Near the end of the novel, Bradbury compares man to the phoenix. How is man similar to this mythical bird and how might this provide future hope?
According to mythology, the phoenix is a bird that every several hundred years burns itself into a pile of ashes and then rises again out of the ashes to live once more. In Fahrenheit 451, at the end of the novel, the city (and beyond) in which Montag lived is destroyed by bombs from a sudden and devastating war. Granger says that the city will rise again, but perhaps this time the people will be smarter than before and not make the same mistakes. Like the phoenix rising from the ashes to live again, so can mankind is Granger's, and Bradbury's, message. Bradbury doesn't want a devastating war to annihilate a city, but he suggests that perhaps mankind can turn around some of its trends and prevent the sort of society depicted in Fahrenheit 451. That is the hope for the future: a society where people read for entertainment and a society not made bland by censorship and political correctness. He wanted a less hurried society with people eager to experience life with all its beauty and its warts.
You have one wonderful answer, but I think it goes further than this.
In the midst of the war at the end of the novel, I think Bradbury is also referring the the ex-professors and others who have dedicated themselves to memorizing certain books. This is the one hope for the future that the books will not be lost forever by the book burners...that people themselves will save them from the fire and they will again hold a place of honor and worth on the shelves of private and public libraries to be enjoyed by all humanity. The people who are brave will memorize the books and the books will again rise from the ashes of the fires which destroyed their counterparts. Therefore, the history, literature, conflicts, humanity, love, hate, revenge, mythology, and all knowledge written in the pages of these memorized works will live on as long as their caretakers live on to recite the words to someone so that they will once again be printed for all to see.
At the end of the novel, Granger tells the dissident group, after the city is destructed by bombs, about a mythical bird, called Phoenix. The special feature of this animal is that it's immortal.It is reincarnated from his own ashes, after burning itself.This could be compared to the human attitude of destroying other civilisations, but in fact we are only fighting ourselves. For example, the two world wars. Germany was nearly ruined, but if you look at it today, you have to recognize that it is some kind of reborn, reborn from it's own ashes.
The "German Reich" can be seen as an example for all human empires, which have raised and fall one time, like the Phoenix. In Fahrenheit 451 the city is no exception and the dissident group wants to build up a new society out of the ruins of the old one. So you can say, that also in this case the circular flow of the Phoenix is not interrupted.
Bradbury's hopes for the future maybe are that humanity stops burning itself by reflecting and thinking about what consequence our acts might have. This is maybe the key to prevent us from further wars. This way the circular flow of the Phoenix would be interrupted, but humanity won't loose it's immortality.