This paper examines the idea of a genetic or evolutionary algorithm being an inspirational or discovery engine. This is illustrated in the particular context of designing electronic circuits. We argue that by connecting pieces of logic together and testing them to see if they carry out the desired function it may be possible to discover new principles of design, and new algebraic techniques. This is illustrated in the design of binary circuits, particularly arithmetic functions, where we demonstrate that by evolving a hierarchical series of examples, it becomes possible to re-discover the well known ripple-carry principle for building adder circuits of any size. We also examine the much
harder case of multiplication. We show also that extending the work into the field of multiple-valued logic, the genetic algorithm is able to produce fully working circuits that lie outside conventional algebra. In addition we look at the issue of principle extraction from evolved data
