Science 2.0: Evolving the Scientific Method from (AI-)Descartes, through Hilbert, to Noether

Industrial Problems Seminar

Lior Horesh
IBM

Abstract

The scientific method has driven humanity's intellectual progress for centuries, yet growing concerns about stagnation call for a fundamental reexamination of how discovery itself proceeds. The rise of large-scale AI systems, whether statistical, generative or symbolic, presents both an opportunity and a necessity to reconceptualize the very process of scientific reasoning.

Recent machine-assisted discovery methods have shown promise in learning physical laws and complex systems directly from data, yet they face persistent limitations: experimental noise, data scarcity and domain constraints. Our recent work addresses these challenges by bringing background scientific knowledge into the discovery process. AI-Descartes introduces a generator-verifier paradigm, coupling inductive hypothesis formation with deductive formal validation against existing theory, while AI-Hilbert unifies these stages within a single polynomial optimization framework.

Beyond discovering new hypotheses, the growing use of large-scale AI systems in discovery raises a parallel need: bridging the gap between machine-generated laws and established scientific theory. One path is abductive inference, the capacity to revise and extend axiom systems so that new, hypotheses become provable within a consistent theoretical framework. AI-Noether addresses this challenge through an algebraic-geometric formulation of abductive reasoning that regards the structure of scientific knowledge itself as an object of inference. It identifies a minimal set of candidate axioms that, once added to the known theory, render the observed hypotheses provable consequences. Ultimately, this talk advocates for the design of scientific reasoning machinery that unites data, theory and computation in the pursuit of interpretable and generalizable knowledge.