Does $X$ denotes a random variable or is a notation for random variable?

Question

In some places $X$ is mentioned as denoting a random variable and in some other places it is mentioned as a notation for random variable.

The meaning of notation is, it stands as a symbol for a mathematical object.

The meaning of denote is, it represents something.

If random variable is a mathematical object, then it must be a notation. Is random variable a mathematical object ?

Answer 1

The popularization of the use of symbol x (as well as y and z) comes from René Descartes. The generally accepted view states that the use of x by Descartes specifically because of his landmark work La Géométrie (1637). Because of that work it ended up instituting the convention of:
• lowercase letters at the beginning of the alphabet for known quantities (such as a, b, c);
• letter at end of the alphabet for unknown quantities (such as x, y, z).
  Reference

When it comes to mathematical object, the belief of their existence is commonly seen as the product of postulation. But I still think its an abstract concept, opened for interesting discussions.