In Greek myths, the character known for flying too close to the sun is Icarus. He, along with his father Daedalus, escapes from the labyrinth using wings made of feathers and wax. Ignoring his father's warnings, Icarus soars higher as he revels in the joy of flight, leading to his tragic demise when the sun melts his wings. This myth serves as a potent allegory about the dangers of excessive ambition and the importance of heeding wisdom and warnings.