but had omitted so many obvious connections.

I will openly admit my knowledge of the history of mathematics and algebra is limited, but there are some historical influences from my studies which may have also impacted the $$x$$.  The time period that algebra was being developed is known as the Abbasid age.  This time period is known as the Golden Age for the medieval Islamic civilization (750-1258 C.E.).  Many classical institutions and ways of thinking were developed and perfected.  This period saw the rise of a new Persian literature where stories such as Aladdin, Sinbad and Arabian Nights were created.  Great progress was also made in the fields of science, mathematics and medicine, with Ibn Sina (Avicenna), a Persian scholar whose treatise on medicine was still used as a medical textbook in the 18th century.

This Golden Age was based on many different factors.  The Muslims were following the words of the Prophet to study and search for knowledge.  The Qur’an itself promoted the pursuit of knowledge “The scholar’s ink is more sacred than the blood of martyrs” and the Prophet had said “For every disease, Allah has given a cure.”   The fact that the Muslim Empire covered a large geographic area, it became easier for scholars to travel throughout the lands and to share ideas.  As the books of many other cultures (Egyptian, Hebrew, Greek, Indian etc.) were being translated into Arabic, this eased the ability for the Muslim scholars to learn others’ ideas.   After learning how to produce paper and books from the Chinese, books became more available to the Muslim scholars and libraries were created in Cairo, Aleppo, Baghdad and other urban centres within the Muslim Empire.  In 1004 C.E. a “University” was created in Baghdad called The House of Wisdom.

During the Abbasid age, great translation projects were undertaken to learn Greek philosophy and science.  The texts written in both Greek and Syric were translated into Arabic.   Many of the achievements for this Golden age were based on the initiatives of the ancient Egyptians, Hebrews, Persians, Greeks and Romans… which were being translated by the Muslims in Baghdad.  Simultaneously the rulers in Islamic Spain were trying to surpass the scholars in Baghdad and were also making significant progress in the areas of science, medicine, technology and philosophy based on the texts they were translating from other cultures as well.

Carmen,

What’s the point here?  Don’t take offense but OMG humanities people are verbose!

Sean,

The point of this historical lesson is that the influence of other cultures on the development of Arabic mathematics and algebra is far reaching indeed.  Perhaps the $$x$$ was developed from the influence of other cultures, and NOT from the Spanish attempting to translate a similar sounding word.  This is a very interesting article on the development of math during the Muslim era and the influence of other cultures on their developments in science and maths.

Now, as a religious studies student I would be remiss not to discuss $$x$$ and its importance in religion.  When I first watched this video, I was expecting a reference to god being the unknown… ergo the $$x$$.  I was sorely disappointed.  I am pretty sure everyone has heard of the “War on Christmas” and how offensive some find the use of the term “X-Mas”.  Where does this $$x$$ come from:  Greek language.   The $$x$$ is Greek letter for $$\chi$$, an abbreviation for Christos, the Messiah. There is also a Hebrew letter $$X$$, which is pronounced Taw. Taw was used as a symbol on the foreheads of those who were righteous and followed Yahweh, the $$X$$ soon became a symbol for Yahweh.  Interestingly enough the Hebrew Taw translates in meaning to one of the definitions of the Greek $$\chi$$.  God is often expressed in Islam and Christianity as something unknown.  I wonder if there was a correlation to the Chi or Taw when trying to express an unknown factor within maths?

Carmen,

What is your brief answer as to why $$x$$ is the unknown then?

Sean,

Overall I think that the explanation provided by the TedX speaker seems to overlook many of the cultural aspects of the time period, as well as the incredibly important influence religion had on these cultures.  Personally I would love to find the correlation between these aspects and the $$x$$ in mathematics.  My best guess is that the $$x$$ is a result of translators using their comtemporary cultural symbol for a profound unknown.  It was basically staring them back in the face in the source documents that were surrounding them.

### 4 thoughts on “On the origin of $$x$$”

1. Too bad that Terry Moore is wrong and the modern use of X in mathematics comes from its use by Descartes in his book “Géométrie“, in 1637. He made the decision to use lowercase letters from the beginning of the alphabet for known quantities and lowercase letters from the end of the alphabet for unknowns. This is generally accepted among historians of mathematics. No european mathematical work used X as unknown before Descates introduced it.

Sad… but all you conversation comes from beautiful legend and misinformation.

• Dear Math Guru and Sean,

Basically the letter x originated from persian. It originates from Omar Khayyam’s work on cubic equations. For the unknown variable Khayyam used the word “shay” which means “thing”.
The andalusian ommayads (basically muslims in Spain.) this word was written as “xay” with the spanish alphabet. After a while only the first letter of this word (x) was used to represent the unknown in equations. Therefore use of x as the unknown became popular. The “y” and “z” came after that.
Considering Khayyam lived around 1100’s I am pretty sure Descartes and mathematicians before him were already using x.

On a further note the word Algebra also originates from a persian mathematician Abdallāh Muḥammad ibn Mūsā al-Khwārizmī’s book “Kitab al-jabr wa al-muqabalah”. Al-jabr roughly translates to “the synthesis”

• Which is why Mr Moore is a hit on TED and all the rest of you are not. He in interesting, keep it simple and, in context, uncommonly accurate.

2. In 1505, Pedro de Alcalá—a linguist, not a mathematician—published a book (De lingua arabica) in Spanish about the Arabic language. Instead of using Arabic script, he transcribed Arabic words in the Roman alphabet. In the glossary, the Spanish word “cosa” (“thing”) is matched (correctly) with the Arabic word that Alcalá transcribed as “xei”. This is a fairly good approximation of Arabic شىء (pronounced somewhat like English “shy” or “Shay”), given that Old Spanish had an “sh” sound that was routinely written as “x”. (Terry Moore was unaware of this fact; evidently he was also unaware that in pronouncing “al-shay-un” he was combining the Arabic definite article with the indefinite suffix.)
In 1883, Alcalá’s work was edited and published by Paul de Lagarde—an “orientalist”, not a mathematician. Evidently Lagarde was aware that Arab mathematicians used that word for the unknown quantity in algebra, and in 1884 he published a speculation that “x” in algebra might have been an abbreviation of the Old Spanish transcription of the Arabic word. That charming theory caught on. Evidently Lagarde was not aware that Spanish mathematicians never used a _transcription_ of the Arabic word—instead, they used the _translation_ in their own language, “cosa”.
Today most historians of mathematics agree that Descartes originated the use of “x” arbitrarily, and first published it in 1637. They would have to revise that belief if an earlier published instance came to light; but so far, no such evidence has been found.