1. How do you interpret Descartes' statement: "I think, therefore I am"? I've always thought he meant that his awareness of his own consciousness is proof to himself that he exists.
2. What is your opinion of the statement? True but, like a lot of philosophical meanderings, essentially trivial, and with a hint of solipsism. In the context of his other writings, I have the impression that he considered it the *only* proof that he exists. It says nothing about anything but his own existence, doesn't demonstrate to anyone else that he exists, or indeed that anything but himself exists. Nor does it say anything useful about the existence of things that don't think, like trees and rocks. He spent a lot of time wondering what he could know and how he could know it, which I think is the subject now called ontology, and I don't know that he ever solved those to his own satisfaction. He should have just gone out into his garden, punched a tree or kicked a big rock a few times, and pondered on how the resulting sensations demonstrated the existence of both himself and solid objects external to himself.
I am reminded of Bill Cosby's story about dating a philosophy major in university, where he was majoring in physical education. "She used to walk around saying things like 'Why is there air?' Well, any phys.ed. major knows why there's air. There's air to blow up volleyballs, blow up basketballs..."