This paper unveils and motivates an ambitious programme of hidden algebraic research in software engineering. We begin with an outline of our general goals, continue with an overview of results, and conclude with a discussion of some future plans. The main contribution is powerful hidden coinduction techniques for proving behavioural correctness of concurrent systems, and several mechanical proofs are given using OBJ3. We also show how modularization, bisimulation, transition systems, concurrency and combinations of the functional, constraint, logic and object paradigms fit into hidden algebra.