**Emile Mathieu** is remembered especially for his discovery (in 1860 and 1873) of five sporadic simple groups named after him.

- Émile Mathieu was brought up in Metz, and he attended school at the Lycée de Metz in that town.
- It took Mathieu only eighteen months to complete the whole course which he had finished by 1856.
- Mathieu published the results from his thesis in two papers Mémoire sur le nombre de valeurs que peut acquérir une fonction quand on y permute ses variables de toutes les manières possibles Ⓣ(Memoir on the number of values) (1860) and Mémoire sur l'étude des fonctions de plusieurs quantités, sur la manière de les former et sur les substitutions qui les laissent invariables Ⓣ(Thesis on the study of the functions of several variables, on the manner of forming them, and on the substitutions which leave them invariate) (1861) both of which were published in Liouville's Journal de mathématiques pures et appliquées.
- Of course this is not always possible but Mathieu claimed that, with an algorithm he had found to construct multiply transitive groups, he could construct a 5-transitive group of degree 12, and a 5-transitive group of degree 24.
- Lamé who at the time was dean of the section asked that the name of Émile Mathieu be placed on the list of candidates.
- Progress as remarkable as that achieved by Mathieu would seem to put him in the ideal position to obtain a university appointment, even though he had failed to be elected to the Académie des Sciences, but this was not forthcoming.
- In 1866 Lamé became ill and requested the Minister of Public Instruction, Victor Duruy, that Mathieu be allowed to take over his teaching at the Sorbonne.
- Mathieu presented to the Minister a list of recommendations signed by Joseph Alfred Serret, Jean Victor Poncelet, Jean-Marie Duhamel, Joseph Liouville, Michel Chasles, Charles Delaunay, and Victor Puiseux.
- Despite these setbacks, in 1867 Mathieu received acknowledgement of the importance of his research with the award of a gold medal at the Congress of the Scientific Societies.
- Other memoirs by M Mathieu, relating to mathematical physics, give evidence, like his algebraical researches, of acute penetration and broad learning.
- As compensation for being passed over in this way, the Minister proposed Mathieu give a supplementary course at the Faculty of Science in 1867-68 so that his teaching ability could be judged.
- Mathieu chose as topics for his course the methods of integration in mathematical physics, the theory of numbers and the algebraic resolution of the equations.
- The dean of the Faculty of Science, Henri Milne-Edwards, arranged for Mathieu's lecture course to be in an inconvenient room outside the Sorbonne, in premises belonging to the 'Association philotechnique'.
- Discouraged by this report and realising that he had little chance of a position in Paris, Mathieu sought a position in the provinces.
- Although there is no direct criticism of Renard in Mathieu's letter, one must assume that he is saying that, in the circumstances, Nancy needs someone of higher quality than Renard.
- Certainly Renard believed that Mathieu was trying to have him sent to Besançon so that he could have the chair of Applied Mathematics at Nancy.
- He absolutely refused to move and Mathieu remained at Besançon where he was appointed to the chair of Pure Mathematics in December 1871.
- In December 1873 Xavier Bach retired from the chair of Pure Mathematics at Nancy and, after five years teaching at Besançon, Mathieu moved to Nancy to take up Bach's chair there.
- However, Mathieu still longed to obtain a position in Paris.
- After the chair was left vacant for a year it was filled by Émile Picard.
- In early 1886 Mathieu was disappointed in his hopes of being awarded the chair of calculus of probabilities and mathematical physics at the Sorbonne held until then by Gabriel Lippmann who, in that year, became Professor of Experimental Physics.
- It was a chair that Mathieu had hoped to obtain ever since he was asked to substitute for Lamé but again he was disappointed.
- There is no doubt who Mathieu blamed for his lack of success, namely Charles Hermite.
- Perhaps had Mathieu continued to follow up his remarkable discoveries in group theory, he might have achieved more fame and better posts in his lifetime.
- Mathieu studied fluids, in particular examining capillary forces.
- In addition to being remembered for the Mathieu groups, he is also remembered for the Mathieu functions.
- Mathieu decided to write eleven treatises describing the applications of mathematics to physics.
- The first of these works was Cours de physique mathématique Ⓣ(Course of mathematical physics) (1873) which Mathieu later wished he had given the title On the methods of integration in mathematical physics.
- In all his books Mathieu kept to the view expressed in his Preface to Cours de physique mathématique Ⓣ(Course of mathematical physics).

Born 15 May 1835, Metz, France. Died 19 October 1890, Nancy, France.

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Algebra, Group Theory

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive