Robotics is the next frontier in the progress of Artificial Intelligence (AI), as the real world in which robots operate represents an enormous, complex, continuous state space with inherent real-time requirements. One extreme challenge in robotics is currently formed by autonomous drone racing. Human drone racers can fly through complex tracks at speeds of up to 190 km/h. Achieving similar speeds with autonomous drones signifies tackling fundamental problems in AI under extreme restrictions in terms of resources. In this article, we present the winning solution of the first AI Robotic Racing (AIRR) Circuit, a competition consisting of four races in which all participating teams used the same drone, to which they had limited access. The core of our approach is inspired by how human pilots combine noisy observations of the race gates with their mental model of the drone's dynamics to achieve fast control. Our approach has a large focus on gate detection with an efficient deep neural segmentation network and active vision. Further, we make contributions to robust state estimation and risk-based control. This allowed us to reach speeds of ~9.2m/s in the last race, unrivaled by previous autonomous drone race competitions. Although our solution was the fastest and most robust, it still lost against one of the best human pilots, Gab707. The presented approach indicates a promising direction to close the gap with human drone pilots, forming an important step in bringing AI to the real world.