In a world with solid coverage of mathematical theory presented informally to appeal to a larger laymen audience, will the world produce more amateur mathematicians that make great contributions to science or less? Will would-be amateur mathematicians be less motivated to learn formal notation given that they can more easily read and understand the same material presented in an informal manner? If they did pick up a base level of formal notation, would they be less motivated to learn how to understand or write rigorous proofs using formal notation for the same reason?

I don't know what the answer is. Maybe there are studies out there that attempt to answer these questions.