**Louis Raffy**was the son of Jean Casimir Raffy (1820-1884) and Marguerite Augustine Guibal (1821-1864). Casimir Raffy was a school teacher who wrote secondary school textbooks. His many popular books included

*Lectures d'histoire ancienne*Ⓣ (1859),

*Lectures d'histoire moderne*Ⓣ (1860),

*Lectures géographiques*Ⓣ (1867) and

*L'Europe géographie physique, politique, agricole, etc. de l'Europe en général et des états qui la composent*Ⓣ. The first two of these both ran to over 20 editions. Louis spent only the first three years of his life in Toulouse for when he was three years old his family moved to Paris. In fact he was to spend the rest of his life in that city.

At the Lycée Saint-Louis, Louis Raffy had brilliant successes in arts subjects as well as in science. He graduated in 1873 as both a 'Bachelier ès lettres' and a 'Bachelier ès sciences'. His remarkable abilities in all he studied gave him a problem in what to study at university. He hesitated for some time, unsure about his choice of a career, but eventually he decided that it was the sciences that he wanted to make his career in and he firmly set his sights on specialising in mathematics. His nature was to put all his energies into everything he did so from that point on he aimed high in his studies of the mathematical sciences.

Raffy was appointed as an assistant teacher at the Lycée Saint-Louis in 1875. In the following year he sat the examinations to enter the École normale supérieure and was awarded a place but he chose not to begin his university career at this time and he continued to work as a teacher at the Lycée Saint-Louis until 1879. In that year he entered the École normale supérieure and, after taking leave in session 1982-83, was ranked first in the agrégation, the highest teaching diploma in France, in 1883 and on the 20 April of that year he was awarded his doctorate in mathematics. His research on the genus of an algebraic curve was highly praised by Charles Hermite. Raffy published two papers which were based on his thesis, namely *Détermination du genre d'une courbe algébrique* Ⓣ (1883) and the 85-page paper *Recherches algébriques sur les intégrales abéliennes* Ⓣ (1883).

For a list of 77 papers and one book published by Raffy during his career, see THIS LINK.

On 19 October 1883 Raffy was appointed as a demonstrator in mathematics at the École Normale Supérieure and in the following year on 6 November 1884 he was put in charge of three courses at the Faculty of Sciences in Paris. From this time on, his career took place between the Sorbonne and the École Normale Supérieure, both institutions that he loved. His excellent work on delivering the three courses in 1884-85 saw him put in charge of four courses at the Faculty of Sciences on 21 March 1885 and later that year, on 1 August, he was appointed as a senior lecturer at the Faculty of Sciences.

Raffy published numerous papers, those published in 1884 and 1885 being the three papers *Sur les transformations invariantes des différentielles elliptiques* Ⓣ, *Sur une proposition de M Hermite* Ⓣ and *Sur les quadratures algébriques et logarithmiques* Ⓣ. Paul Appell spoke about his research as follows [2]:-

In the list of publications which we have found written by Raffy, there are 77 papers and one book as we mentioned above. This constitutes a high output achieved over 28 years. We display these publications at THIS LINK.Louis Raffy had definitively found his way in infinitesimal geometry, which he never ceased to cultivate and enrich until his last day; his work on surfaces and curved lines, on the deformation of surfaces, succeeded one another without interruption, noticed by the learned world, and rewarded by the Academy of Sciences.

On 14 September 1887 Raffy married Gabrielle Mathilde Thérèse Fontolive (born 2 December 1865 in Paris), the daughter of Antoine Fontolive, a dentist, and his wife Marie-Thérèse Rossignol. Louis and Gabrielle Raffy had three children, Louise Emilie Andrée Raffy, Lucienne Amélie Georgette Raffy (born 17 December 1891 in Paris), and Paul Jean Léon Raffy (born 27 January 1897 in Paris). We note that his eldest daughter Louise married Edmond Paul Ouivet who had studied mathematics advised by Raffy. Edmond Ouivet published *Melanges recherches sur les mouvements plans a deux paramètres* Ⓣ in the *Bulletin des Sciences Mathématiques* in 1917.

