As we look ahead through the vista of science with its tremendous possibilities for progress in peacetime, let us not feel that we are looking beyond the horizon of hope. The outlook is not discouraging, for there is no limit to man’s ingenuity and no end to the opportunities for progress.

Do not try the parallels in that way: I know that way all along. I have measured that bottomless night, and all the light and all the joy of my life went out there.
Having himself spent a lifetime unsuccessfully trying to prove Euclid's postulate that parallel lines do not meet, Farkas discouraged his son János from any further attempt.

For God’s sake, please give it up. Fear it no less than the sensual passion, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in life.
Having himself spent a lifetime unsuccessfully trying to prove Euclid's postulate that parallel lines do not meet, Farkas discouraged his son János from any further attempt.

Good work is no done by “humble” men. It is one of the first duties of a professor, for example, in any subject, to exaggerate a little both the importance of his subject and his own importance in it. 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. This is not too difficult: it is harder not to make his subject and himself ridiculous by shutting his eyes too tightly.

I am very sorry, Pyrophilus, that to the many (elsewhere enumerated) difficulties which you may meet with, and must therefore surmount, in the serious and effectual prosecution of experimental philosophy I must add one discouragement more, which will perhaps is much surprise as dishearten you; and it is, that besides that you will find (as we elsewhere mention) many of the experiments published by authors, or related to you by the persons you converse with, false and unsuccessful (besides this, I say), you will meet with several observations and experiments which, though communicated for true by candid authors or undistrusted eye-witnesses, or perhaps recommended by your own experience, may, upon further trial, disappoint your expectation, either not at all succeeding constantly, or at least varying much from what you expected.

I came to realize that exaggerated concern about what others are doing can be foolish. It can paralyze effort, and stifle a good idea. One finds that in the history of science almost every problem has been worked out by someone else. This should not discourage anyone from pursuing his own path.

I can remember … starting to gather all sorts of things like rocks and beetles when I was about nine years old. There was no parental encouragement—nor discouragement either—nor any outside influence that I can remember in these early stages. By about the age of twelve, I had settled pretty definitely on butterflies, largely I think because the rocks around my home were limited to limestone, while the butterflies were varied, exciting, and fairly easy to preserve with household moth-balls. … I was fourteen, I remember, when … I decided to be scientific, caught in some net of emulation, and resolutely threw away all of my “childish” specimens, mounted haphazard on “common pins” and without “proper labels.” The purge cost me a great inward struggle, still one of my most vivid memories, and must have been forced by a conflict between a love of my specimens and a love for orderliness, for having everything just exactly right according to what happened to be my current standards.

I never allow myself to become discouraged under any circumstances. … After we had conducted thousands of experiments on a certain project without solving the problem, … we had learned something. For we had learned for a certainty that the thing couldn’t be done that way, and that we would have to try some other way. We sometimes learn a lot from our failures if we have put into the effort the best thought and work we are capable of.

More and more of out colleagues fail to understand our work because of the high specialization of research problems. We must not be discouraged if the products of our labor are not read or even known to exist. The joy of research must be found in doing since every other harvest is uncertain.

What merely annoys and discourages a person not accustomed to thinking … is a stimulus and guide to the trained enquirer. … It either brings to light a new problem or helps to define and clarify the problem.