The main reason why Polonius thinks that Hamlet is mad is because of his obsessive love for Ophelia. As a result, he forbids his daughter to communicate with the prince for her safety and dignity.
Detailed answer:
Firstly, Polonius is so sure of Hamlet’s insanity that he forbids his daughter to communicate with him. Throughout the play, he is confident in the emotional sickness of Hamlet comes from his feelings. The prince suffers from the firm, allegedly unhealthy feelings towards his daughter, Ophelia. Polonius observes how the main character struggles when she rejects him. He assumes that this heightened, even depressive reaction is provoked by a heartbreak. He claims that love is a self-destructive and brutal emotion. It can lead people to lose their minds, which highlights Hamlet’s tragic flaw.
The final evidence for Polonius is how Ophelia describes one of his peculiar visits. After her speech, he becomes confident in Hamlet’s insanity. The prince came to her room in dirty clothes, as if “he had been loosed out of hell.” He shook Ophelia in the act of overreaction without saying a word. Such violent actions and the daughter’s shock persuade Polonius to believe in Hamlet’s insanity. The prince’s plan to pretend to be mad is successful. However, it foreshadows some future plot transformations.
As a result of the belief in Hamlet’s madness, lord Polonius forbids his daughter to interact with him. He demands it to sustain her dignity and safety. It is notable how differently Polonius approaches the topic of Hamlet’s insanity with his children. To his son, Laertes, he expresses concerns about Hamlet’s obsession and discusses his findings and evidence. Yet, he mocks Ophelia for her feelings towards an unstable man. He claims that she is deceived by his untrue statements and obsession only driven by his impulse.
Thus, as the story progresses, the lord limits Ophelia from seeing, writing, and talking to Hamlet. As an obedient daughter, she complies, which saddens her even further. It pushes both Ophelia and Hamlet into the realm of depression.
As apparent from this portion of the play, Ophelia appears to be naïve and lacks control over her own life. Her father is in charge of her life decision. That might be the reason why she agrees to follow Polonius’ directions. Per his request, she sends all Hamlet’s letters back. Then she denies him the visits to her room, separating from a loved one altogether.
Despite Polonius’ efforts to protect his family and others from Hamlet, he fails. He is the one who causes an irreversible chain of events that lead to an unhappy ending. To further prove Hamlet’s madness, he explains his findings to the king and queen. In need of more evidence, Polonius plots another plan. He hides behind the curtain and observes Gertrude and Hamlet interacting, looking for signs of insanity. This attempt ends lethally. The prince kills Polonius by accident, which enhances his madness. It affects Ophelia’s sanity, starting a downfall caused by his tragic flaw and moral dilemma.