Hamlet, why so crazy?

After discovering his father's true reason for dying, Hamlet has gone crazy. I can understand his overwhelming anger and hatred towards Claudius and maybe some towards his mother, but why is he acting so insane? In the scene where Hamlet is talking with Polonius, Polonius asks Hamlet if he knows who he is, and Hamlet responds with "fishmonger." I get the feeling that Hamlet knows that Polonius is not a fishmonger, and is saying it to annoy Polonius, but why? And, maybe it is the Shakespeare's unique writing, but on page 95, Hamlet says "For if the sun breed maggots in a dead dog, being a good kissing carrion - Have you a daughter?" Hamlet is speaking to Polonius. Hamlet seems to be expressing love towards Ophelia, so Hamlet may or may not have known who Polonius was. Besides that, Hamlet had written a love letter of sorts to Ophelia and she showed Polonius. I wonder if Hamlet intended that letter to get to Polonius, and then Claudius. I wonder: does Hamlet have a plan? Is he acting crazy, and trying to get this letter to Claudius on purpose?