To what extent, if any, is an understanding of mathematical proofs required for a scientist? I can empathize with a need for an understanding of the general machinery of the tools you are using (understanding, for example, how it is the chain rule came about, ie, how it was derived) but, using the aforementioned example, does a scientist need to know that the chain rule applies to all x in R and how it is so? In other words, when prompted, would a good scientist be able to formulate a proof for the validity of the chain rule for all x in R? I ask because I consider the study of proofs to be monotonous and time consuming and I'd like to circumvent the problem if I may. By the way, I don't mean to suggest that it is a waste of time to learn how to prove. I think it a good exercise in problem solving but I have a friend (a student of mathematics) who becomes infuriated when I use a tool in study without knowing the proof for the theorem. Must I know how to prove every theorem I use?