The Myth of the Polytechnic School

Abstract

From 1806 on, polytechnic schools were founded in various European states. According to traditional historiography, and in particular to the Festschriften of these institutions published at some anniversary, these schools took the École polytechnique in Paris as a model, with descriptive geometry as a key teaching discipline. A closer investigation shows, however, that these schools began at a rather low educational level, often as commercial schools and dependent on the ministry of commerce, and taught quite elementary mathematics. The only institution projected at the level of higher education in the first half of nineteenth century Europe was a Polytechnic Institute in Berlin: its rationale was to be mathematics teacher education. It was only in the second half of the nineteenth century that these institutions, after steady rise in the status and level of formation provided, succeeded in attaining the level of higher education and in offering demanding mathematical courses. The question is hence why a structure, which proved so successful in France, was not viable in other countries—at least in the first half of the nineteenth century.

What is crucial proves to be the character of applications of mathematics as demanded and as practiced in the respective countries. The paper will study these differences in the level and degree of development of applications of mathematics in these countries on the one hand and, on the other hand, the differing demands in these countries for such applications and, in particular, of the requisite geometrical knowledge and the functions being realised by descriptive geometry. This investigation reveals a very specific and telling pattern that enabled the functioning of the École polytechnique in a unique way.