AI systems generating formal mathematics face a fundamental tradeoff: they must produce some correct-but-worthless statements to discover truly valuable new theorems, and this requirement is mathematically unavoidable, not a bug to fix.
This paper models how AI systems generate valuable mathematics using proof assistants. It shows that to discover new valuable theorems while avoiding false statements, systems must generate some 'trivial' (correct but uninteresting) statements—and the amount needed depends sharply on how much of the valuable mathematics is already known.