We discuss progress in the design of an apprentice program S3 whose goal is to recapitulate certain aspects of the conceptual development in an important branch of physics, hydrodynamics. The program is initially endowed with a bag of "mathematical tricks" and hydrodynamics knowledge as known in the scientific community around 1830. The program not only solves water wave problems but also acquires new concepts and theories in light of its problem solving experiences. We show how the problem solver might discover the concept of group velocity by examining the solution trace of a typical wave problem. The discovery process is based on a combination of careful observations and justifiable mathematical speculations. Little search is required.