Related papers: Apriori Knowledge in an Era of Computational Opacity: The Role of AI in Mathematical Discovery

Apriori Knowledge in an Era of Computational Opacity: The Role of AI in Mathematical Discovery

URL: http://arxiv.org/abs/2403.15437v1
Date: Fri, 15 Mar 2024 21:38:26 GMT
Title: Apriori Knowledge in an Era of Computational Opacity: The Role of AI in Mathematical Discovery
Authors: Eamon Duede, Kevin Davey,
Abstract summary: We argue that if a proof-checker is attached to such machines, then we can obtain apriori mathematical knowledge from them. Many accept that we can acquire genuine mathematical knowledge of the Four Color Theorem from Appel and Haken's program.
Score: 0.7673339435080445
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Computation is central to contemporary mathematics. Many accept that we can acquire genuine mathematical knowledge of the Four Color Theorem from Appel and Haken's program insofar as it is simply a repetitive application of human forms of mathematical reasoning. Modern LLMs / DNNs are, by contrast, opaque to us in significant ways, and this creates obstacles in obtaining mathematical knowledge from them. We argue, however, that if a proof-checker automating human forms of proof-checking is attached to such machines, then we can obtain apriori mathematical knowledge from them, even though the original machines are entirely opaque to us and the proofs they output are not human-surveyable.

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