I don't think many serious deep learning researchers claim that it will solve any kind of problems. Instead, it allows us to make significant strides in areas that have been stagnant for many years now (e.g., image recognition, speech recognition, some natural language tasks, and other domain-specific tasks). The potential impact based on these "narrow" domains is already huge (voice commands, image search, analyze medical images, analyze legal/medical documents, aid self-driving cars, etc.). Basically, it allows us to turn data that is highly structured but in a complex way (e.g., images, voice) into standard classification/regression problems. So far, I don't think it does much more than that.