I'm a physics graduate student, and while I'm not quite in the same boat as the mathematicians, I'm familiar with the problem. You spend a lot of time trying and failing to figure out what's going on. You have to be comfortable with not knowing things you want to know. I think that's a really useful ability because you don't demand easily digestible answers for everything. Such answers rarely exist, although many people seek them from short articles and soundbites.
It think it also has larger philosophical implications.. Forgive me for bringing up religion, but most (albeit not an overwhelming majority of) physicists do not believe in any higher power. If you're comfortable with not knowing things, then the answers provided by belief in a higher power doesn't provide additional comfort. You have no need for that hypothesis. (I'm not saying that people like religion simply because it provides easily digestible answers -- although religious groups *cough* young earth creationists *cough* certainly go for that. Many religious Jews spend their lives studying and debating the meaning of the bible; it's anything but easily digestible.)