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I should probably add why I think the motivation is so important here. For pure engineers, numbers are a tool. They ask: What can I build with numbers? Pure mathematicians ask a different question. They are interested in the limits of numbers. They ask: What can I not build with numbers? Studying these two questions is deeply related but also a constant source of frustration for engineers taking math courses designed for mathematicians by mathematicians.

Galois theory, is a theory of "no". It ultimately serves to answer several "Can I build this?" questions with no. This makes it very interesting to pure mathematicians. However, for pure engineers that are looking for numeric machine parts that can be assembled in other useful ways to actually build something... Galois theory can be quite disappointing.




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