\documentclass[12pt]{article}

\begin{document}

%%\hfill{Final English version edited by ES 2.5.99}\\
\noindent {\bf Sim\'eon-Denis POISSON}\\
b. 21 June 1781, d. 25 April 1840
\vspace{.5cm}

\noindent
{\bf Summary}  Poisson, the apostle of Laplacian science, was the master of
French mathematics from 1815 to 1840. His contribution to probability theory is
not confined to the distribution which bears his name or to the expression ``Law
of Large Numbers", but bears on various areas ranging from pure mathematics to
the mathematics of artillery.
\vspace{.5cm}

Sim\'eon-Denis Poisson who was born in Pithiviers and died in Sceaux,
came from a modest background.  His father, who had been a soldier,
held a minor administrative post and became president of the Pithiviers 
district 
(Loiret) during the French Revolution.  As a child, Sim\'eon-Denis was 
first educated within
his family, and later in the {\it \'ecole centrale} at Fontainebleau, one 
of the secondary
schools created by the Directoire between 1795 and 1799.  He owed his social 
and 
scientific rise to the new scientific institutions such as the Institut de 
France, 
the \'Ecole Polytechnique, and the Bureau des Longitudes, created by the French 
Revolution, as well as the unconditional and very effective support of 
Laplace (q.v.), his 
mentor in all things.

   Poisson was admitted as the top candidate to the \'Ecole Polytechnique in 
1798.  
Singled out by his teachers, he was appointed as Associate Professor in 1802, 
and  Professor in 1806 to replace Fourier 
who had 
been named Prefect.  In 1809, he was the first Professor of Mechanics in 
the 
new Faculty of Sciences of the University of Paris, which Napoleon had just 
created.
He became an astronomer at the Bureau des Longitudes in 1808, and a member 
of the 
Institut de France in 1812.  In short, Poisson gathered all the possible 
laurels
available under the new French academic nomenclature.  At the fall of the 
Emperor 
Napoleon in 1815, Poisson, whose political flexibility was as remarkable as the 
rigidity of his scientific convictions, was given supreme powers over the 
French 
universities.  For 25 years, he was to reign without sharing of power over 
scientific education at all 
levels.  It was he alone who decided on the appointment of Professors at every 
scientific institution, large or small, and he determined their teaching 
programs in 
the minutest detail.  One can well imagine that this concentration of power 
earned 
him many enemies.  Nevertheless, his administrative achievement was 
considerable, and  
devoted entirely to the service of a cause:  the development and use of 
Laplacian science, of which he was the main heir after his mentor's death 
in 1827. 

   Poisson's scientific achievement is impressive both in its quantity 
and quality:
it covers all of the physics and mathematical analysis of the period.  Poisson 
was a very thorough analyst who solved problems  by direct 
attack 
on the most complex and delicate of points.  We may mention his 
work on the 
differential equations of mechanics, which are at the very basis of the 
fundamental 
researches of Hamilton and Jacobi 30 years later and also 
his work on
domains of attraction which inspired the most beautiful discoveries of Green.  
One
could equally well single out his work on the various ``definite integrals" 
with 
which he toyed.  Poisson is remembered in history more for his mathematical
virtuosity than for his corpuscular physical models.  These were the cause of 
many 
of his controversies, for example with Laplace on capillarity, with Fourier 
on heat, 
with Fresnel on light and with Navier on elasticity.  According to P. 
Costabel, his
strength lay rather in his ``sense of formalism, which uncovers analogies, 
unifies 
problems or areas which have so far been distinct, and extends decisively 
the use 
of the calculus."
 
The clarity of his exposition, whether oral or written, was such that 
his teachings encapsulated in his {\it Trait\'e de Mecanique} (1st edition 
1811) served as a basic text
during the 19th century.

Together with Fourier, Poisson was among the first to understand the 
fundamental 
importance of Laplace's probabilistic opus.  It was Poisson who gave the first 
convincing if not definitive proofs of Chapter 4 of the second volume of the 
{\it Th\'eorie 
analytique} of 1812 containing ``Laplace's Theorem".  This states that the 
sum of a 
large number of errors having any distributions is asymptotically Gaussian,
whence 
``Laplace's formula" allows us to calculate the parameters of the limiting 
distribution to good precision from the observations 
alone.
Poisson, who helped to create the first chair in the Calculus of 
Probabilities for 
his friend Libri in the Faculty of Sciences of the University of Paris, was 
also the 
first to teach Laplace's formulae in his lectures at the Sorbonne in 1836.  
These
lectures, later published as a large 415 page book in 1837, served as a model 
for the 
teaching of the asymptotic theory of probabilities throughout Europe, 
particularly 
in Berlin, Cambridge and St Petersburg.  The title {\it Recherches sur la 
probabilit\'e
des jugements} of this treatise is misleading.  Only the last quarter of 
the volume is
concerned with judgements;  the rest of the work is a complete treatise on 
probability,
in which several important theoretical concepts are to be found, at 
least between the 
lines and without specific announcements.  Among them are those of random 
variable and 
distribution function (p.140).

