To 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. FeynmanWhen you're thinking about something that you don't understand, you have a terrible, uncomfortable feeling called confusion... Now, is the confusion's because we're all some kind of apes that are kind of stupid working against this, trying to figure out [how] to put the two sticks together to reach the banana and we can't quite make it... So I always feel stupid. Once in a while, though, the sticks go together on me and I reach the banana.
Richard P. FeynmanIt is going to be necessary that everything that happens in a finite volume of space and time would have to be analyzable with a finite number of logical operations. The present theory of physics is not that way, apparently. It allows space to go down into infinitesimal distances, wavelengths to get infinitely great, terms to be summed in infinite order, and so forth; and therefore, if this proposition [that physics is computer-simulatable] is right, physical law is wrong.
Richard P. Feynman