HAMLET (THE MADMAN?)

 There is more depth in Hamlet than to just assume that he is a madman. I madman be definition is a man who is mentally ill, and Hamlet doesn't seem lost enough to be considered ill. Now I'm not saying that ill  means that you lose your mental capacity I would say that at a certain point you do but lets take as an example a mad scientist. A mad scientist is crazy enough to think of something unnatural or supernatural like bringing someone back to life. See madmen can still have capacity to make their goals come true, but I feel that they think of themselves of having no limitations, and that's totally different to Hamlet he is a very intelligent and calculative person  enough to make anybody second guess themselves about their idea of him.
I t does take King Claudius a while to realize that Hamlet poses an actual threat, because in the beginning he wouldn't have thought Hamlet was capable of doing anything against him. Hamlet was very calculative in the beginning of the play and very sane. A madman in my perception wouldn't have been able to sustain such a persona they might still be intelligent but they might have not been able to hide their feelings as well as Hamlet. I feel a madman would be even weaker when talking to the person they love unable to hide their true feelings well enough to actually make it believable. Like how Hamlet made Ophelia believe that he no longer loved her even though he did. Ophelia was brought into a depression because she was fooled by Hamlet's measured and knowledgeable responses.
I feel that the reason for some to view Hamlet as a madman would be because we aren't to his mental capacity for example Galileo who at his time was the only one to believe that the earth revolved around the sun instead of the sun around earth. He at his time was also believed to be a madman because what he believed seemed ludicrous to those around him even though we know now that he was right. That's why I feel that if a certain group or a majority isn't able to completely understand something or someone we would set them off as weird or mad.