Was Hamlet mad??

Was Hamlet Mad?
Hamlet was a very sane man. There is a clear reason why Hamlet had to act crazy. He was to further his plans for revenge on King Claudius. Hamlets words were so carefully thought and spoken that everyone else in the play would think of him as being crazy. Can an insane person be so genius? Many people agree that Hamlet was brilliant.
After Hamlet, Horatio, and Marcellus see the ghost, Hamlet tells Horatio that he is going to put on an antic disposition. "How strange or odd some'er I bear myself (As I perchance hereafter shall think meet To put an antic disposition on)…