Declarative learning by experience is a foundation cognitive c^ability, and w e argue that, over and above the normal processes of declarative learning, the ability for truly novel learning is the critical capability which bootstraps human cognition. Next w e assert that none of the established models of machine learning and no established architecture for cognition have adequate declarative learning capabilities, in that all depend for their success on some pre-characterisation of the learning domain in terms of state space or pre-existing primitives geared to the domain. Finally we describe briefly the Contextual Memory System, which was designed explicitly to sup{>ort all five declarative learning capabilities. The C M S underlies the Maths Understander machine learning system which 'reads' mathematics texts from scratch, assimilating mathematics concepts, and using them not only to check proofs but also to solve problems.