The problem of externality refers to the challenge of defining externality in a manner consistent with the rest of economic theory. The problem of externality has been expressed at least as early as 1924, when Frank Knight's critique of Arthur Pigou's The Economics of Welfare was published. This paper is a summary of the problem of externality and the progress that has been made on it in the last hundred years. I argue that little to no progress has been made on the problem of externality, as the supposed special relationship between externality and transaction costs does not exist. Drawing on scientific and mathematical concepts outside of the usual domain of economics, I describe four paths by which progress on the problem of externality might be made. <br>