. . . engineering is all mathematics but I feel like since it is so application based, there is little room for creativity since many places in private industry do not pioneer products, but simply make widgets to supply to the next tier of company. . . . QUOTE]
A good school can make an engineer of a capable student. Such engineers are an essential cog in industry. There is also a need for a different type of engineer: one who is a born, not merely trained, engineer such as Leonardo da Vinci, Benjamin Franklin, John M. Browning, Thomas Edison, the Wright Brothers, etc. We used to see this in small town mechanics. Before the days of factory trained specialists, these unsung geniuses tackled almost any repair job. Often they saw a need for something unavailable on the market, and engineered and built it. It may seem to an outsider that the repairman had a simpler task than the engineer. This is true to some extent. However, a born repairman had the ability to recognize what a perhaps unfamiliar device was intended to do, and to analyze what it failed to do, and to create a solution, and to fabricate repair parts. The modern mechanic relies more on computer diagnostics and a supply of factory replacement parts instead of that special intellect of a born repairman/engineer.
During a career in electronics repair, I had to work around the problems caused by a few inept engineers. I certainly couldn't have done their job, and they obviously didn't understand mine. A horrible example is the modern automobile. Engineers have made them safe, durable, and somewhat more efficient than the cars of many decades ago. Today's spark plugs may last 100,000 miles, but can require an engine to be partly removed for replacement. Regaping or replacing spark plugs was once a routine job that many drivers could easily do every 10,000 miles or so. Over the lifetime of an old car it required less effort and money than just one replacement in today's cars. Ah, progress!