It is due to Odysseus's nerve, resourcefulness, strength, cunning, and leadership that he survives his encounter with Polyphemus. After the cyclops eats four of Odysseus's men and traps Odysseus and his crew in the cave, Odysseus spots an olive wood club and directs his men to cut it down to a fathom's length, plane it, and sharpen and harden the tip to a "stabbing point." Odysseus bravely confronts Polyphemus about his barbarity and pretends to be appeasing him by offering him wine, but he is really manipulating Polyphemus to get drunk enough to pass out. Once Polyphemus is deeply asleep, Odysseus and his men heat the tip of the club and corkscrew it into the giant's single eye.
Odysseus had told Polyphemus that his name was "Nobody," so when neighboring cyclopes heard him say "Nobody's killing me," they don't move to help him.
Ultimately, Odysseus and his men escape by executing his audacious plan; they hide beneath Polyphemus's sheep when he releases them from the cave to graze in the morning. When the freed men begin to falter and grieve the men who have been killed, Odysseus puts a stop to their wailing and gets them safely aboard ship.
At this point in his journey, Odysseus has begun to develop more prudence, or wisdom, about his actions although he continues to make serious mistakes. He is clever to tell the Cyclops that his ship was smashed so that the giant can't attack his other men and that his name is "Nobody," a move that insures the other Cyclopes will not come to Polyphemus' aid. Also he manages to get the one-eyed monster drunk, blind him, and then hide under the sheep to escape the cave. All of these actions reveal Odysseus' guile and prudence, traits that help him survive.
Nevertheless, he does lose six men in the cave because of his own curiosity, and once on his ship again, his proud nature leads him to boast to Polyphemus, and he tells the Cyclops his real name and where he lives. Thus he brings on the problems at sea Poseidon causes because his son was blinded. Odysseus is heroic and clever, but he has not yet learned to be as wise as he should be.