# Georges Darmois

### Born: 24 June 1888 in Éply, Meurthe-et-Moselle, France

Died: 3 January 1960 in Paris, France

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**Georges Darmois**'s parents were Charles Émile Darmois (1857-1917) and Elizabeth Virginie Dardar (1859-1915), who were both born in Éply. Georges had an older brother Eugène, born in 1884, who went on to study mathematics and physics, becoming a professor of physics. He also has a sister Gabrielle. The small village of Éply in which he was born is equidistant from Nancy, Metz and Pont à Mousson. Daniel Dugué writes [7] (see also [8]):-

He excelled at school, studying at the Collège de Toul and then the lycée in Nancy. In his final year at the lycée he took the competitive examinations for entry to the École Polytechnique and the École Normale Supérieure and, given his outstanding performance, was offered a place in both. He chose to study at the École Normale Supérieure where his brother Eugène had already been studying for two years. He began his studies in 1906 and graduated with a first degree in mathematics in 1909. He was then given the position of 'Agrégé préparateur' which was reserved for the most brilliant students, assisting Émile Borel who was director of the École Normale Supérieure. As an undergraduate, he had taken courses given by Gaston Darboux andHe was what we call "un homme l'Est." Born at the foothills of the Vosges, he liked to explain that his name came from the land of the Armoises, on which his ancestors had laboured and which had been, in the fifteenth century, the home of the false Jeanne d'Arc, Jeanne des Armoises.

**Édouard Goursat and, in 1911, encouraged by Darboux, he began to undertake research on a topic involving both geometry and analysis. He published four papers between 1910 and 1914:**

*Sur les correspondances à normales concourantes*Ⓣ (1910);

*Sur les courbes algébriques à torsion constante*Ⓣ (1913);

*Sur les courbes à torsion constante*Ⓣ (1914); and

*Sur la méthode de Laplace*Ⓣ (1914). His thesis was almost complete when World War I broke out in July 1914 but he had to stop work on it to undertake military duty.

For his war service, Darmois served in the artillery, in particular being assigned to work on anti-aircraft batteries. Later on he worked for Section 25, under the command of the physicist Gustave Ribaud, on the transmission of sound. He wrote about how this experience changed the direction of his mathematical interests in [7]:-

After he had been released from military service, Darmois was appointed as a lecturer at the Faculty of Sciences at Nancy. His interest in the topic of his thesisThe1914-1918war, having oriented me towards ballistics and artillery problems, and then towards location by sound and the problems of measuring and of wave propagation, had deeply inflected my spirit towards mathematical physics and the calculus of probability.

*Sur les courbes algébriques à torsion constante*Ⓣ did not carry on after he took his oral examination in 1921. He was promoted to professor at Nancy in 1921, and he became interested in both the theory of relativity and in applications of probability theory. He wrote many excellent papers on relativity beginning with

*Sur l'intégration locale des équations d'Einstein*Ⓣ (1923). These publications include the outstanding memoir

*Les Équations de la Gravitation Einsteinienne*Ⓣ (1927) and an important book

*La relativité*Ⓣ published in 1932. He also published on topics which he had worked on during his military service such as (with F Croze)

*La construction de Huygens et la théorie mécanique de la propogation des ondes*Ⓣ (1927). Although he continued his interest in relativity, he began to become seriously interested in statistics from around 1923. He wrote [7]:-

In fact in 1925 he began teaching the course on probability and statistics at the Institute of Statistics of the University of Paris. This came about because Émile Borel, who had set up the course in 1923, had been elected to the Chamber of Deputies in 1925 and looked for someone he could trust to give the course for him. He chose Darmois who, of course, he knew well from working with him before World War I. In 1928 Darmois' first publication on statistics appeared being the monographThe decision I took in Nancy in1923, to connect the teaching and investigations of the calculus of probability with several applications to statistics, stemmed from the desire of constituting in France a school of theoretical and practical statistics. Great Britain and the United States showed the way, and it was important to follow their example. I was thus led to participate in national, and later international, statistical activities.

