This may be self rationalizing or 20/20 hind sight. Looking back of my life endeavor of some 65+ years (since my first published paper in 1955), I am what the world would classified as a scientist or engineer. But with a couple of  exceptions I have not done a single experiment or practical applications as popular notion have scientists/enginers do. Yet this is not to say that my work have not been useful or applied by others to solve real problems of the world which nowadays increasingly dependent on expensive equipment or resources from government or coporations to supply. The days where a scientist/engineer can work alone to create new discovery of truth or new application of knowledge for human benefit is increasingly rare. In this sense, I was able to work/create alone without the need of huge equipment outlay or collaboration from a team of other scientists/engineers is because my work deals with my mind alone. With a problem-driven (not methodology driven) mind, I was able to derive algorithms and results that other engineers find useful. and thus justify my existence. But then pure mathematicians do not consider what I do as MATHEMATICS - an attitude I completely understand and does not bother me. Applied Mathematics have to deal with the inconvenience of reality. It is not Art for art sake. In this sense, I am a theoretical engineer rather than an Applied mathematician.