If you're doing an experiment, you should report everything that you think might make it invalid - not only what you think is right about it; other causes that could possibly explain your results; and things you thought of that you've eliminated by some other experiment, and how they worked -to make sure the other fellow can tell they have been eliminated.
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. FeynmanTo do any important work in physics a very good mathematical ability and aptitude are required. Some work in applications can be done without this, but it will not be very inspired. If you must satisfy your "personal curiosity concerning the mysteries of nature" what will happen if these mysteries turn out to be laws expressed in mathematical terms (as they do turn out to be)? You cannot understand the physical world in any deep or satisfying way without using mathematical reasoning with facility.
Richard P. Feynman