Did Einstein try to do the impossible? No, yet looking back it seems like he accomplished an impossible (for that time) feat doesn’t it. So what exactly did he do? He worked on something he felt was:
and probably more to the point,
2.) passionate about.
Did he run the probabilities of whether he would accomplish his goal? I don’t think so, if anything he used the fact that the problem has not been solved so far and the problem is of such difficulty only to fuel his curiosity and desire to work on the problem even more. He worked at it every day because he was receiving value simply by doing the work, from being on the journey. He couldn’t or wouldn’t want to be doing anything else (patent clerk payed the bills, but his mind was elsewhere).
So instead of worrying about whether you are going to solve an impossible problem or not, just worry about whether you are doing something you love and usually if you are a smart and sincere person, that thing you love will more often than not turn out to be pretty important.
Ben Franklin wrote something relevant when talking about playing games:
”...the persons playing, if they would play well, ought not much to regard the consequence of the game, for that diverts and makes the player liable to make many false open moves; and I will venture to lay it down for an infallible rule, that, if two persons equal in judgment play for a considerable sum, he that loves money most shall lose; his anxiety for the success of the game confounds him. Courage is almost as requisite for the good conduct of this game as in a real battle; for, if he imagines himself opposed by one that is much his superior in
skill, his mind is so intent on the defensive part, that an advantage passes unobserved.”