How does Gatsby represent the idea of American dream?
I think that in many ways Gatsby's characterization does represent the American Dream. Initially, Gatsby's notion of self definition and self conception is a major part of the American Dream. Gatsby redefines himself, changing his name and his occupation as well as his background. This is concurrent with the notion of freedom in the American Dream, as individuals are able to go as far as their freedom will take them. Additionally, Gatsby predicates his dream on the premise of wealth acquisition. Simply put, Gatsby believes in the fulfillment of his dreams as being contingent on acquiring more money. This is another component of the American Dream, whereas success is defined by monetary growth. Sadly for him, this turns out to be a monument built upon the firmament of sand which the tide washes away.
I'm not completely convinced that he does represent the pure American dream. I'll talk a bit about how he does and doesn't (to me).
He does represent the dream in that he is born poor and gets to be rich. He represents the dream because he has this real drive to "make it" that is central to the American dream.
But he is not the classic rags-to-riches story that I associate with the idea of the American dream. A person who was really living the dream would not have quit the janitorial job at college. The real American dream doesn't include making money illegally.
So it seems to me that he's sort of a perversion of the dream. He wants the end result, but he doesn't want to do it the right way, and I think that doing it the right way is central to the dream.
Yes, Gatsby exemplifies the American Dream. The American Dream can be looked at in two different ways.
1) The sense of limitless possibility at teh heart of America in that every American can make something of themselves so long they make use of their natural talents and hard work and the likes. It is the embodiment of human potential and this is seen in Gatsby's "extraordinary gift for hope". Gatsby has hope that he can recapture/relive the past with Daisy Buchanan and he believes in this illusion so much that he has made Daisy the object of his dream. And he lives his life in such a way that Daisy is the basis. There is the green light at the end of Daisy's dock, the lavish parties hoping that Daisy may someday return, etc. Everything he does is for the belief that Daisy may declare true love for him and they may live happily ever after.
2) The materialistic aspect of the American Dream where everyone's main focus is on getting rich - which ever way. Gatsby had a dream (you can even argue, a hope) to be a better man. To make something of himself. Rise above his father's material status because he was/is a nobody and also he wanted to get rich for this "excitingly desirable" girl, Daisy. He does this through corrupt means and this is the negativity portrayed in the American Dream in that people are so engrossed in getting materialistc wealth that they end up failing in terms of morality.
There is an idea of moral failure and material success (and vice versa) and Gatsby has failed morally but succeeded materially (contrasting with his father who is poor but presumably generally good.)