Why, according to Polonius, has Hamlet gone mad??
is it (a)He grieves too much for his father. (b)He despises Claudius for marring Gertrude (c)He is in love with Ophelia..or (d)He is jealous of Laertes and longs to return to Wittenberg???
Well, process of elimination as well as Polonius's own words will quickly answer this question.
a) Both Claudius and Gertrude make several comments regarding Hamlet's excessive mourning for his dead father. They say this to Rosencrantz and Guildenstern, to Polonius, to each other, and to Hamlet. Polonius never says it.
b) Hamlet does, indeed, despise Claudius for marrying his mother--among other things, of course. Hamlet says so to himself, to his freinds, and to his mother. Even if he believed it, Polonius would never dare say such a thing to his boss, the king.
d) Hamlet is envious of anyone who can leave Denmark, the place he has come to see as a "prison." This, though, is the least likely answer because it demonstrates the weakest emotion on the list. If he really wanted to leave the country he could; he cannot change his father's death nor his mother's remarrying.
So, that leaves the correct answer.
c) Polonius asks Ophelia to give him anything Hamlet gives her; when she does, he discovers Hamlet's passionate (though ill-written) love for Ophelia. In whatever form they were written (as true expressions of love or as indicators of some melodramatic, overacted passion), Polonius believes them. He takes them to the King and hopes to win his favor once again by solving the mystery of Hamlet's melancholy madness. In one his most humorous speeches (IIii), he says:
"...I have found
The very cause of Hamlet's lunacy."
A hundred likes later, he finally announces that he has commanded his daughter to rebuff any advances or tokens from Hamlet, which has, in turn, driven him mad.
"That she should lock herself from his resort,
Admit no messengers, receive no tokens,
Which done, she took the fruits of my advice,
And he, repelled, a short tale to make,
Fell into a sadness, then into a fast,
Thence to a watch, thence into a weakness,
Thence to a lightness, and by this declension,
Into the madnes wherein he now raves...."
Clearly Polonius wants to believe Hamlet is mourning the lost love of his daughter. It's in his won best interests to think so, of course, but he also thinks he's been pretty clever in rooting out the cause when no one else can.