Someone who is mad has no sense of their actions and is insane. A person who has gone insane will not plan out their actions or have the motivation to accomplish it as well. Evidence in Shakespeare's play demonstrates quite clearly that while Hamlet's madness may seem real on the surface, it was very clearly feigned. Hamlet proves this when he is talking to Polonius, Horatio, and Ophelia.
In the very beginning of the play Hamlet is encountered by the ghost of King Hamlet, his father. The spirit of his father tells him the truth of his murder by Claudius. This news disturbed Hamlet greatly and he immediately began to develop a plan to discover the truth of what the ghost has told him. Hamlet of course told his best friend, Horatio, about what the ghost has informed him of. Horatio had asked Hamlet to think about what might happen if the ghost "assume some other horrible form, which might deprive your sovereignty of reason and draw you into madness" (Hamlet I iv, 72-74). Horatio believes that the ghost is not Hamlet's father in the form of a ghost, but a spirit in the form of Hamlet's father that could instantly take another shape or lure Hamlet to act crazy. Hamlet tells Horatio that is behavior is going to change, but not to pay any attention to it. He says, "How strange or odd some"er I bear myself as I perchance hereafter shall think meet to put an antic disposition on" (I.v.171-172). In the course of swearing them to secrecy about the Ghost, Hamlet adds that they can't so much as hint that they know anything, even if he should act "strange or odd." Hamlet says himself that he is not indeed mad. This scene with Horatio undeniably confirms that Hamlet will begin to feign his madness.
Other characters throughout the play also become aware of Hamlet's feign acts of madness. Polonius, Ophelia's father says, "Though this be madness, yet there is a method to it" (II.ii.205-206).