Maybe you could try approaching the problem from another direction,
"What is it that you would like to achieve? what is the purpose of your research?"
There are millions of problems in life at the moment, and finding things to research is not the problem at all, even though it may seem that way. Inspiration is not purely found in a textbook, but are a function of the mind and soul and body.
Experience is what probably allows your professor to come up with constant questions. He probably practices free thinking, whereby he doesn't feel constrained in any way by other people and current belief systems. Maybe a lot of the problems that actually need to be understood, such as mental health and problems that people and our planet, experience everyday, just aren't being taken into your current world-view.
Science in itself is not an end. Science is a state of being, including understanding; and is a way that you as an intelligent, caring and investigative person (I presume) approach problems. A classic example of a problem is, that we don't understand. However, simply not understanding something is not a problem. A problem is something that has effects in the real world, such as, how can we help infertile couples reproduce and have children? Although it appears that now that we have resolved this in some detail, that it was the problem of not understanding DNA and the details of reproduction that probably is what resulted, with in vitro fertilisation, and even in vivo transplants etc. If one were to take the time to step out of this 'curiosity breeds progress' mindset, it would appear that these problems weren't purely driven by a quest for knowledge, but from real world problems, that have fortunately been solved.
I'd be interested in further discussion, as I have only this evening come up with an idea myself!
There's always a thirst for improvement, and this won't cease until people realize that happiness doesn't come from materials. Happiness is within all of us, all we have to do is tap into it. Being only 24 I have seen some truly eye-opening things and I am very humble to each of our personal strengths, but I do feel its a shame that research has become so fascinated with one-upmanship, and away from the real potential and benefit of being so intelligent.