I don't understand why this is down-voted. This is probably pretty perplexing to the lay-person. When a mathematician writes "relatively little mathematical background," what that constitutes from their perspective is probably radically different from what a lay-person considers to be "relatively little mathematical background"

When I see "minimal mathematical background" or the like, I usually think: "Understands basic set theory, the concept of a function, and has familiarity with basic proof structures"

When I see "mathematical maturity", I think "Understands, real analysis, abstract algebra, and topology."

Hope that helps.