But there are activities where an inherently high-temperature assistant (e.g. some Instruct-inspired tune) are a great fit, and those are almost definitionally at the boundary of “objectively faithful” and “a bit stochastic”.
I’ve never done any work in novel mathematics myself, but I’m a big fan of those who do, and any study of those who do paints a picture of roughly that boundary: those who are proficient can easily spot a falsehood but only with difficulty generate inspiration for a new idea.
Of all the highly optimistic applications for 2024 LLMs, mathematics sounds pretty plausible?