A 'few' years back, I got out of the Army after my 4 year tour in West Berlin. I went home, and went back to college. (I had dropped out after my first year as a physics major to join the Army, because what I really wanted was to go fight the communists.) I went back to the college of engineering, and studied computer programming at Big State University.
In the two and a half years I stayed in college that time, I learned something about programming exactly twice. The first time was when I was introduced to the concept of trees, from whence most other computing concepts flow. The second was a class where, in 10 weeks, we worked in teams to create virtual computers, with operating system, assembly language, and a linker-loader. All of this had to be properly documented in comments and with paper user guides. We also had to make a useful program run on the machine using the assembly language. Also properly documented. Did I mention that we did this in pairs, and in only 10 weeks? While taking other classes and working. I had to learn C programming over the first weekend to even start work on the project.
I told you that story to tell you this one. Most classes in a university don't really teach much of anything useful. In the Army, I had been a signals intercept analyst. I helped intercept Warsaw Pact transmissions, and took them apart to see what made them tick. It was challenging, and a lot of fun. I finished my four years as one of the top ten in the field - I was considered a rising star. And then we all got let go by the 'peace dividend.'
When I was wandering around the engineering college, I interacted with the other geeks there, especially in the electronics departments. When I asked them about electronic signals, they immediately started writing down math that I frankly couldn't understand.
Then I asked them what it actually was that they were writing formulas for - and they just gave me blank looks. They had no idea. They had never even though of the formulas as describing actual things. The students studying advanced electronic signalling concepts had no idea how to work an oscilloscope or a spectrum analyzer. They had no idea what the wave forms actually looked like on paper or on a screen. They just understood the math, as completely divorced from the reality of the thing.
I saw this later with other engineers, as did my father in law. The young mechanical engineers he worked with had no idea what anything really was. They just knew how to do the math and work the simulators. They had no idea about practical tests, or even what some of the tools were, much less how to use them.
This is a general problem I see in science, lo these last few years (decades). It has become so focused on the math, the formulas, the simulations, that they have forgotten to take the step back, look up, and really see what it is they're supposed to be working on.
That's why string theory has taken up decades of work of hundreds (if not thousands) of physicists, and produced nothing but new fields of abstract mathematical inquiry.
In this blog, I have learned for myself the basic principles of special and general relativity. I don't claim to be able to do the advanced math. (I'm working on it - I just got a book on how to do matrix algebra.) But I can follow the logic and the ideas to natural conclusions. Not because I can do the math - in many cases, I can't. But I can see it all in my head, the interrelations, and how it all works together. I can see the big picture that they are trying to encode, bit by bit, as a jpeg file. They see a vast field of numbers and complex formulae. I see a beautiful, simple, powerful picture.