Post-human mathematics
I think one of the greatest difficulties in completely automated mathematics would be the discovery of mostly those things which are <i>interesting</i>. If computer mathematics is ever to diverge from human thinking, someone must pay to keep the lights on. Since nobody would pay for random points in theorem-space, it must have some way of figuring out what the human brains down at the breaker box actually want. This to me looks a lot like the problem of computer automated storytelling or even art.<p>Also, I don't think the alien-ness of computer proofs is a given. Perhaps someday some psychologist or philosopher might work out exactly what our cognition likes to work with, upon which time you could write a proof compiler that outputted those things.<p>That raises and interesting question. Can all interesting proofs be built with human-friendly steps? Maybe that's why we haven't worked out P and NP.