Abstract: Creativity may be a trait, a state or just a process defined by its products. It can be contrasted with certain cognitive activities that are not ordinarily creative, such as problem-solving, deduction, induction, learning, imitation, trial-and-error, heuristics and "abduction," however, all of these can be done creatively too. There are four kinds of theories, attributing creativity respectively to (1) method, (2) "memory" (innate structure), (3) magic or (4) mutation. These theories variously emphasize the role of an unconscious mind, innate constraints, analogy, aesthetics, anomalies, formal constraints, serendipity, mental analogs, heuristic strategies, improvisatory performance and cumulative collaboration. There is some virtue in each, but the best model is still the one implicit in Pasteur's dictum: "Chance favors the prepared mind." And because the exercise and even the definition of creativity requires constraints, it is unlikely that "creativity training" or an emphasis on freedom in education can play a productive role in this preparation.