Archive for History of Exact Sciences

, Volume 68, Issue 5, pp 547–597

Integral equations between theory and practice: the cases of Italy and France to 1920


DOI: 10.1007/s00407-013-0132-2

Cite this article as:
Archibald, T. & Tazzioli, R. Arch. Hist. Exact Sci. (2014) 68: 547. doi:10.1007/s00407-013-0132-2


In 1899, Ivar Fredholm discovered how to treat an integral equation using conceptual methods from linear algebra and use these ideas to solve certain classes of boundary value problems. He formulated a theory allowing him both to unify large classes of problems and to attack several problems fruitfully. The historical literature on the theory of integral equations has concentrated largely on the unification that was afforded by Hilbert and his school, but has not throughly investigated the roots of the subject in the older theory of partial differential equations, as developed for instance by Fredholm himself but also by Volterra and Levi-Civita. By concentrating on work issuing from this older tradition, in particular on French and Italian work, the paper shows how the new theory of integral equations was enthusiastically received, especially for its fruitful applications to areas of mathematical physics such as hydrodynamics, elasticity, and heat theory.

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  2. 2.UFR de mathématiques, Laboratoire Paul Painlevé, UMR CNRS 8524Université de Sciences et Technologie de LilleLilleFrance

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