Existential Nihilism
The main premise and theme of the novel is Existential Nihilism. This is the philosophy that says nothing means anything. Life is meaningless, human beings are meaningless, and are unable to effect anything that happens, therefore since they have no influence on the universe they are completely meaningless and without merit.
This is the theme that Pierre Anton introduces with his statement to the rest of his seventh grade class and the Heap of Meaning is a childish game version of nihilism. He claims that their willingness to add their most meaningful possession onto the pile validates his philosophy because if it had meant something to them they would never have added it to the pile in the first place.
Death
The theme of death in this novel might also extend to "violent" death, because the body count in the book is actually quite high, particularly amongst the animals mentioned. The book climaxes with Pierre Anton's murder. For his part, Pierre Anton seems to understand that he would have to die in order to prove his own philosophy but doesn't care because he already believes that his life is meaningless. If life is meaningless then death cannot be considered something to be scared of.
Savagery
"Nothing" is a book that describes an over-abundance of savagery and violence. There is the chopping off of a finger. Pierre Anton is murdered. Sofie is raped by more than one boy in her class. What makes this savagery, rather than simply very violent, is the way in which the children seem so disconnected from it. They are emotionless in their violence, the only exception to this "norm" being Sofie, who chops off Jon-Johan's finger out of rage and revenge for his participation in her rape. This act of violence is strangely less disturbing because it comes from a place of rage and a thirst for revenge - in other words, there is an emotion and a feeling behind it. Killing Pierre Anton, harming the animals and raping Sofie are done with a soullessness that seems to validate Pierre Anton's assertion that everything is meaningless. The kids are savage in their actions as though the living beings they are harming have no meaning whatsoever.
The Emperor's New Clothes: The Fake Nature of Art
The fake nature of the art world is one of the themes of this book. It can be summed up by the old children's story of "The Emperor's New Clothes", in which the Emperor demands new and ever more elaborate outfits and is subsequently praised for them, until his dressmakers run out of ideas and tell him how wonderful he looks when he is not wearing anything at all - his birthday suit is the Emperor's new clothes.
The art world is shown to be this way and is personified by the television reporters who first cover the Heap of Meaning at the sawmill. At first they think it is ridiculous and denounce it as a waste of their time. Their story captures their attention and the Museum of Modern Art purchase the Heap as modern art. The television reporters then praise the Heap saying that they only denounced it because they hadn't seen it properly from every side. This shows that they only agree that it is art because they are told it is.
Revenge
The theme of revenge is really the only legitimate emotion or meaning included in the novel. It is also completely understandable, which does not negate the violence meted out in the name of revenge but at least there is one character in the book who actually does find meaning in something. Sofie is not doing well with the concept of meaninglessness and sets out to take her revenge on her rapists. She cuts of Joh-Johan's finger which is definitely a metaphor for her revenge - this is the finger he penetrated her with.