Mesopotamian Mathematics, Seen “from the Inside” (by Assyriologists) and “from the Outside” (by Historians of Mathematics)

Since the 1950s, “Babylonian mathematics” has often served to open expositions
of the general history of mathematics. Since it is written in a language and a
script which only specialists understand, it has always been dealt with differently
by the “insiders”, the Assyriologists who approached the texts where it manifests
itself as philologists and historians of Mesopotamian culture, and by “outsiders”,
historians of mathematics who had to rely on second-hand understanding of the
material (actually, of as much of this material as they wanted to take into
account), but who saw it as a constituent of the history of mathematics. The
article deals with how these different approaches have looked in various periods:
pre-decipherment speculations; the early period of deciphering, 1847–1929; the
“golden decade”, 1929–1938, where workers with double competence (primarily
Neugebauer and Thureau-Dangin) attacked the corpus and demonstrated the
Babylonians to have possessed unexpectedly sophisticated mathematical
knowledge; and the ensuing four decades, where some mopping-up without
change of perspective was all that was done by a handful of Assyriologists and
Assyriologically competent historians of mathematics, while most Assyriologists
lost interest completely, and historians of mathematics believed to possess the
definitive truth about the topic in Neugebauer’s popularizations.