• # Why do we use "X" in mathematics as an unknown variable?

Have you ever noticed why we use X as an unknown variable in solving equations?

In algebra, we solve equations and most of the time we are asked to find the value of X when there is one unknown variable. When there is more than one variable we use letters Y and Z. Why is it so why don't we use A, B or any other letter. Have you thought of it ever?

What's the reason or logic behind it?.
• This is an interesting query posted in AE category but moved to Forum to generate a good discussion and get the view of our members.
Regards,
Jagdish

• An amusing and interesting observation by the author.

In the beginning, the scholars used a, b and c or alpha, beta and gamma to represent the points in the geometry or the length of the lines or values respectively.

When the methods of working out unknowns were devised then to avoid the confusion between known and unknown someone started to use different nomenclature for the unknowns and chose the other end of alphabet that is x, y and z for them.

So this practice was started just to distinguish between the two types and has been in practice since then.

Knowledge is power.

• I don't agree with the author that only x, y, z are used in mathematics. A, b, c are equally used in mathematics. I still remember the equation (a+b)² = a² + b² + 2ab.
When you talk, you are only repeating what you already know. But if you listen, you may learn something new!

• We also use 'a', 'y', 'theta', 'alpha' to indicate an unknown number or an unknown angle (in Trigonometry). However, 'x' is used more frequently. It may be because writing 'x' is the easiest. This is my personal opinion.
Beware! I question everything and everybody.

• There are other quantities as well for the determination of unknown quantities such as we may use 2l +3m =13 and l+m=5 and apart from it, we may use p, q, r or other sets such as a and b etc in addition to our usual convention of assumption X, Y, Z for the unknown quantities to be determined ultimately in process of solving equations.
General perception is that we use a single unknown quantity for determining a single quantity and in case of two unknown variables we use two unknown quantities connecting the same with some known quantity satisfying the both two equations. For three unknown quantities, we may choose three unknown variables satisfying three known quantity in each case. Of course, the known variable will be indicated in the question to be solved.

• I know that in many places other alphabets are also used for determining the unknown factors. It is only a random selection I think. We are using a,b, c, m,n and other alphabets also in many places. I don't know any specific reason for this. But after seeing this I have just searched in google. I got the following information.
An "unknown thing" is called in Arabic is al-shalan. In the Spanish language there is no corresponding sound for "sh," the scholars in that country started using the "ck" sound. This is written in classical Greek with the chi symbol, X. Later on, it was converted to Latin x. That is how this usage of x has come into use. This is like calling Christmas as Xmas. But there is no proof for this explanation.
This is the information I obtained from the google search. May not be very logical. Even after seeing this information also I think it is a selection done at random.

drrao
always confident

• In Mathematics there are two quantities generally referred as variables and constants. In 17th century, famous French Philosopher and Mathematician Rene Descartes used the first few alphabets (a,b,c ...) for representing the known values and parameters (constants). For the unknown and variables, the last few alphabets (x, y, z,...) also was used by him.
Similarly the French Philosopher and Mathematician Rene Descartes(17th c.) too used these pattern. Thus these got transferred to the followers. Since it was convenient and easy to follow the system all mathematicians started using the same, everywhere.

tmsankaran

• It seems to me because everyone is accustomed to the fact that the unknown is X

• Nice observation by the author. Many members have explained how known and unknown variables were denoted since long and this has become the usual practice.

After noticing this thread one thing suddenly came to my mind. When we are to give an example we use the term 'for example'. This example may be known to us or something unknown. Now 'example' starts with the 'ex' which can easily be shortened to 'x' to signify something unknown. This is just my imagination and has got nothing to do about how the use of the term originated.

Sankalan

"Life is easier when you enjoy what you do"