Notes from the Underground presents a fascinating twist on the classic fate vs. free will argument. Fate in this case has nothing to do with divine will. If man is "fated" in any way, it is only because he is beholden to the laws of nature, like science or mathematics. 2+2=4, and this holds true whether we like it or not. How can there be free will if the world has such laws? The Underground Man argues that the only way to preserve free will is to beat one's head against the stone wall that is mathematical certainty. You may not be able to make 2+2=5, but you have to try if you want to be free. Additionally, he offers a terrifying vision of what might happen if we were to figure out all the laws of nature. If man always acts according to reason and the laws of nature, then we could predict everything man would ever think or do. The Underground Man argues that man will act against reason in order to prove his free will. He is willing to suffer, destroy, and abandon reason all for the sake of his own freedom.
The Underground Man does not have free will; he only thinks he does.
The Underground Man's inability to do anything except find fault is the best evidence that he lacks free will.