Émile Léonard Mathieu

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Émile Léonard Mathieu (born May 15, 1835 in Metz , † October 19, 1890 in Nancy ) was a French mathematician . He is known as the discoverer of the first five sporadic groups , which are called mathieusche groups after him .


Mathieu came from a family of minor officials. He attended the lyceum in Metz, where his mother was from and where an uncle (Pierre Aubertin), who was also an artillery colonel and graduated from the École Polytechnique , had a cannon foundry. Mathieu was a very good student both in the classical languages ​​and in mathematics and studied from 1854 at the École Polytechnique in Paris, where he also excelled as a student and completed the prescribed courses in 18 months. Initially he pursued a military career, but then switched to an academic career in mathematics. He published his first mathematical works in 1856 and received his doctorate in mathematics at the Sorbonne in 1859 (dissertation: Sur le nombre de valeurs que peut acquérir une fonction quand on y permute ses lettres de toutes les manières possibles). The dissertation also contained the beginnings of the discovery of the sporadic groups named after him (as transitive subgroups of permutation groups that had already been investigated by Augustin-Louis Cauchy ) and it was published in 1860/61. - He explicitly described the math groups M12 and M24 in a paper published in 1873. In 1862 Gabriel Lamé , supported by Joseph Liouville , proposed his admission to the Academie des Sciences in the Geometry section on the basis of this work , but this never materialized. Mathieu then turned to applied mathematics. He gave private tuition in mathematics and courses at the Lycée Charlemagne , the Lycée Saint-Louis and the Lyceum of Metz. In 1863 he was ill for a long time and moved back to live with his mother. An application to teach at the Sorbonne was not accepted despite the advocacy of important mathematicians such as Liouville, Michel Chasles , Charles Delaunay , Victor Puiseux , Jean-Marie Duhamel , Joseph Serret and Jean Victor Poncelet ( Charles Auguste Briot received the post ). He was invited to trial lectures (1867/68), but these were held outside the Sorbonne and attracted few students and were a failure. His lectures were judged to be correct, but his demeanor as a teacher and his teaching skills left something to be desired in the eyes of his superiors. He was by nature reserved and introverted. Mathieu then looked for a professorship in the province. From 1869 Émile Mathieu taught in Besançon , where he became a professor of pure mathematics in 1871. In 1871 he married Marie Joséphine Guisse. In the same year he applied to Nancy , where many French professors from Strasbourg sought refuge after the German occupation. Among them was Xavier Dagobert Bach (1813–1885), and after he gave up his professorship in Nancy in 1873, Mathieu became professor of pure mathematics there in 1874. He did not give up his applications for a chair in Paris, however, his applications repeatedly failed, often very narrowly. In particular, he had hoped for Gabriel Lamé's chair for mathematical physics, especially since that was his specialty and he had already jumped in for Lamé (who gave up his chair in 1862 due to deafness, but this was not filled until 1886). Mathieu himself blamed the influence of Charles Hermite , who played a central role in mathematics in Paris.

In addition to the Mathieu groups, which he discovered between 1860 and 1873, the Mathieu differential equation and the Mathieu inequalities are named after him. In mathematical physics, he dealt with diffraction, elasticity theory, vibrations of bells, heat conduction, the three-body problem (disturbances of Jupiter and Saturn), capillary forces and magnetic induction. He planned an eleven-volume series of monographs on mathematical physics, eight volumes of which were published by the time he died.


  • Mémoire sur le nombre de valeurs que peut acquérir une fonction quand on y permute ses variables de toutes les manières possibles, Journal de mathématiques pures et appliquées, series 2, volume 5, 1860, pp. 9-42, online
  • Mémoire sur l'étude des fonctions de plusieurs quantités, sur la manière de les former et sur les substitutions qui les laissent invariables, Journal de mathématiques pures et appliquées, Series 2, Volume 6, 1861, pp. 241–323, online
  • Sur la fonction cinq fois transitive de 24 quantités, Journal de mathématiques pures et appliquées, 2nd series, Volume 18, 1873, pp. 25-46, online
  • Cours de physique mathématique, 1874
  • Dynamique analytique 1878
  • Theorie de la capillarité, 1883
  • Théorie du potentiel et ses applications à l'électrostatique et au magnétisme, I (Théorie du potentiel), 1885, II (Electrostatique et magnétisme) 1886
  • Théorie de l'électrodynamique 1888
  • Théorie de l'élasticité des corps solides. I (Considérations générales sur l'élasticité; emploi des coordonnées curvilignes; Problem relatifs à l'équilibre de l'élasticité; plaques vibrantes) 1890, II (Mouvements vibratoires des corps solides; équilibre de l'élasticité du prisme rectangle), 1890

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