Wolpert & Kinney (2024) formalize mathematics as a stochastic system, where individual mathematicians form “epistemic attitudes” from question-answer distributions. Using the self-referential nature of mathematics—“Mathematics is what mathematicians do”—as a starting point, they define the future community of all mathematicians to be the arbiter of “correct” answers to mathematical questions:
An important normative motivation for mathematicians is almost always that their probability distributions over answers to possible questions be very close to those that would arise if they had access to some oracle. … Many mathematicians would feel they have made a “good” prediction for the answer to a question if it is the same one that would be given by a far-future community [located anywhere in the universe].
Unlike the scientist and the universe encompassing the results of physical experiments, the mathematician has no a priori relationship with this ground truth.