**Jean-Marie Le Roux** was a French applied mathematician who worked on partial differential equations, integral equations, and differential geometry.

- We say more about his work with Breton dialects at the end of this biography.
- We have found it difficult to sort out exactly how Le Roux achieved his mathematical education.
- The agrégation is a competitive examination which qualifies students to teach in lycées and, having passed the examination, Le Roux became a teacher of mathematics at the lycée at Brest in 1889.
- While Le Roux was Professor of Special Mathematics at the lycée in Brest, he was also working towards his doctorate.
- He submitted his doctoral thesis Sur les intégrales des équations linéaires aux dérivées partielles du second ordre à deux variables indépendantes Ⓣ(On integrals of linear second order partial differential equations with two independent variables) to the Sorbonne in Paris in 1894 and he was examined by the jury consisting of Gaston Darboux, Gabriel Koenigs and Paul Appell on 24 January 1895.
- Certainly the level of science teaching at the University of Rennes was low at this time so, whatever route Le Roux adopted, he must have reached a high level of mathematical achievement mainly though his own studies.
- Le Roux published a 20-page paper with the same title as his thesis in the Annales scientifiques de l'École Normale Supérieure in 1895.
- This paper is essentially his thesis while the thesis itself was published in Paris by Gauthier-Villars et Fils, also in 1895.
- Le Roux moved from Brest to Montpellier in 1896.
- For example, his next publications were Sur une équation linéaire aux dérivées partielles du second ordre Ⓣ(On a linear second-order partial differential equation) (1896), Sur une forme analytique des intégrales des équations linéaires aux dérivées partielles à deux variables indépendantes Ⓣ(On an analytical form of the integrals of linear partial differential equations with two independent variables) (1897), Sur l"équation des télégraphistes Ⓣ(On the equation of telegraph operators) (1897), Sur l"équation linéaire aux dérivées partielles du premier ordre Ⓣ(On a linear first-order partial differential equation) (1897), Sur les invariants des équations linéaires aux dérivées partielles à deux variables indépendantes Ⓣ(On the invariants of linear partial differential equations with two independent variables) (1898), Sur l"intégrabilité des équations linéaires aux dérivées partielles du second ordre par la méthode de Laplace Ⓣ(On the integrability of linear second order partial differential equations by the Laplace method) (1898), and Sur les équations linéaires aux dérivées partielles Ⓣ(On linear partial differential equations) (1898).
- The last mentioned of these publications Sur les équations linéaires aux dérivées partielles Ⓣ(On linear partial differential equations) was published as a 50-page paper in the Journal des Mathématiques Pures et Appliquées and as a 50 page book in Paris.
- This is an in-depth study of linear partial differential equations of higher order with two independent variables, based on the results obtained for those of second order.
- This work contains results already published in earlier papers by Le Roux and may have been written for him to gain admission as a university teacher since it reads like an habilitation.
- Her primary education had been with the Sisters of the Holy Spirit on the Rue du Cleumeur, and her secondary education was at a boarding school in Plestin-les-Grèves.
- We have not been able, however, to find any information about his previous marriage.
- Jean Marie Le Roux had just been appointed a Lecturer in Mathematics at the Faculty of Science at the University of Rennes.
- At the time of his marriage, Le Roux was working in Montpellier.
- The first of these seems more likely since Le Roux was very much a Brittany person so one would not expect him to go from a lycée in Brest to a lycée Montpellier.
- To go to Montpellier to an appointment in the Faculty of Science would make more sense as would his return from Montpellier to Rennes in 1898 to an assistant lecturer position at the University of Rennes.
- Certainly in 1898 Le Roux was appointed as an assistant lecturer at the University of Rennes, was promoted to Professor of Applied Mathematics in 1902, and remained at Rennes for the rest of his career.
- Here are his eleven publications from 1899 to 1903: Extension de la méthode de Laplace aux équations linéaires aux dérivées partielles d"ordre supérieur au second Ⓣ(Extension of the Laplace method to linear equations with partial derivatives of higher order than the second) (1899), Sur une inversion d"intégrale double Ⓣ(On a double integral inversion) (1900), Sur l"intégration des équations linéaires aux dérivées partielles Ⓣ(On the integration of linear partial differential equations) (1900), Sur l"intégration des équations linéaires à discriminant non nul Ⓣ(On the integration of linear equations with non-zero discriminants) (1900), Sur un invariant d"un système de deux triangles et la théorie des intégrales doubles Ⓣ(On an invariant of a system of two triangles and the theory of double integrals) (1900), Sur les fonctions qui dépendent d"une infinité de constantes arbitraires Ⓣ(On functions which depend on an infinity of arbitrary constants) (1902), Sur une classe de groupes infinis Ⓣ(On a class of infinite groups) (1902), Sur les intégrales des équations linéaires aux dérivées partielles Ⓣ(On integrals of linear partial differential equations) (1903), Recherches sur les équations aux dérivées partielles Ⓣ(Research on partial differential equations) (1903), Intégration d"une èquation aux dérivées partielles à une infinité de variables indépendantes Ⓣ(Integration of a partial differential equation with an infinity of independent variables) (1903), and Les fonctions d"une infinité de variables indépendantes Ⓣ(The functions of an infinity of independent variables) (1903).
- Le Roux attended the Congress but did not give a lecture.
- Le Roux has a strong publication record up to 1914, having at least 38 publications up to this time.
- It is difficult to single out one paper from this list which is the most important but looking at the citations to his papers it would appear that Étude géométrique de la torsion et de la flexion dans la déformation infinitésimale d'un milieu continu Ⓣ(Geometric study of torsion and bending in the infinitesimal deformation of a continuous medium) (1911) is the one most often referenced.
