# Robert de Montessus de Ballore

### Quick Info

Born
20 May 1870
Villeurbanne, Rhône, France
Died
26 January 1937
Arcachon, Gironde, France

Summary
Robert de Montessus was a French mathematician, known for his work on continued fractions and Padé approximants.

### Biography

Robert de Montessus de Ballore was born in Villeurbanne, in the suburbs of Lyon. His father, Philippe-George (1825-1890), was an officer in the French army who had graduated from the Saint Cyr military school. He left the French army to become a farmer in the Charolais. Robert's mother was a great-granddaughter of Philibert de Commerson, a naturalist on Bougainville's expedition and a member of the French Academy of Sciences. Robert was the youngest of his parents' four children. The oldest child was Fernand (1851-1923), who graduated from the École Polytechnique and became a famous seismologist.

Robert de Montessus obtained his baccalaureate in 1886. He continued his education at Saint Étienne for two further years. Unfortunately, his parents were on the road to financial ruin. Thus, he joined the French army but left in 1893 to take up a job at the Compagnie des Chemins de Fer de Paris à Lyon et à la Méditerranée.

During the years 1895-1902, Robert de Montessus taught in different secondary schools (in Evreux, Yzeure, and Senlis). During the academic year 1898-1899, he followed the lectures of Paul Appell, Gaston Darboux and Émile Picard at the Sorbonne. Thus, he obtained his Licence ès Sciences on 24 October 1901. Next, he worked for his doctorate in mathematics under Appell's supervision.

The first contribution of Robert de Montessus in mathematics was to help Giuseppe Peano in editing the Introduction of the Formulaire in 1897.

In 1902, his friend, the French mathematician Robert d'Adhémar, helped him to join the Catholic University of Lille. In the same year, Robert de Montessus published a paper entitled Sur les fractions continues algébriques in the Bulletin de la Société Mathématique de France. In this paper he proved his famous theorem on the convergence of the rows of a Padé's table associated to a meromorphic function analytic at the origin. At the same time, Henri Padé worked on related topics and the two mathematicians were in contact. However, they ended up arguing about the priority of certain convergence results (see [2]).

In 1903, Robert de Montessus became Maître de Conférences at the Lille Catholic University.

Robert de Montessus defended his doctoral thesis Sur les fractions continues algébriques on 8 May 1905. The examiners were his supervisor Paul Appell, together with Henri Poincaré and Édouard Goursat. In the first part of the thesis, Robert de Montessus dealt with different problems of convergence of algebraic continued fractions. The second part was on probabilities (errors theory). The first part of his thesis was published in the Rendiconti del Circolo Mathematico di Palermo in 1905.

In 1906, the subject proposed for the Grand Prix of the Paris Academy of 1906 was on the convergence of algebraic continued fractions. The Grand Prix was awarded to Robert de Montessus, Henri Padé and A Auric (see [2]). Moreover, Montessus de Ballore's theorem was soon cited by mathematicians such as Edward van Vleck, Niels Norlund, Oskar Perron and Edwin Wilson. Joseph Walsh cited the theorem in 1935 and again after World War II. Today, the Robert de Montessus theorem remains of great interest (see [4]).

Robert de Montessus married Suzanne Montaudon (1884-1983) on the 29 March 1906.

In 1908, Robert de Montessus wrote a book on probability theory entitled Leçons élémentaires sur le Calcul des Probabilités . From this text it is clear that Robert de Montessus was familiar with the work of Louis Bachelier on the theory of speculation (see [3]). De Montessus continued to publish works on continued fractions up to 1909. Afterwards, he wrote papers on algebraic space curves and the paramatrisation of such a curve by elliptic functions. So, he followed George Halphen's works.

At the beginning of World War I, he left Lille. During the war, he gave some lectures at the Sorbonne, particularly on elliptic functions and algebraic space curves. In 1917, Robert de Montessus joined the editorial team of the Journal de Mathématiques Pures et Appliquée headed by Camille Jordan. In the same year de Montessus was employed to work on ballistics by the French government.

After 1919, Robert de Montessus devoted much attention to the theory of probability and applied statistics. In fact he was in correspondence with several Belgian mathematicians such as Paul Mansion, Charles de La Vallée Poussin, Maurice Alliaume, but also with Maurice Fréchet and Charles Jordan. In 1924, he was appointed as a researcher at the French National Office of Meteorology at Paris. In 1925, he published a book, in collaboration with José Duarte, on tables for $\log n!$.

In 1919, Robert de Montessus created the Index Generalis (see [5]), a very ambitious project as explained by Henri Villat (see [7]):-
About twenty years ago, de Montessus undertook the publication of the "Index Generalis", an annual reference work now well known throughout the scientific world and of inestimable value to every investigator. It is hard to conjecture the number of practical difficulties which de Montessus had to overcome in organizing this immense mass of data on the universities and learned societies of the world; the scientific qualities of which he had given evidence elsewhere came to his aid here.
Between the two world wars, Robert de Montessus gave courses of lectures on various branches of mathematics in Warsaw, Kraków, Lwów (now Lviv in Ukraine), Budapest, Vienna and at other universities such as Lausanne and Geneva.

In conclusion, let us quote from Henri Villat (see [6]):-
Robert de Montessus est mort au début de l'année 1937 d'une façon brusque et inattendue; il a laissé autour de lui le souvenir d'un savant modeste et consciencieux, d'un homme droit et d'un ami sûr .

En 1917, Camille Jordan avait introduit R de Montessus à la rédaction du Journal de Mathématiques. La direction du journal tient à donner ici à sa mémoire un hommage auquel il aurait été sensible, et un souvenir ému.

### References (show)

1. C Brezinski, H Padé, Oeuvres (Librairie scientifique et technique Albert Blanchard, Paris, 1984).
2. C Brezinski, History of continued fractions and Padé approximants (Springer Verlag, Berlin, 1991).
3. J-M Courtault, Y Kabanov , B Bru , P Crepel , I Lebon and A Le Marchand, Louis Bachelier: On the centenary of Théorie de la spéculation, Mathematical Finance 10 (3) (2000), 341-353.
4. H Le Ferrand, Diffusion d'un théorème : l'exemple d'un théorème de Robert de Montessus de Ballore, de 1902 à nos jours. http://hal.archives-ouvertes.fr/hal-00521135/fr/
5. H Le Ferrand, Robert de Montessus de Ballore, mathématicien, éditeur de l'Index Generalis 1919-1937. http://hal.archives-ouvertes.fr/hal-00533453/fr/
6. H Villat, Robert de Montessus de Ballore, Journal de Mathématiques Pures et Appliquées 16 (1937), 425-426.
7. H Villat, in Nature 140 (3536) (1937), 226-227.
8. Ph Wehrlé, R de Montessus de Ballore (1870-1937), La Météorologie (janvier-février 1937), 85-87. Cote P0057C.