Observing surgical practice has historically relied on fixed vantage points or recollections, leaving the egocentric visual perspectives that guide clinical decisions undocumented. Fixed-camera video can capture surgical workflows at the room-scale, but cannot reconstruct what each team member actually saw. Thus, these videos only provide limited insights into how decisions that affect surgical safety, training, and workflow optimization are made. Here we introduce EgoSurg, the first framework to reconstruct the dynamic, egocentric replays for any operating room (OR) staff directly from wall-mounted fixed-camera video, and thus, without intervention to clinical workflow. EgoSurg couples geometry-driven neural rendering with diffusion-based view enhancement, enabling high-visual fidelity synthesis of arbitrary and egocentric viewpoints at any moment. In evaluation across multi-site surgical cases and controlled studies, EgoSurg reconstructs person-specific visual fields and arbitrary viewpoints with high visual quality and fidelity. By transforming existing OR camera infrastructure into a navigable dynamic 3D record, EgoSurg establishes a new foundation for immersive surgical data science, enabling surgical practice to be visualized, experienced, and analyzed from every angle.