This is a well-known issue. Basically, a mathematical problem tends to involve several non-trivial steps. If you are too pessimistic, it is impossible to see all these steps (because you get bogged down in proving details and lose track of the point of the problem.) On the other hand, if you are too optimistic, you will take too long to debunk an incorrect sequence of steps, leading to the problem you describe.
One solution is to work with someone else, and take turns being optimistic. (E.g., one person proposes a solution, then the other tries to shoot... (read more)
This is a well-known issue. Basically, a mathematical problem tends to involve several non-trivial steps. If you are too pessimistic, it is impossible to see all these steps (because you get bogged down in proving details and lose track of the point of the problem.) On the other hand, if you are too optimistic, you will take too long to debunk an incorrect sequence of steps, leading to the problem you describe.
One solution is to work with someone else, and take turns being optimistic. (E.g., one person proposes a solution, then the other tries to shoot... (read more)