In Section 3 of Fahrenheit 451, "Burning Bright," the mythological allusion on the first page is in the unstated comparison of Montag to Icarus:
Old Montag wanted to fly near the sun and now that he's burnt his damn wings, he wonders why.
Icarus and his father Daedalus attempted an escape from Crete flying with wings fashioned with feathers and wax. Daedalus warned his son not to fly too low or too high as the sea's dampness or the sun's heat would impair the wings. But, in his pride, Icarus ignores his father's warning and flies high in the sky, too high and the sun melts the wax of his wings, causing Icarus to crash into the sea.
In his fervor to acquire the knowledge contained in books and to feel true human emotions and have some depth of thought, like Icarus in his high-flying ambition, Montag ignores the possible implications of his actions; now, he has become a suspect himself because his wife Mildred and reported him for having books. His house is burnt.
As the previous educator has commented, this mythical allusion is to Icarus, a character who ignored the warnings of his further and flew so close to the sun that the wax of his wings melted. As a result, Icarus plummeted into the sea and died.
By comparing Montag to Icarus, Beatty is suggesting that Montag has taken far too many risks: he did not take Beatty's advice and hand in his stolen books, for example, and he read a poem to Mrs Bowles and Mrs Phelps who both reported him to the authorities. Now, like Icarus, Montag is about to lose everything since his wife has left him and the authorities are going to make him torch his own house.
But this allusion to Icarus is not completely accurate. Montag shifts the balance of power when he sets fire to Beatty instead of his house and is able to flee the city before the Mechanical Hound catches him.