Metaphorical reactions in 1932: from the mathematical ‘crisis of intuition’ to ‘reconstruction in the exact sciences’

In 1932, the mathematician Hans Hahn delivered a lecture titled ‘The crisis of intuition’, held within a lecture series called ‘Crisis and Reconstruction in the Exact Sciences’, organized by Karl Menger. In order to account for the various crises, Hahn and his colleagues employed various metaphors. That being said, the dominant metaphor was architectural. Why was this particular metaphor used? And were there other metaphors that were equally important? In this paper, I aim not only to answer these questions, taking into account the image of mathematics and of the mathematician which was conveyed by those metaphors, but also to examine how the various crises were considered via these metaphorical reactions.