[stuxnet79]

> "we never really understand higher mathematics, we just get used to it"

Correct me if I am wrong but I believe this statement is attributed to Von Neumann. It has really stuck with me over the years, just because of how true it is.

I agree that what is important is self-consistency, precision and rigor. Intuition is for the birds. Like you have stated it is ambiguous and often deceptive. Mathematical abstractions enable us to circumvent these pitfalls.