嘈杂的演绎推理：人类如何构建数学，以及数学如何构建宇宙
Noisy Deductive Reasoning: How Humans Construct Math, and How Math Constructs Universes
摘要：
我们提出了一个数学推理的计算模型，根据这个模型，数学从根本上说是一个随机过程。也就是说，在我们的模型中，一个给定的公式是否被认为是某个公理系统中的定理并不是确定性的问题，而是由一个概率分布决定的。然后，我们表明，这个框架给出了一个令人信服的帐户的几个方面的数学实践。其中包括：1）数学家生成研究程序的方式，2）数学推理的贝叶斯模型的适用性，3）溯因推理在数学中的作用，4）一个命题的多个证明可以加强我们对该命题的信念程度的方式，以及5）存在多个形式系统同构于物理上可能的宇宙的假设的性质。因此，通过拥抱一个模型的数学不完全可预测的，我们产生了一个新的和富有成效的观点认识论和实践的数学。
英文摘要：
We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a matter of certainty, but is instead governed by a probability distribution. We then show that this framework gives a compelling account of several aspects of mathematical practice. These include: 1) the way in which mathematicians generate research programs, 2) the applicability of Bayesian models of mathematical heuristics, 3) the role of abductive reasoning in mathematics, 4) the way in which multiple proofs of a proposition can strengthen our degree of belief in that proposition, and 5) the nature of the hypothesis that there are multiple formal systems that are isomorphic to physically possible universes. Thus, by embracing a model of mathematics as not perfectly predictable, we generate a new and fruitful perspective on the epistemology and practice of mathematics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
