Isn't the fraction of computer free math/physics vastly, vastly smaller than the computer-ful math/physics research though?It shouldn't discourage you. There is plenty of research that doesn't involve much computer work. So if you don't like computers, then you certainly don't have to spend all day long coding. However, saying you don't want to deal with computers AT ALL will close a lot of nice opportunities. So you should definitely learn how to code in a program like sage or matlab.
The slice of the pie left for mathematica and blackboards is pretty tiny from what I understand, but I'm really asking a question since I don't know for sure.