I have been posing this question to friends and acquaintances (and to myself) in one form or another for a while now. The answers I have received have varied significantly. I am not the first to pose this question of course. Here is one of several online polls, posing the same question, with 700+ responses so far. Here are some others. Some of the responses I have received personally and gathered from various online postings like the ones above, in no particular order include:
||Poverty, Hunger, clean drinking water
|The P vs NP problem
||Communication between people
|Lack of tolerance
||Lack of genuine love, hatred
||Apathy, lack of empathy
|Love for Money
|Forgetfulness of God
||Overpopulation, limited world resources
||All –isms: Nationalism, sexism, racism..
One of the problems with the way the question is posed above is that it does not specify what 'problem' and 'biggest' mean.
Define problem. We will define problem as 'That which brings suffering to humans'.
Define biggest. Biggest could mean 'one that affects the largest number of people', 'the scientific problem that would create the biggest impact if solved', or 'one with the greatest economic impact', etc. I am interested in a specific version of this question, in which 'biggest' means 'most fundamental', i.e. one which can be said to be a root cause of many other problems.
Causal structure. A natural question to pose in order to move in the direction of getting an answer to my version of 'biggest problem' is: how many degrees of freedom are really present in the above responses (and what are they)? That is, are they all independent problems, or do they stem from a relatively small set (1-2) of root causes (with others being effects)? For example, lack of tolerance and energy shortage can be said to be causes of war. It is also clear that not all the problems listed above are at the same level of generality -- some seem intuitively more abstract or fundamental than others. For e.g., war seems more in the realm of effects or symptoms, compared to say anger, fear or greed. In other words, even though they are all problems, some of the items in the list above are really effects rather than causes, and I am interested in the causes. To restate the question properly:
What is the true causal structure of the world problems?
Here is a small toy example of what I mean by causal structure:
An arrow from A to B indicates 'A causes B'. In the above example, energy shortage is stated to be a cause for war, and lack of tolerance is also stated as a cause for war. Also, once energy shortage is taken into account as a cause for war, then war is not caused by overpopulation or consumerism. In other words, overpopulation and consumerism do lead to war, but only through energy shortage.
One correct answer. What strikes me most about the restated question above is that there must exist a definite answer to it. That is, there is an objective reality associated with the question. The causal structure is not a matter of subjective opinion. There is one true structure of cause and effect. I am not claiming the number of independent root causes at the very top of the causal structure is 1 (perhaps this is the case). All I am saying there is one definite causal structure. The 'one correct answer' aspect is interesting because while it is arduous to build a causal structure, checking whether a proposed structure makes sense should be much easier.
I am looking for this causal structure. I think that gaining an understanding of the causal structure can be more insightful than an understanding of the each of the problems in isolation . If you think you have have a causal structure of even part of the list of problems above, please write to me or leave me a comment. If you contact me with a proposed causal structure, please use the following format:
Cause1 -> Effect1
Cause2 -> Effect2
and so on, with one cause-effect pair per line. For the above toy example, this would be:
Overpopulation -> Energy shortage
Consumerism -> Energy shortage
Energy shortage -> War
Lack of tolerance -> War
Think of this as a jigsaw puzzle, in which the problems are the blocks (feel free to pick whatever set of problems you want from the above list, or otherwise. Of course, the more complete the set, the better.), and one has access to as many arrows as needed (The fewer the arrows, the better).
 I think this may be true in general. In middle school I recall homework and exam questions in various subjects asking us to fill in the blanks or match entries in column A with the entries in column B. I feel explaining the causal structure between a set of things would make a very instructive exercise in school because it would force a student to think.