Once, I was walking down along with my prof, discussing a result I had just managed to prove. He said “well, you have managed to prove it, but you should also understand your result”. We generally believe we certainly understand something that we developed ourselves. For the first time, I was talking to someone who had, in his mind, a genuine definition of understanding. I knew how I arrived at the result, but it was counter intuitive. That means, there is a flaw in our mental picture of the subject. So, reconstructing our intuition, based on this result is a more important part of understanding it. In fact, this is the value attached to the result.
The above instance speaks also about the value hidden behind a mystery. A mystery points at something that we don’t understand. A counter intuitive result is also a mystery. The moment we encounter a mystery, we can hope for something radical, coming out of resolving the mystery. In fact, look at almost any radical change in human thinking, there would have been a mystery out of which it emerged! Quantum mechanics was itself found hidden behind a mystery. Also, the theory of relativity was born out of a mystery!. Another classic example is quantum computation. This example is too technical to be written in a blog, but I prefer to mention it because, I myself solidified the thoughts behind this post using this example. It all started with Einstein pointing out an apparent contradiction in quantum mechanics, and Bell clarifying that this was no contradiction, but it was only a mystery. They called this mystery ‘entanglement’. It took a while for people to understand it; but a revolutionary looking idea did emerge out of it. That was quantum computing.
The examples I gave are of a huge magnitude :D, and very specific(to physics). One may not expect to encounter mysteries of this magnitude, but the idea works at all scales. A big mystery leads to a big revolution; a small one to a small one :D. So when we confront a mystery, we can expect something new coming out of resolving it. However, every mystery need not lead to something fruitful, but we can hope!.