Your over-all statement is certainly somewhat accurate, though I'd disagree with various segments.
Artistic design conveys a pattern of linguistics itself, various cultures have different methods for conveying their method of communication visually.
Both of those subjects utilize the core concept of linguistical convention to allow the people participating to understand a specific sequence of communication, "Mathematics" itself is essentially a system of theoretical and logical concepts.
N...
"You need math to make art"
Well, usage of mathematical knowledge can allow you to revise your logical thinking to solve artistic problems.
"Art" itself is a system of components working together, just as "Mathematics" is.