A Moonshot for AI Oracles in the Sciences
This work addresses a foundational problem in AI and philosophy of science, aiming to advance machine capabilities in scientific discovery, though it is conceptual and incremental in nature.
The paper tackles the challenge of enabling AI to generate revolutionary mathematical theories, proposing necessary conditions for such a mechanism and a heuristic definition of intelligibility to guide development.
Nobel laureate Philip Anderson and Elihu Abrahams once stated that, "even if machines did contribute to normal science, we see no mechanism by which they could create a Kuhnian revolution and thereby establish a new physical law." In this Perspective, we draw upon insights from the philosophies of science and artificial intelligence (AI) to propose necessary conditions of precisely such a mechanism for generating revolutionary mathematical theories. Recent advancements in AI suggest that satisfying the proposed necessary conditions by machines may be plausible; thus, our proposed necessary conditions also define a moonshot challenge. We also propose a heuristic definition of the intelligibility of mathematical theories to accelerate the development of machine theorists.