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\noindent {\bf Georges DARMOIS}\\
b. 24 June 1888, d. 3 January 1960
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\noindent{\bf Summary}. Darmois was the first French mathematician to teach and
popularize British mathematical statistics. He was a pioneer in the theory of
the statistical concept of sufficiency, in stellar statistics, and in
factorial analysis.\\
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Georges Darmois was born at Eply in the district of Meurthe-et-Moselle,
France and died in Paris. He entered the
\'Ecole Normale Superi\'eure (ENS) in 1906, and defended a beautiful thesis in
geometry which he had begun under the supervision of G. Darboux.
From 1911 to 1914, he was a qualified assistant (agr\'eg\'e pr\'eparateur)
at the
ENS, whose scientific activities were then directed by \'Emile Borel (q.v.) who
rapidly grew to appreciate Darmois' energy and intelligence. Darmois'
work was interrupted by the First World War, during which he served in the
artillery, in particular with anti-aircraft batteries, and later in a section
working on location by sound. This was Section 25, under the command of the
physicist Gustave Ribaud (1884-1963), who had graduated with Darmois from the
ENS, and with whom he collaborated on various technical studies. Ribaud was
later to become a Professor in Strasbourg and Paris.
Darmois had a brilliant and practical mind, and was an enthusiastic and
sound teacher. He discovered the calculus of probabilities by teaching its
applications to military studies in the framework of the \'Ecole des
G\'en\'eraux (School for
Generals) in 1919. He was not the only scientific worker who had discovered
probability and its applications during the 1914 war: other examples are
Jules Haag with his treatise
{\it Applications au tir (Applications to Gunnery)}, and Paul L\'evy,
although his case is not quite so clear.
On his discharge from the army, Darmois was appointed lecturer (charg\'e de
cours) at the University of Nancy, where he was later Professor from 1921 to
1933. Once he had defended his thesis, he became interested in the new
problems arising in the general theory of relativity. Fortet wrote
in his obituary, ``there is no doubt that this part of Georges Darmois' work
was the most important thing he did, and it is first rate". Darmois' volume,
published in 1927 in the {\it M\'emorial des Sciences Math\'ematiques}
initiated a
large number of subsequent works, such as his pupil Andr\'e
Lichn\'erovicz's
thesis of 1939.
It was also at Nancy that Darmois discovered English mathematical
statistics through the work of Galton (q.v.), Karl Pearson (q.v.),
Yule (q.v.), Spearman and especially
R.A. Fisher (q.v.), whose genius he was among the first to recognize. Darmois
began
to teach this statistics in France in 1923. Thus it was to him that Borel
decided to hand over his course in probability and statistics at the Institute
of Statistics of the University of Paris (ISUP), created in 1923, when Borel
was
elected to the Chamber of Deputies in 1925. Darmois rapidly understood the
fundamental importance which statistics must shortly assume in all
branches of science and economics, a cause for which Borel had fought from the
very beginning of the century. Starting in 1923, Darmois appears to have had
``the will to create a school of theoretical and applied statistics in France"
(Fortet 1960). One could say that the ISUP, of which he was the Director
of Studies from 1944 on, and the centres which gradually became attached
to it, were basically his creation. Darmois' statistics course, very
Anglocentric
in its style and spirit, was published in 1928 and translated into Spanish,
Chinese and even into English. One should also mention his small book of 1934
which contains interesting comments on the applications of statistics to
economics and psychology. Thus Georges Darmois swam against the French
probabilistic current between 1930 and 1950; the opinion of French
probabilists
on British researchers was lukewarm, and they sought ``to take inspiration
from physics rather than economics or sociology", as Fortet puts it in his note
of 1960. Moreover, the French School of statistics had difficulty in grasping
the direction in which history was moving after the Second World War, just at
the time when theoretical and applied statistics suddenly acquired an added
dimension, and came to the forefront almost everywhere in the world.
In mathematical statistics, Darmois' original contributions of the 1930's
and 1940's
are particularly
interesting. Let us note particularly his work on the
concept of sufficiency; Darmois appears to have been the first to study
it in the general framework of exponential models. We should also
point out that the general Cram\'er-Rao inequality is partly due to Darmois, as
well as others before and after him (see the note by L.Lebart on this topic in
Benz\'ecri, 1982). Darmois was also one of the pioneers of stellar
statistics; and of
factorial analysis. As an outcome of this last interest, his name is
commemorated in the
Skitovich-Darmois Theorem for the characterization of the normal distribution
by the independence
of linear forms, although he did little more than enunciate a general form
(Darmois, 1951). The case of two
variables had been initiated by S. Bernstein (q.v.) in 1941, and is known as
Bernstein's Theorem.
