I agree with Jamie in saying that Hamlet is definitely NOT mad. And, yes, much scholarship has been spent on arguing the contrary. And certainly he has good reason to go mad. But he doesn't. He tells us early on that madness is the ruse he will use to get to his ends met and, though his patience and sanity is stretched in unimaginable ways, he maintains his persona even though it costs him the life of his former love, Ophelia.
Scholars have debated this question for hundreds of years, but the general consensus seems to be that Hamlet is not mad, but terribly conflicted. This confliction often looks like madness, as when he verbally abuses Ophelia, or has a meaningful conversation with Yorick's skull. And, of course, speaking to the Ghost of his father.
Hamlet's conflicts are understandable. His father has been murdered by his uncle, his mother betrays his father's memory by marrying the evil Claudius; Hamlet's friends turn out to be "sponges" for the false king, and he accidentally kills his girlfriend's father. Despite all this evidence, Hamlet has to bring himself to act out the revenge he knows is necessary, not an easy thing to do.
Was/is Hamlet mad?
Mad means crazy, unconscious of the values of the world, engaged to perform his task on any cost .we see Hamlet in stress due to the death of his father and unexpected marriage of his mother to Claudius. In his stress, more addition is made by ghost disclosing the truth .Now; Hamlet wishes to kill his uncle because he is killer. He admits that his goal is to punish the murderer. It is his craze, but is not over dominated, for he insists on the proof. After the proof he nurtures craze to kill the king, but it is the fortunate of the king that is praying. So sense comes and suspends to kill him by uttering that he will go to heaven.
He says,’ To be or not to be’, but comes to the conclusion that it is taboo and avoids killing him. His words with Ophelia are having a great wisdom. His talking with Laerates at the time of burying Ophelia reveals love and sagacity. His behaviour towards pirates and mother shows his wisdom.
Now we come to the conclusion that mad never delays in his action or never thinks that one is praying. The mad never says,’ to be or not to be.’ He deals with great consciousness and meditation. At last he kills Claudius it does not show his madness but it is love for her mother and behind nothing remains to love, so in this spirit he loves and takes revenge. Now it is clear that he feigns to be mad. To be very frank we don’t watch him in such real spirit, though he pretends to be.