Evolution produced many species whose members are pre programmed with almost all the competences and knowledge they will ever need. Others appear to start with very little and learn what they need, but appearances can deceive. I conjecture that evolution produced powerful innate meta knowledge about a class of environments containing 3 D structures and processes involving materials of many kinds. In humans and several other species these innate learning mechanisms seem initially to use exploration techniques to capture a variety of useful generalisations after which there is a "phase transition" in which learnt generalisations are displaced by a new generative architecture that allows novel situations and problems to be dealt with by reasoning -- a pre cursor to explicit mathematical theorem proving in topology, geometry, arithmetic, and kinematics. This process seems to occur in some non human animals and in pre verbal human toddlers, but is clearest in the switch from pattern based to syntax based language use. The discovery of non linguistic toddler theorems has largely gone unnoticed, though Piaget investigated some of the phenomena, and creative problem solving in some other animals also provides clues. A later evolutionary development seems to have enabled humans to cope with domains that involve both regularities and exceptions, explaining "U shaped" language learning. Only humans appear to be able to develop meta meta competences needed for teaching learnt "theorems" and their proofs. I'll sketch a speculative theory, present examples, and propose a research programme, reducing the 'G' in AGI, while promising increased power in return. DRAFT Extended Abstract...