I only got to a nonverbal level of understanding of advanced math fairly recently, and the first time I experienced it I think it might have permanently changed my life. But if you dream about math...well, that means I still have a long way to go and deeper levels of understanding to discover. Yay!
Follow-up question (just because I'm curious): how do you approach math problems differently when working on them from the angle of engineering, as opposed to pure math?
It seemed to me that the people I knew who were studying pure math spent a lot of time on proofs, and that math was taught to them with very little context for how the math might be used in the real world, and without a view as to which parts were more important than others.
In engineering classes we proved things too, but that was usually only a first step to using the concepts to work on some other problem. There was more time spent on some types of math than on others. Some things were considered to be more useful and important than others. Usually so...
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