I fully agree with all of this. Some of the best counsel I got when I was co-oping at DuPont during my junior year of college was when one of the other engineers told me: “Every engineer is good at math. What will set you apart is your ability to communicate — both written and spoken.” This has indeed been absolutely true in my own career.
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My guess is that there are a roughly optimal number of Americans entering the engineering profession to meet industry demand. Unfortunately, that number is not as high as deans of engineering schools or university presidents would like it to be.