*Statistique Mathématique, Encyclopédie scientifique appliquées*Ⓣ which was a published version of the lectures he was giving at the Institute of Statistics of the University of Paris. This was, in fact, the first French textbook on mathematical statistics. Major Greenwood wrote in a review:-

At the International Congress of Mathematicians held at Bologna in September 1928, one of the plenary talks was given by Émile Borel who gave the address... this is an excellent treatise to put in the hands of statistical students with a fair grounding in mathematics who are also doing laboratory work. It might also be useful to young mathematicians who wish to have some idea of what statistics is about.

*Le calcul des probabilités et les sciences exactes.*Darmois was also an invited speaker at the Congress (although not a plenary speaker) and he gave the lecture

*Sur l'analyse et comparasion des séries statistiques qui se développent dans le temps*Ⓣ. André Danjon writes in [5] about the energetic way that Darmois went about promoting statistics in France:-

Darmois left Nancy in 1933 when he was appointed to the Faculty of Science in Paris. As well as the Institute of Statistics in Paris, there was also the Institut Henri Poincaré set up in 1928, with Borel as its head, to facilitate interactions between researchers in probability and mathematical physics. Darmois had been involved with the Institut from its beginnings, giving lectures there while still on the faculty at Nancy. An announcement for the first session in 1928-29 says [4]:-Georges Darmois set himself two tasks. Firstly, to disseminate the power of statistical methods applied to sciences of observation, to biometrics, to applied psychology, to econometrics, to production control, to operational research, and so on. The astronomers cannot forget that he was the first in France to teach statistics and stellar dynamics as early as1928-29. His apostolic mission for statistics was pursued relentlessly in the form of lectures, conferences, seminars. In some domains, success was instantaneous; George Darmois' ideas, by dint of obstinacy, managed to permeate the least prepared environments and eventually made them prevail against routine. Moreover, he tried to improve those parts of the theory which seemed to deserve special attention. And so he especially cared about the general theories of estimation from random sampling, of which the general theory of errors is a particular case

These lectures were published asG Darmois, professor at the University of Nancy, will give a series of four lectures on the following topic: Statistical laws, correlation and covariance with applications to heredity, to social and economic sciences.

*La méthode statistique dans les sciences d'observation*Ⓣ. Darmois writes in the introduction (see [4]):-

The Institut also had Maurice Fréchet, who had strong interests in statistics, as a member and it encouraged links with other statisticians. Darmois had always been influenced by R A Fisher's work in statistics and in 1934 Fisher began interacting with those at the Institut Henri Poincaré. In 1934 Darmois published the bookThe aim of these lectures is to emphasize several fundamental ideas of statistics and the character of the special order they can bring into some sets of experimental results. A research project usually stems from the desire to verify, deepen and link a group of ideas, either because of its practical importance, or from its unquestionable presence. As observation advances in the field under study, the accumulated results are thus placed either within the framework of a prior theory, sometimes vague, or in a purely pragmatic order, generally with some logical threads running through it. This provisional organization, as a convenient description of the observed material, allows the mind to handle large sets more easily. After that, one looks for what we may generally call persistences, which is to say relations commonly observed which constitute empirical laws for the observed phenomena. ... Once these empirical laws are obtained, the subsequent process of the mind aims at understanding them, explaining them, relating them. In parallel with the descriptive order, the explanatory or logical orders, scientific theories and laws develop. This development, which is constructed from several basic notions, must then recover the results of the experiment.

