How to identify the subject of a sentence

How are we going to identify the subject of a sentence? A subject can be defined in two ways.

First, the subject of the sentence is the doer of the action. So you can easily identify the subject by asking the question "Who is the doer of the action?"

In this sentence, My father fixes his car, the action here is fixes and the one who does it is my father. Therefore, my father is the subject of that sentence.

Now, what if there's no action indicated in the sentence? How then are you going to know its subject?

A subject can also be defined as the main idea of a sentence. So if there's no action involved, simply ask yourself "What is the main idea of this sentence?" Your answer to this question is the subject.

Mathematics is quite hard. What is the main idea of this sentence? Obviously, the sentence is talking about Mathematics. Therefore, it is the subject of this sentence.