I am sorry to be rather realistic, but I feel it is necessary. The most important problem? Any problem annoying anyone. When you suffer from severe toothache, I bet you can't even imagine to ponder on war, selfishness, world-hunger, education, etc. So does this really increase the importance of your problem to that extreme?
In fact, my friends, man is ignorant and stupid. He is not designed to be objective. He thinks and acts under the influence of what he is, and has been. So many guesses at the most important problem of the world are nothing more or less than guesses. Even if the whole world agrees that war is the most terrible problem with the world, it cannot end. At least, man cannot end it. Because at a very critical moment, he may go mad, he may get sick, he may become emotional, death may come to him. Not to be pessimistic, even if he remains extra conscious of the situation, that may be a problem by itself. To err is human!
Then, there is another point to be noted. Ideally, to solve a problem, you must have a thorough and absolute knowledge about it. How can man, whose knowledge has not yet allowed him to agree on "the most important", and who does not even know the potential consequences of his last meal, solve the most important problem of the world ? We do not know what results from what, so we cannot cure it. May be what we are thinking of as a problem, is protecting us against a greater potential danger.
But the problems get solved. Even the most important problems get solved. We are often happy, appreciating the beauty and sublimity of the world in various ways, indicating that there are no problems we should be concerned about at the moment.
So, my friends, man is ignorant. Man is stupid. We are talking about problems. There are many out there who are praising God for making such a beautiful, perfect world. Perhaps they'll complain soon, and perhaps we'll get rid of (thinking about?) the most important problems even sooner.
Problems are neither created nor solved. They are only perceived by humans. The most important problem with the world, among a hell lot of many others not less important, is that it appears problematic!