At the 8:00 mark of this video, he claims that proving things is itself an NP problem. I'm looking for more insight into this. Could someone help explain this concept to me and also provide a link to some further reading? I'm trying to get a better understanding of the relationships between complexity classes.
Here is a link to some lecture notes that answer my question - http://www.cs.cornell.edu/~sabhar/publications/iaspcmi-proofcomplexity00.pdf
Proof complexity is a vast field of mathematics.