Scientist or Engineer

During my first year in engineering, I was quite distressed by the way we were being taught how to solve differential equations. Just the method : all that CFs and PIs. And then how polynomials got constructed by replacing the differentials (d/dx) by D's. And then you could treat them as polynomials in D, factorise them, and solve the monomials by integration. There wasn't even a hint given as to why it was to be done that way. It wasn't absolutely the first instance when no one seemed to be concerned about telling us why we were doing something, but this was the first time that I remember when I felt that I would probably not be able find the answer to my 'why's without the help of the teacher. I asked a more toned down question in the class that wouldn't make it appear as if I was questioning the very method of teaching. That question got killed by the teacher without much difficulty. My 'why', however, remained unanswered.

There was a discussion between classmates after the lecture where I got a more open atmosphere to voice my doubt. One of my friends reprimanded me, 'If you are so concerned about maths, why didn't you do a math degree? You are here to become an engineer. You are supposed to be a user of maths. Just use it. Don't get lost in its details.' I found his stand a fairly matured one for our age. It had a point of view that I had never considered. In my opinion, I considered myself no different from a science student. My friend seemed to say that there was already too much engineering to learn. We would eventually have to stop at some point of granularity. My friend seemed to have found out where he would stop. I hadn't. I felt respectful about him for this feat. I couldn't, however, figure how I would use this approach to my benefit. There came a spate of topics during our engineering studies that got told to us like revelations of a mystic: Fourier analysis, Laplace transforms, z-transforms etc. Just use them and don't ask questions about their internal mechanics. The bag of doubts I carried by the end of my undergraduate studies had grown quite heavy! I would look at many of my friends with a sense of envy when I found that they were superbly proficient in many an engineering tool they had no clue about the concepts of. They would top university exams while I would struggle to pass; they would learn several things while they were fashionable -- they were tech savvy, while I would struggle with the simple ideas they seemed to be based upon. I didn't know how to stop the claws of curiosity from gnawing at my heart, and yet I had no clue how I could quench it.

I really don't want to go on and on. Dale Carnegie said that you should start your talk -- or whatever -- with a story to hold the attention of the audience. So frankly, the above was a cheap trick I played to hold your attention till I got to the point. And my point is nothing. Just a few questions. What's this thing about engineering and science? I understand that there's just too much to understand and learn. Knowing all of them isn't either useful or possible. Then? Where do we stop? Is it a good idea to be absolutely utilitarian in such things? As long as you can work out the solution of a differential equations, is it OK not to understand how the solution works? As long as you can compute the poles and zeros of the control system you are designing, is it OK not to bother what really these poles and zeros really are?

I don't understand this topic. It's a big muddle in my head. But I understand that it's an awfully important topic to talk about. I wish someone better qualified than me would write on this subject. I would definitely like to read it, without the lure of a story as an opener.