However, Darmois soon lost his interest in contemporary research in
mathematical statistics.
Whether because of his nature or through choice, Darmois progressively devoted
himself to
teaching and the dissemination of statistical methods at all levels. This
included the work of Neyman (q.v.), Wald (q.v.) and the various American
Schools of the
post-war years of which he knew, and had encouraged in their early years, but
whose developments he had not kept up with, possibly because of his loyalty
to Fisher, and certainly because he was busy with other projects.
Nevertheless,
we should note that among those researchers who learned their probabilistic
statistics from Darmois were such remarkable personalities as Doeblin, Lo\`eve,
Halphen, Mal\'ecot, Guilbaud, Mass\'e, LeCam and others. Thus Edmond
Malinvaud
reminiscing about his master, who in 1953-54 had asked him to give an
innovative
course on econometric methods, found a beautiful form of words to speak of
``Georges Darmois, who thought so well and taught so well, but wrote
so little (though I should have said `but published so little')".
Darmois was appointed to the Facult\'e des Sciences de Paris in 1933 on the
death of Painlev\'e. He was tenured in 1942 while he was in Britain
``appointed
irrespective of his will" (Archives Nationales AJ/16/5737). In fact, Darmois
was part of the Anglo-French Scientific Mission which happened to be in Britain
at the time of France's collapse in June 1940. He decided, or had it decided
on his behalf, that he should not return to France. From 1940 to 1944, he was
entrusted with teaching and research assignments for the Free French, first in
London and later in Algiers, where no one held him by force. Exempted from
Army service, he taught at the University of Algiers, where he supervised two
theses in statistics. The administrative fiction of Darmois' being held in
Britain against his will allowed him to retain his salary, and to pursue his
career most honorably. In contrast, his brother Eug\`ene (1884-1958), a
physicist who was Professor in the Facult\'e 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 December 1944, and was even elected to the Academy of Science
in 1951.
It was Darmois who succeeded Fr\'echet (q.v.) in the Chair of the Calculus of
Probabilities and Mathematical Physics at the Sorbonne in 1949. He retired
in 1958, shortly before his death in January 1960. His successor,
Fortet, was the
last holder of the historical chair of the Calculus of Probabilities, which was
abolished together with all other chairs by the Loi
d'orientation (Orientation Law) of 1968. Dugu\'e was then appointed director
of the ISUP, a
responsibilility which he fulfilled for twenty years until his retirement.
Georges Darmois was elected to the Academy of Science in 1955 in the
Astronomy Section, to take up Jean Chazy's (1882-1955) place. Among
positions held by him, were the Presidencies of the Soci\'et\'e
Math\'ematique de
France and the Soci\'et\'e Statistique de Paris. He represented France
in all the
international statistical institutions, and from 1953 until the time of his
death in 1960, served as the ninth President of the International Statistical
Institute. One should add that Darmois for a long time managed a family
smelting works, and always retained close contacts with French industrial
circles.
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.
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\begin{thebibliography}{3}
\bibitem{1} Benz\'ecri, J.P. (1982). {\it Histoire et Pr\'ehistoire de l'Analyse
des Donn\'ees}. Paris, Dunod.
\bibitem{2} Darmois, G. (1927). Les \'equations de la gravitation einsteinienne.
M\'emorial des Sciences Math\'ematiques, Vol. XXV.
\bibitem{3} Darmois, G. (1928). {\it Statistique math\'ematique.} Encyclop\'edie
Scientifique des Math\'ematiques Appliqu\'ees. Paris, Drouin.
\bibitem{4} Darmois, G. (1934). {\it Statistique et Applications}. Paris,
Armand-Colin.
\bibitem{5} Darmois, G. (1935). Sur les lois de probabilit\'e \`a estimation
exhaustive. {\it Comptes Rendus de l'Acad\'emie des Sciences, Paris}, {\bf 200}
(1936), 1265-1266.
Darmois, G. (1951). Sur une propri\'et\'e caract\'eristique de la loi de
probabilit\'e de Laplace. {\it Comptes Rendus de l'Acad\'emie
des Sciences, Paris}, {\bf 232}, 1999-2000.
\bibitem{6} Fortet, R. (1960). Note sur G. Darmois. Archives de l'Acad\'emie
des Sciences, Darmois dossier.
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\hfill{Bernard Bru}
\end{thebibliography}
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