Is the set of all mathematical truths countable or uncountable? Is the set of all theorems countable or uncountable?

Maybe its a stupid question. I just wanted to know. I am led to think that since, we use a finite set of symbols and English letters, the set of theorems is countable.

EDIT: The set of theorems is not just a set of linguistic combinations, but a set of mathematical truths.
A theorem is, by definition, a finite string of symbols that can be derived by some specified proof system. Because there are countably many finite strings of symbols, there are at most countably many theorems in any given theory.

Speaking of "a set of mathematical truths", where the elements of that set is supposed to be something different from symbolic representations, is not well defined. What kind of object is "a mathematical truth" to you such that you can put them into a set and count them? There is no definition of such a thing in general use, except for the formulas of symbolic logic.

In model theory one can speak of theories where the set of possible symbols are uncountable, such as a symbol for each real number. Such a theory, of course, has uncountably many theorems of the form $c=c$. However, these theories are generally considered artificial objects of study. Studying them can be useful as a stepping stone in proving things about ordinary countable theories, but their formulas are not considered to directly represent "mathematical truth".
The set of all theorems is countable. The set of all mathematical truths isn't. You even could see this like a very basic proof of Gödel incompleteness: It's impossible to prove all mathematical proofs since there are less theorems than truths (which are different things). You can find this question and more interesting stuff on this topic in Geoffrey Hunter's book: Metalogic: An Introduction to the Metatheory of Standard First Order Logic.