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"Local-Global": the first twenty years

Renaud Chorlay
Archive for History of Exact Sciences
Vol. 65, No. 1 (January 2011), pp. 1-66
Published by: Springer
Stable URL: http://www.jstor.org/stable/41134338
Page Count: 66
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"Local-Global": the first twenty years
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Abstract

This paper investigates how and when pairs of terms such as "local-global" and "im Kleinen-im Grossen" began to be used by mathematicians as explicit reflexive categories. A first phase of automatic search led to the delineation of the relevant corpus, and to the identification of the period from 1898 to 1918 as that of emergence. The emergence appears to have been, from the very start, both transdisciplinary (function theory, calculus of variations, differential geometry) and international, although the AMS-Göttingen connection played a specific part. First used as an expository and didactic tool (e.g. by Osgood), it soon played a crucial part in the creation of new mathematical concepts (e.g. in Hahn's work), in the shaping of research agendas (e.g. Blaschke's global differential geometry), and in Weyl's axiomatic foundation of the manifold concept. We finally turn to France, where in the 1910s, in the wake of Poincaré's work, Hadamard began to promote a research agenda in terms of "passage du local au general."

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