No, not every one was born to become a mathematician, but that is besides the point. Future biologists dissect worms and frogs in biology labs as do future engineers and literary agents. Without creativity and imagination mathematics would not be possible. I suspect that good math instruction should foster students' creativity in a deliberate manner and as a part of curriculum. In B. Edwards' terminology, positive spaces comprise objects drawn intentionally.
Negative spaces combine into the set-theoretical complement of the positive spaces.
Naturally, both define the same shape. However, concentrating on the positive spaces is liable to activate our object recognition mechanism and reinforce the L-mode . Any parallel to mathematics would probably be too farfetched. The game called Solitaire pleases me much. I take it in reverse order.