I have a question to those of you who plan their career in mathematics, esp. pure mathematics, or already work as mathematicians. Aren't you disconcerted by the possible lack of any meaningful application of your future work? I mean the ethical side of it - does the fact that your work might not help to improve anyone's life at all bother you? Clearly many areas of maths do have useful applications in physics, engineering, biology etc., but some are very unlikely to have any "real world" (=outside mathematics) effect, e.g. very advanced algebraic topology or number theory, and other only have influence which is very indirect or obscure. Is it ethical to pursue such topics, devote your time and resources, for their own sake while there are so many appaling real problems around? Of course it can be argued that even highly theoretical research may some day yield tangible results (as in mathematical physics), but this way everything can be justified by saying "it might be useful some day", even most esoteric research. I plan a scientific career in mathematics or theoretical computer science (complexity theory etc.), and I wonder whether I should devote my efforts towards something which can really improve this world and not only be "beautiful and useless".