I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.
Only as you do know yourself can your brain serve you as a sharp and efficient tool. Know your failings, passions, and prejudices so you can separate them from what you see. Know also when you actually have thought through to the nature of the thing with which you are dealing and when you are not thinking at all.
There was a man that hated his footprints and his shadow, so one day he thought that if he ran fast enough, his footprints and shadow would not be able to follow him and then he never ever had to look at them again. He ran and he ran as fast as he could, but the shadow and the footprints had no problems keeping up to him. And he ran even faster and all of a sudden he fell dead to the ground. But if he been standing still there hadn't been any footprints and if he had been resting under a tree his shadow had been swallowed of the trees shadow.