Those who nowadays work on the history of advanced-level Babylonian mathematics do so as if everything had begun with the publication of Neugebauer's Mathematische Keilschrift-Texte from 1935-37 and Thureau-Dangin's Textes mathématiques babyloniens from 1938, or at most with the articles published by Neugebauer and Thureau-Dangin during the few preceding years. Of course they/we know better, but often that is only in principle. The present paper is a sketch of how knowledge of Babylonian mathematics developed from the beginnings of Assyriology until the 1930s, and raises the question why an outsider was able to create a breakthrough where Assyriologists, in spite of the best will, had been blocked. One may see it as the anatomy of a particular "Kuhnian revolution".