*Statistique et Applications*Ⓣ which considers applications of statistics to areas such as economics and psychology. In his paper

*Développements récents de la technique statistique*Ⓣ (1934) [1]:-

The links between Fisher and the Institut Henri Poincaré continued. Daniel Dugué (the author of [8] and [9]) was a doctoral student of Darmois' and he spent session 1937-38 in London as part of the collaboration. Fisher lectured in Paris in 1938 and, in the first half of 1940, Darmois visited London. In June of that year, while he was in London, France capitulated to the German invaders and it was decided that Darmois should not return to France. He stayed in London for some time teaching and undertaking research for the 'Free French'. Later he went to Algiers where he taught and undertook research at the University of Algiers. While there he supervised the writing of two doctoral theses in statistics. Bernard Bru writes [2] (or [3]):-Darmois discusses Fisher's work on estimation - he already knew of Fisher's work in time series analysis and population genetics - yet even so his note in the 'Comptes Rendus'('Sur les lois de probabilité à estimation exhaustive',Ⓣ(1935)comes as a surprise for it contained an important contribution to Fisher's theory of estimation: Darmois(1935)considered distributions admitting a sufficient statistic, what are now called the exponential, or Koopman-Pitman-Darmois, family of distributions - B O Koopman and E J Pitman were based in the United States and Australia respectively and their works appeared somewhat later. Fisher's theory of estimation, which originated in the early1920s, had attracted some American attention(Hotelling and Doob)and Darmois was the first European to contribute to the theory. His next book, or pamphlet, 'L'Emploides Observations Statistiques: Méthodes d'Estimation'Ⓣ(1936)expounded a fresh the theory and Darmois sent Fisher a copy. This approach was quite different from Fréchet's for it was an expression of solidarity and not of veiled criticism. Fisher replied in June1936thanking Darmois for his "excellent little book" and a brief correspondence on the theory of maximum likelihood ensued.

After the end of World War II, Darmois returned to his post in Paris and was appointed as head of the Institute of Statistics of the University of Paris. He served as President of the Société Mathématique de France in 1945. In 1949 he succeeded Fréchet when appointed Professor of the Calculus of Probabilities and Mathematical Physics at the Sorbonne. He was President of the International Institute of Statistics from 1954 until his death, and was elected to the Academy of Sciences in 1955 in the Astronomy Section.The administrative fiction of Darmois' being held in Britain against his will allowed him to retain his salary, and to pursue his career most honourably. In contrast, his brother Eugène(1884-1958), a physicist who was Professor in the Faculté des Sciences de Paris, was accused of being a collaborator after the liberation of France. Suspended from his duties for a time, like Julia and de Broglie, he was reinstated "with a reprimand" in December1944.

As to Darmois' personality, Bernard Bru writes [2] (or [3]):-

His former student, Daniel Dugué writes [8]:-On the basis of the opinions of all who knew him, Darmois was an extraordinarily dynamic man, who was open to the influences of both things and people. The number of his pupils and the diversity of subjects in which he guided them bear witness to this. He was gifted with a brilliant vitality, an illuminating intelligence and immense goodwill. Most of this he directed towards the young researchers who came to him from all parts of the world, many of whom continue to recall him with profound gratitude.

In 1964, four years after his death,He was, in French University circles, one of those who most welcomed colleagues from abroad, aided by the smiling amiability of Madame Darmois. How many illustrious statisticians have I met at his home, near the Sorbonne, in the Odéon quarter, where the principals of the French revolution lived ... It is in this harmonious setting that I shall always imagine my master, discussing, with his jovial good-will and deep competence, the latest youthful work that I had come to submit to him for presentation to the 'Comptes Rendus' of the Académie des Sciences. For he was always passionately concerned with youth and with the efforts of young scientists to extend the scientific patrimony they had received.

*Calcul des probabilités*Ⓣ was published. This book was in two parts:

*Variables aléatoires d'ordre fini*Ⓣ; and

*Théorie générale des variables aléatoires quelconques*Ⓣ. Octav Onicescu writes in a review:-

The first part of these lessons shows the common models of probability theory for the case of a finite number of states. ... In the second part the general space of states, constituting a Borel field, is considered, with probability defined, as usual, as an additive function of states. Distribution functions, mean values, characteristic functions with their various properties, and moments are presented in a very simple manner. Equally simple is the presentation of pairs of variables with the corresponding Laplace-Gauss law, convergence theorems, domains of attraction of the Laplace-Gauss law, with elements of the theory of errors and the influence of dependence on random quantities. The last section is devoted to linear and parabolic regressions.

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

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