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We present a computational model of mathematical reasoning according to whichmathematics is a fundamentally stochastic process. That is, on our model,whether or not a given formula is deemed a theorem in some axiomatic system isnot a matter of certainty, but is instead governed by a probabilitydistribution. We then show that this framework gives a compelling account ofseveral aspects of mathematical practice. These include: 1) the way in whichmathematicians generate research programs, 2) the applicability of Bayesianmodels of mathematical heuristics, 3) the role of abductive reasoning inmathematics, 4) the way in which multiple proofs of a proposition canstrengthen our degree of belief in that proposition, and 5) the nature of thehypothesis that there are multiple formal systems that are isomorphic tophysically possible universes. Thus, by embracing a model of mathematics as notperfectly predictable, we generate a new and fruitful perspective on theepistemology and practice of mathematics.

Noisy Deductive Reasoning: How Humans Construct Math, and How Math Constructs Universes