> don't even include proofs in their mental concept of what math involves

Technically, the largest majority are the people who go: "What are proofs?" :P

A majority? I doubt it, simply because the majority doesn't know what math is at all.

At university level introductory calculus, the person teaching class had to reassure students that math wasn't entirely arithmetic or adding up numbers. He did this because it's a common misunderstanding.