Kepler’s discovery of planetary laws—rooted in Tycho Brahe’s precise data and iterative model refinement—illustrates how profound insights can emerge from limited evidence and heuristic judgment, not just formal proof. The podcast contrasts this with modern AI-driven science, where idea generation is cheap but evaluation remains slow and human-dependent—highlighting enduring bottlenecks in verification, persuasion, and conceptual coherence. It examines why some theories (e.g., heliocentrism, natural selection) gained traction only after decades or centuries, despite early predictive weaknesses, underscoring the role of narrative, cumulative evidence, and sociological factors in scientific acceptance. AI excels at breadth—enriching papers, verifying proofs, scaling computation—but still lags in depth: inventing novel techniques, building intuition, or navigating epistemic uncertainty without human guidance. The discussion emphasizes hybrid human-AI workflows, the need for semi-formal frameworks to assess conjectures, and the irreplaceable value of serendipity, collaboration, and adaptive reasoning in frontier mathematics.