[chongli]

I would disagree. Engineers, scientists, etc. have their own notation conventions as well. They may be aware of mathematical notation but only in specific areas of math related to their field (i.e. calculus and linear algebra for Newtonian physics). I would not expect a mechanical engineer to understand the notation used by graph theorists or algebraic geometers.

[diffeomorphism]

Neither would I expect this of mathematicians. If you never use graph theory there is no reason to know all the quirks of the domain-specific notation. This would be like expecting any programmer to be familiar with all programming languages.