Human-AI Synergy and the Dynamical Paradigm: A Research Program for Mathematics and Physics in the Age of AI

Traditional mathematical and physical research has long been dominated by static theorem proving and reductionist analysis as its core paradigms. As artificial intelligence capabilities continue to evolve, merely employing AI as a computational tool is no longer sufficient to unlock its potential in fundamental science. This paper proposes a human-AI synergistic dynamical research paradigm for the AI era: treating humans and artificial-intelligence systems as two distinct cognitive systems, constructing a dual-loop collaborative structure; shifting the research focus from "proving static propositions" to "identifying precursors of dynamical evolution"; and advocating the reconciliation of four divides—between Eastern and Western scholarship, holism and reductionism, humanities and sciences, and humans and intelligent systems. Classical mathematical problems—such as the Navier–Stokes equations, the Riemann Hypothesis, the BSD Conjecture, the Twin Prime Conjecture, and Goldbach's Conjecture—may serve as touchstones for testing the explanatory power and operability of this paradigm; the paradigm itself, however, constitutes the long-lasting research infrastructure that can be inherited and extended by future generations. This program articulates research methodology only and makes no ontological presuppositions.