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Differential equations and algebraic transcendents: French efforts at the creation of a Galois theory of differential equations 1880-1910. (Équations différentielles et transcendants algébriques : les efforts français sur la création d’une théorie de Galois pour les équations différentielles 1880-1910.) (English. French summary) Zbl 1234.01002

The reception of the work of Évariste Galois on the solution of polynomial equations, and the way in which the name of Galois became emblematic for a certain kind of mathematical creativity, make a complicated story.
In this paper the question is discussed what it meant in the context of the study of ordinary differential equations. Émile Picard published a first paper on this subject in 1883. His main results were limited by unnecessary hypotheses, as shown in 1892 by his student Ernest Vessiot. The subject became interesting to a number of French mathematicians. Jules Drach discussed the results of Picard and Vessiot in his doctoral thesis in 1898. This led to a further reworking of the subject by Vessiot. In 1902, the ‘Grand Prix’ of the French Academy in Paris was announced to this question. The success of the area producing concrete results was limited in the period to 1910.
The present paper recounts the events, looking at the tools created and the interpretation of the Galois legacy manifest in different attempts.

MSC:

01A55 History of mathematics in the 19th century
01A60 History of mathematics in the 20th century
34-03 History of ordinary differential equations
12-02 Research exposition (monographs, survey articles) pertaining to field theory
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