When a scientist doesn't know the answer to a problem, he is ignorant. When he has a hunch as to what the result is, he is uncertain. And when he is pretty darn sure of what the result is going to be, he is in some doubt.
Richard P. FeynmanWhat is the fundamental hypothesis of science, the fundamental philosophy? We stated it in the first chapter: the sole test of the validity of any idea is experiment. ... If we are told that the same experiment will always produce the same result, that is all very well, but if when we try it, it does not, then it does not. We just have to take what we see, and then formulate all the rest of our ideas in terms of our actual experience.
Richard P. FeynmanDuring the Middle Ages there were all kinds of crazy ideas, such as that a piece of rhinoceros horn would increase potency. Then a method was discovered for separating the ideas - which was to try one to see if it worked, and if it didn't work, to eliminate it. This method became organized, of course, into science.
Richard P. FeynmanSo, ultimately, in order to understand nature it may be necessary to have a deeper understanding of mathematical relationships. But the real reason is that the subject is enjoyable, and although we humans cut nature up in different ways, and we have different courses in different departments, such compartmentaliz ation is really artificial, and we should take our intellectual pleasures where we find them.
Richard P. Feynman