Differential equations and algebraic transcendents: french efforts at the creation of a Galois theory of differential equations 1880–1910

Tom Archibald

Revue d'histoire des mathématiques (2011)

  • Volume: 17, Issue: 2, page 373-401
  • ISSN: 1262-022X

Abstract

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A “Galois theory” of differential equations was first proposed by Émile Picard in 1883. Picard, then a young mathematician in the course of making his name, sought an analogue to Galois’s theory of polynomial equations for linear differential equations with rational coefficients. His main results were limited by unnecessary hypotheses, as was shown in 1892 by his student Ernest Vessiot, who both improved Picard’s results and altered his approach, leading Picard to assert that his lay closest to the path of Galois. The subject became interesting to a number of French researchers in the next decade and more, most importantly Jules Drach, whose flawed 1898 doctoral thesis led to a further reworking of the subject by Vessiot. The present paper recounts these events, looking at the tools created and at the interpretation of the Galois legacy manifest in these different attempts.

How to cite

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Archibald, Tom. "Differential equations and algebraic transcendents: french efforts at the creation of a Galois theory of differential equations 1880–1910." Revue d'histoire des mathématiques 17.2 (2011): 373-401. <http://eudml.org/doc/274953>.

@article{Archibald2011,
abstract = {A “Galois theory” of differential equations was first proposed by Émile Picard in 1883. Picard, then a young mathematician in the course of making his name, sought an analogue to Galois’s theory of polynomial equations for linear differential equations with rational coefficients. His main results were limited by unnecessary hypotheses, as was shown in 1892 by his student Ernest Vessiot, who both improved Picard’s results and altered his approach, leading Picard to assert that his lay closest to the path of Galois. The subject became interesting to a number of French researchers in the next decade and more, most importantly Jules Drach, whose flawed 1898 doctoral thesis led to a further reworking of the subject by Vessiot. The present paper recounts these events, looking at the tools created and at the interpretation of the Galois legacy manifest in these different attempts.},
author = {Archibald, Tom},
journal = {Revue d'histoire des mathématiques},
keywords = {Galois theory; differential equation; Lie theory; Borel; Drach; Lie; Mintwoski; Picard; differential Galois theory; group theory},
language = {eng},
number = {2},
pages = {373-401},
publisher = {Société mathématique de France},
title = {Differential equations and algebraic transcendents: french efforts at the creation of a Galois theory of differential equations 1880–1910},
url = {http://eudml.org/doc/274953},
volume = {17},
year = {2011},
}

TY - JOUR
AU - Archibald, Tom
TI - Differential equations and algebraic transcendents: french efforts at the creation of a Galois theory of differential equations 1880–1910
JO - Revue d'histoire des mathématiques
PY - 2011
PB - Société mathématique de France
VL - 17
IS - 2
SP - 373
EP - 401
AB - A “Galois theory” of differential equations was first proposed by Émile Picard in 1883. Picard, then a young mathematician in the course of making his name, sought an analogue to Galois’s theory of polynomial equations for linear differential equations with rational coefficients. His main results were limited by unnecessary hypotheses, as was shown in 1892 by his student Ernest Vessiot, who both improved Picard’s results and altered his approach, leading Picard to assert that his lay closest to the path of Galois. The subject became interesting to a number of French researchers in the next decade and more, most importantly Jules Drach, whose flawed 1898 doctoral thesis led to a further reworking of the subject by Vessiot. The present paper recounts these events, looking at the tools created and at the interpretation of the Galois legacy manifest in these different attempts.
LA - eng
KW - Galois theory; differential equation; Lie theory; Borel; Drach; Lie; Mintwoski; Picard; differential Galois theory; group theory
UR - http://eudml.org/doc/274953
ER -

References

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