### Abstract

I will argue, provocatively, that the answer to the question raised in the title is NO, and that a much more detailed understanding of the regularity properties of solutions of the Einstein equations is required. There are examples of solutions which do not satisfy the usual smoothness or even the curvature square-integrable conditions, and many "weak" definitions of "solution" can be envisaged. Moreover, the criterion of well-posedness (existence, uniqueness and continuous dependence on initial conditions) may be too restrictive a requirement, and I will argue that a weaker condition, "stably-posed", may be more appropriate.