Can anyone who is strong at mathematics do well in computer programming languages as well as all fields of science and engineering?

Not everybody can do well in computer programming, that is strong in mathematics. It depends on how your mind operates. For example a person that is Very highly dyslexic may be great at remembering things from years ago, but still be extremely bad at using those memories in order to make wise decisions in everyday choices.

This clearly shows that a person with only base skills in one area, doesn't always exceed at being good at other things branching off of that particular area. (i hope this makes since... hopefully somebody can improve this answer.)