Scientific Discovery without Search

We discuss progress in the design of an apprentice program $3 whose goal is to recapitulate certain aspects of the conceptual development in an im-portant branch of physics, hydrodynamics. The program is initially endowed with a bag of "math-ematical tricks " and hydrodynamics knowledge as known in the scientific community around 1830. The program not only solves water wave prob-lems 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 solu-tion trace of a typical wave problem. The discov-ery process is based on a combination of careful observations and justifiable mathematical specu-lations. Little search is required