- They are consequently differential elements of the second order of the deformation, whose role can be compared to that of curvature in the theory of surfaces.
- On the contrary the dilation and the average rotation are elements of the first order, like the tangent plane and the linear element in geometry.
- It seemed to me that knowing the necessary laws of the distribution of second order deformations could be as useful an introduction to the study of the mechanics of continuous media as knowing the elements of curvature when studying mechanics of a point.
- It has been found, moreover, that this theory, in addition to its practical utility, presents its own interest by the simple manner in which the results are grouped and are coordinated.
- The secondary elements of strain are the curvature and twist of slender filaments, and the curvature of thin sheets of the material, the filaments and sheets being straight and plane in the unstrained state.
- There is a seven year gap in Le Roux's publications with nothing appearing between 1914 and 1921.
- He was invited to be a plenary speaker at the following International Congress of Mathematicians which was held in Toronto in 1924.
- He sailed 2nd class on the ship Suffren, leaving Le Havre on 28 July and arriving in New York on 5 August.
- Le Roux gives his French address as 47 Aubourg de Fougères, Rennes, and the immigration details also give his height as 5 ft 5 ins, hair grey and eyes blue.
- He delivered his plenary address Considérations sur une équation aux dérivées partielles de la physique mathématique Ⓣ(Considerations on a partial differential equation of mathematical physics) on Saturday 16 August: it was the last lecture of the Congress.
- We note that Le Roux had a number of other roles at this Congress.
- He was a member of the Special Mission of the French Ministry of Public Instruction which was chaired by Gabriel Koenigs and, in addition to Le Roux, had members Émile Borel, Élie Cartan, Maurice Fréchet and Jean Mascart.
- Le Roux was also a member of the French National Committee of Mathematics along with Jules Haag and Jean Mascart.
- He gave the lecture La relativité du langage et la théorie de la Gravitation Ⓣ(The relativity of language and the theory of gravitation) at the 1928 Congress in Bologna, the lecture Les groupes de transformations et la théorie de la relativité Ⓣ(Transformation groups and the theory of relativity) at the 1932 Congress in Zurich and attended the 1936 Congress in Oslo but did not deliver a lecture.
- We see from the titles of the lectures that Le Roux gave at the 1928 and 1932 Congresses that he had turned his attention to relativity theory.
- This led to an unfortunate end to Le Roux's research career for during the last 25 years of his life he argued strongly against the general theory of relativity.
- It is surprising that, despite his excellent earlier work, he now seemed to fail to understand the mathematics.
- Let us give some details about this part of Le Roux's career.
- Le Roux led the opposition at this time and it would be fair to say that a majority of members of the Academy took the same view.
- His argument in this paper is not unreasonable, since he is claiming that to verify a scientific theory it must make predictions which can then he checked experimentally.
- This was not Le Roux's only paper on relativity in 1921, for he also published Le temps dans la mécanique classique et dans la théorie de la relativité Ⓣ(Time in classical mechanics and in the theory of relativity) and La loi de gravitation et ses conséquences Ⓣ(The law of gravitation and its consequences).
- Now it happens that Einstein's fundamental hypothesis is incompatible with the existence of mutual actions and disturbances as they are considered in classical mechanics.
- In the meantime, it should be noted that Einstein's theory, in its current state, neither makes it possible to explain or predict, even with the roughest approximation, the secular movement of Mercury.
- Marcel Brillouin published a reply to Le Roux in November 1922 with the paper Gravitation einsteinienne et gravitation newtonienne; à propos d"une récente note de M Le Roux Ⓣ(Einsteinian gravitation and Newtonian gravitation; comments on a recent note from M Le Roux).
- The Note from M Le Roux shows that it is nevertheless useful to recall it.
- The criticisms, of M Le Roux, are completely unfounded.
- The principle of special relativity, in the sense of Einstein, is sometimes superficial and sometimes absurd, depending on the field to which it is applied.
- But the statements of the author break open doors when he shows again in long calculations that for the theory of a wave process with constant propagation speed due to the wave equation a relativity principle of the Lorentzian type applies.
- By 1924 it would appear that Le Roux was a lone voice in the Paris Academy of Sciences opposing Einstein's theory.
- In addition to many papers (over 30 in the 3 years 1931-33 and 10 more in 1935), he wrote the two books Principes mathématiques de la théorie de la gravitation Ⓣ(Mathematical principles of the theory of gravitation) (1931) and Principes et méthodes de la mécanique invariante Ⓣ(Principles and methods of invariant mechanics) (1935).
- Le Roux was making translations into Breton and attempting to standardise spelling in different Breton dialects at around the same time that he was involved in arguments over relativity.
- He published Le roman de Pérédur Ⓣ(The novel of Peredur) in 1923.
- It is subtitled, Texte Gallois, Tranduit en Breton par J Le Roux, Professer à l'Université de Rennes avec une traduction Française d'après J Loth Ⓣ(A Welsh text, Translated into Breton by J Le Roux, Professor at the University of Rennes with a French translation by J Loth).
- He was a professor at the University of Rennes from 1883 to 1910 but by the time he translated Le Roux's Breton into French he was a professor at the Collège de France.
- It seemed to me that the orthographic system used since the Le Gouidec reform has various drawbacks which oppose the unification of the written language.

Born 4 April 1863, Prat, Côtes-d'Armor, France. Died 1949, Rennes, France.

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