Polonius thinks that Hamlet is mad because Ophelia is ignoring him and Hamlet is madly in love with her.
The above scene is taken from Hamlet Act 2 written by William Shakespeare. This scene starts with Reynaldo, a spy sent by Polonius, who travels to France to keep a watch on Laertes. As soon as Ophelia walks in, she informs Polonius that Hamlet stormed into her room, holding her wrists, and stared crazily into her eyes. She continues by saying that she has severed all ties with Hamlet. Polonius decides to meet with the king to devise a method to eavesdrop on Hamlet speaking to Ophelia since he is convinced that Hamlet is madly in love with her and that Ophelia's rejection is what put him in this situation. Rosencrantz and Guildenstern, two of Hamlet's classmates from high school, have been invited by Gertrude to investigate the origin of his insanity. Hamlet avoids their queries because he is wary of them.
Here madness has two meanings, that is one immediately thinks of a lunatic in an asylum who is unable to understand reality when it is used frequently in phrases to suggest unreasonable insanity.
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