Some thoughts from A Mathematician Apology by G. H. Hardy, (I often think the same things and some of his thoughts make me feel optimistic) :
… why is it really worth while to make a serious study of mathematics? [...] And my answer will be, for the most part, such as are to be expected from a mathematician : I think that it is worth while, that there is ample justification.
A man who is always asking ‘Is what I do worth while?’ and ‘Am I the right person to do it?’ will always be ineffective himself and a discouragement to others. He must shut his eyes a little and think a little more of his subject and himself than they deserve.
A man who sets out to justify his existence and his activities has to distinguish two different questions. The first is whether the work which he does is worth doing; and the second is why he does it, whatever its value may be. [...] Their answers, if they honest, will usually take one or other of two forms [...]
1. I do what I do because it is the one and only thing that I can do at all well. I am a lawyer, or a stockbroker, or a professional cricketer, because I have some real talent for that particular job.
2.There is nothing that I can do particularly well. I do what I do because it came my way. I really never had a chance of doing anything else.
I emphasized the permanence of mathematical achievement -
What we do may be small, but it has a certain character of permanence; and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men.
No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world. [...] (but) I have added something to knowledge, and helped others to add more; and that these somethings have a value which differs in degree only, and not in kind, from that of the creations of the great mathematicians, or of any of the other artists, great or small, who have left some kind of memorial behind them.
(written on March 16, 2006)