Well, the average engineer does not really know much about pure or more abstract math topics. He is taught to handle or process formulas or equations, but is not taught about the fundamentals of mathematics like a math major is. Some of the engineers do take some more advanced math classes when pursuing post-graduate degrees, but not all take the more abstract subjects.
I have had problems explaining to engineer coworkers (those with Master or PhD) the principle of cardinality, or in laymen's terms, different levels of infinity of different infinite sets. Heck, they even call "real numbers" the floating point representation of numbers by digital computers, not realizing that computers can only define rational numbers, and actually a very small, meaning finite, subset of all rational numbers, let alone "real" numbers.
I had exposure to these topics in freshman year in college prior to emigrating to the US. The program required an entrance exam, which admitted 15 students from across the nation that year. In that 1st year, we learned Linear Algebra, Abstract Algebra (or the Theory of Numbers), and Real Analysis ("Real" as opposed to "Complex", and not "phony").
Coming to the States, I switched to engineering as it would pay better, plus I already played with electronics since 12, so it was not all that hard. Only in graduate school that I really had to study when dealing with advanced engineering subjects like Optimal Control Theory, Digital Signal Processing, Random Processes and Estimation Theory, Error Correcting Codes, etc...
So, I did not have a Math degree, but had a taste of the stuff, and knew a bit more than the typical engineer. However, my knowledge is far short of what would be needed to read Wiles's proof of Fermat's Conjecture, a riddle that persisted for nearly 400 years until proven true in 1993.
