There's a weird non-intuitive thing I notice about the process of learning something new. I find that when I'm in the thick of absorbing new stuff that I don't understand very well, I feel arrogant and in a way, better than everyone else, or at least different from everyone else. Its as if I'm the only one who could possibly understand this really hard thing. The strange thing is that the feeling fades away after I actually understand the stuff I'm trying to learn.
I guess this is just another way of saying that arrogance is usally a sign of insecurity. Its a defense mechanism when your grasp of the facts is tenuous. To avoid slipping into arrogance, one can just describe oneself as out of commision in certain ways during those times. In academic or other environments where grasp of information is key, arrogance is always a job hazzard- both for yourself and for the other people you have to work with.
I have to remind myself of this process sometimes. I'm pretty good at math, but each time I learn something new, I have this feeling that if I learn this new thing, I'll have so much knowledge that I'll never be able to relate to normal people again. But as I mentioned, this feeling fades away after I actually learn the thing, and in fact, once its internalized, the math feels very human and I can even explain it relatively easy. I suppose there's a danger of trying to learn things that I'll never understand and getting stuck in a purgatory as a result. Anyway, all jobs have their hazards as well as their rewards.