Can events be accurately described as historic at the time they are happening? Claims of this sort are in effect predictions about the evaluations of future historians; that is, that they will regard the events in question as significant. Here we provide empirical evidence in support of earlier philosophical arguments that such claims are likely to be spurious and that, conversely, many events that will one day be viewed as historic attract little attention at the time. We introduce a conceptual and methodological framework for applying machine learning prediction models to large corpora of digitized historical archives. We find that although such models can correctly identify some historically important documents, they tend to overpredict historical significance while also failing to identify many documents that will later be deemed important, where both types of error increase monotonically with the number of documents under consideration. On balance, we conclude that historical significance is extremely difficult to predict, consistent with other recent work on intrinsic limits to predictability in complex social systems. However, the results also indicate the feasibility of developing ‘artificial archivists’ to identify potentially historic documents in very large digital corpora.