zornthewise

Finding [Ramsey numbers](http://en.wikipedia.org/wiki/Ramsey%27s_theorem) is one. They are hard to calculate even for small values. Most open problems are either to prove something because we can make a good guess to what the answer should be.

What kind of answer would satisfy your questions of why these theories are true anyway. I am not sure I can even imagine an ideal answer and this might be a clue that we are asking the completely wrong question.

This isn't really true as far as I am aware. If you are getting this from the Robber's Cave Experiment(HPMOR), it was misrepresented there. They were only hostile after it was induced and they went back to being nice in the last stage too.