AI is becoming ubiquitous, revolutionizing many aspects of our lives. In surgery, it is still a promise. AI has the potential to improve surgeon performance and impact patient care, from post-operative debrief to real-time decision support. But, how much data is needed by an AI-based system to learn surgical context with high fidelity? To answer this question, we leveraged a large-scale, diverse, cholecystectomy video dataset. We assessed surgical workflow recognition and report a deep learning system, that not only detects surgical phases, but does so with high accuracy and is able to generalize to new settings and unseen medical centers. Our findings provide a solid foundation for translating AI applications from research to practice, ushering in a new era of surgical intelligence.