Paul Appell spoke about Raffy's teaching as follows [2]:-

Raffy was appointed as a senior lecturer for the teaching of the agrégation, the highest teaching diploma in France, at the Faculty of Sciences from 7 November 1885. He held this position until 1893. He became a senior lecturer delivering courses leading to the first degree in mathematics on 9 November 1893, and an assistant professor of analysis on 27 July 1895. All these positions were at the Faculty of Sciences but on 13 January 1897 he was appointed as a senior lecturer at the École Normale Supérieure.In his teaching, he was deeply imbued with his duties: he prepared his courses and lectures with meticulous care, loving his pupils, taking an interest in the detail of their work, correcting and annotating their copies with admirable knowledge, bringing to examinations a high idea of his mission.

At the École Normale Supérieure, Raffy became a senior lecturer in analysis and, beginning in July 1897, he taught courses on the Elements of Analysis and on Mechanics. We have a record of Raffy's courses for he published them as the 251-page book *Leçons sur les applications géométriques de l'analyse *(*éléments de la théorie des courbes et des surfaces*) Ⓣ (1897) [2]:-

On 9 December 1899 he was promoted to adjunct professor at the Sorbonne. He took leave in session 1900-1901. On 26 July 1904 he was appointed to the chair of Applications of Analysis to geometry at the Sorbonne, a chair was specially created for Raffy.His lessons were published in a work remarkable for his composition, his precision and the perfection of language.

Raffy is one of many people who make a huge contribution to mathematics yet their contributions have not been made in ways that lead to them being known to mathematicians today. We know of no theorem named for him nor any concept being named for him. He was unlucky with his paper *Sur une classe nouvelle de surfaces isothermiques et sur les surfaces deformaties sans alteration des courbures principales* Ⓣ (1893) which contains a statement that a necessary condition that a surface *S* admits ∞^{1} surfaces applicable to it with preservation of both curvatures is that the surface *S* be isometric. Sadly Raffy's proof is incorrect but he was unlucky in that the error was as a result of using a result of Théodule Caronnet (born 1864) which was fallacious. Théodule Caronnet was, in 1893, a research student at the University of Paris and he was awarded his doctorate in mathematical sciences in 1894. He was later known for being the author of a large number of highly successful textbooks on geometry and mechanics. A correct proof of the result stated by Raffy was proved correctly by Ioannis Hazzidakis, the father of Nikolaos Hatzidakis, in *Biegung mit Erhaltung der Hauptkrümmungsradien* Ⓣ (1897).

There is another important contribution which Raffy made to mathematics in France which we must record and that is his contributions to the French Mathematical Society. He became a member of that Society in 1883 and served the Society for the rest of his life taking on the most important and arduous tasks. Raffy died in 1910, at the age of 55. The President of the French Mathematical Society at the time of Raffy's death was Raoul Bricard (1870-1943). Bricard was a professor of applied geometry at the National Conservatory of Arts and Crafts in Paris. He explained Raffy's contribution to the French Mathematical Society in his funeral oration [2]:-

We have quoted above from Paul Appell's oration at Raffy's funeral and we now give a further quote from this oration [2]:-As secretary, he took care of editing the 'Bulletin' until about1900. Called to the presidency in1902by the unanimous wish of his colleagues, he resumed, some time after, the functions of secretary which he continued until his death. Not only did he edit our 'Bulletin' with as much awareness as skill, but nothing that touched the life of the Society left him indifferent, and we can rightly say that he was its soul, not missing hardly any meetings and making frequent communications which constituted one of their most serious attractions. By the affection he bore to the Society, Louis Raffy showed the excellence of his character, I mean the love of science for itself, and not only for the successes it won him. Finally, I will not forget that for many years we have been able to appreciate what the man was worth beside the scientist, his inexhaustible obligingness, and his eagerness to defend the ideas he believed to be right. The memory of Louis Raffy, of all he did for our Society and dreamed of doing, will not fade from our memory.

Finally let us quote from the obituary [2]:-Thus arrived at the end of his ambitions, having not sought any function outside his service to the University to which he devoted all his efforts, he could hope for a beautiful end to his career surrounded by his dearly loved family. ... Three weeks ago he had to cease all service and was quickly taken from us. ... In the dreadful sadness of such a separation, all the professors and students of the Faculty are united in the same feeling of admiration for a life so upright, so pure, so courageous; of grief and mourning before such an untimely end.

French science has suffered a significant loss in the person of M Louis Raffy, professor at the Faculty of Sciences of Paris, who died on9June, at the age of55years. The career of the scientist was entirely devoted to science and the teaching of infinitesimal geometry which he delivered with so much care at the Sorbonne.

**Article by:** *J J O'Connor* and *E F Robertson*