Reasoning is the derivation of new knowledge from old. The reasoner must represent both the old and new knowledge. This representation will change as reasoning proceeds. This change will not just be the addition of the new knowledge. We claim that therepresentationof the old knowledge will also often change as a side effect of the reasoning process. For instance, the old knowledge may contain errors, be insufficiently detailed or require new concepts to be introduced. Representational change triggered by reasoning is a common feature of human reasoning but it has been neglected both in Cognitive Science and Artificial Intelligence. We aim to put that right. We exemplify this claim by analysing Imre Lakatos’s rational reconstruction of the evolution of mathematical methodology. We then describe the abduction, belief revision and conceptual change (ABC) theory repair system, which can automate such representational change. We further claim that the ABC system has a diverse range of applications to successfully repair faulty representations.This article is part of a discussion meeting issue ‘Cognitive artificial intelligence’.