G. Mark’s Answer
It would be irresponsible for me to cite an area that uses the most or the least math. The reason is that engineering is problem-solving. A wide range of skills, expertise and knowledge are invaluable. In any particular situation, every narrow-studied engineer, or any scientist or anyone for that matter, are ill-served if they rely only on their primary study area. The adage, "If all you have is a hammer, everything looks like a nail," is very true. At first glance, I would say that biomechanics is the most math-oriented. But I would be willing to bet that the most successful problem-solvers in the general field of biomedical engineering would say that they relied solely on their primary areas of study. In actuality, it's been estimated that over 80 percent of innovations -- read as "solutions to persistent problems" -- are due to applying principles and solutions from areas other than the obvious one in which the original problem seems to have occurred. So you can take my original answer about biomechanics, or you can remain open-minded and enjoy not only a more interesting career, but a more successful one in innovative solutions.