Ever since 1956 when details of the Logic Theorist were published by Newell and Simon, a large literature has accumulated on computational models and theories of the creative process, especially in science, invention and design. But what exactly do these computational models/theories tell us about the way that humans have actually conducted acts of creation in the past? What light has computation shed on our understanding of the creative process? Addressing these questions, we put forth three propositions: (I) Computational models of the creative process are fundamentally flawed as theories of human creativity. Rather, the universal power of computational models lies elsewhere: (II) Computational models of particular acts of creation can serve as effective experiments to test universal hypotheses about creative processes and mechanisms; and (III) Computation-based architectures of the creative mind provide metaphorical frameworks that, like all good metaphors, can serve as rich sources of insight into aspects of the creative process. In this paper, we provide evidence for these three propositions by drawing upon some particular episodes in the cognitive history of science, technology, and art.