   Poisson's interest in the calculus of probabilities was probably evoked 
by the 
abstracts (comptes rendus) of Laplace's and Fourier's papers, which he 
prepared for 
the {\it  Bulletin de la Soci\'et\'e Philomatique}, dating from 
1808-1810.  His 
first  
publication on probabilities discusses the banker's advantage in the game 
of ``trente 
et quarante" which was very popular in 1820;  in it he adapts some 
Laplacian ideas 
on characteristic functions.  A short time after, he studies certain noteworthy 
Fourier transforms, such as that of the Cauchy distribution.  Poisson was 
thus one 
of the first to consider a theory of errors where the error distribution was 
not 
necessarily Gaussian (Normal).

   Poisson lived through the extraordinary development of statistics in the 
first 
half of the 19th century.  In every one of the positions which he held, he 
tried to demonstrate how Laplacian theory could be used to validate 
statistical data.  
It was he who introduced Laplacian theory into the probabilistic problems of 
target 
practice.  In his articles in the {\it M\'emorial de l'Artillerie} of 1829, he 
defined the
problem of dispersion of shots in a probabilistic setting, where these shots 
follow 
what we would now refer to as a bivariate Gaussian distribution.  This was the 
starting point of the remarkable and unacknowledged works of French 
artillery men of the 
19th century, trained at the \'Ecole Polytechnique and the \'Ecole 
d'Application 
d'Artillerie et du G\'enie in Metz, such as I. Didion, 
G. Piobert, or E. Jouffret.
These works foreshadow many aspects of modern mathematical statistics.

   Poisson's name remains best known for the most famous scientific metaphor 
in the
history of statistics, namely the ``Law of Large Numbers", which he published 
in 1835.
This was to become the main inspirational source for Quetelet (q.v.), and later of the 
so-called Continental School of statistics.  By the Law of Large Numbers, 
Poisson 
meant that the proportion of successes in independent trials shows statistical
regularity even if the probability of success in each trial is not the same.
This version of the Law
has come to be known more specifically as Poisson's Law of Large Numbers, 
being a
generalization of the famous Law of J. Bernoulli (q.v.). It explained
theoretically the fact that descriptive statistics in the moral sciences had
been observed in the 1830's to
display numerical regularity, but gave rise to many memorable 
controversies, particularly in the decade following 1830, not only at the 
Academy 
of Sciences but also in the Chamber of Deputies.  The more general question 
in dispute was the 
relevance of the calculus of probabilities, or even more simply ``quantitative 
methods" in medicine (with Louis, Gavarret, etc.) as well as in criminology and 
demography. Poisson's Law  was, in particular, unjustly attacked by 
Bienaym\'e (q.v.)
after Poisson had
devoted the last hundred pages of his famous work of 1837  to it,
extending the work of Condorcet (q.v.).
 
   As for the Poisson distribution, it may be found highlighted in his 
treatise of 
1837, but he himself would have been very surprised to learn that in 
probability theory
he was to be 
remembered in our time almost entirely for this single minor contribution,
especially since the distribution itself had already been found by 
de Moivre (q.v.).
It was mainly around 1900, 
following the researches of Bortkiewicz (q.v.), Erlang (q.v.), Bateman and 
others, that the Poisson 
distribution acquired a renewed practical significance. It is particularly 
prominent in
connection with the ``Poisson process". Of course, Poisson's name is
attached to a number of concepts outside of probability. To mention two: 
Dirac has
acknowledged ``Poisson brackets", and students of analysis continue to learn 
about "Poisson's integral".  Thus Poisson may well rest in peace. 
\vspace{.5 cm}

\noindent{\bf References}

\noindent Bru, B. (1996). Le probl\`eme de l'efficacit\'e du tir \`a
l'Ecole de Metz: aspects th\'eoriques et exp\'erimentaux. In B.
Belhoste and A. Picon, {\it L'\'Ecole d'application de l'artillerie
et du g\'enie de Metz (1802-1870)}, Mus\'ee des plans-reliefs, Paris,
pp. 61-70.

\noindent Haight, F. (1967). {\it Handbook of the Poisson Distribution}.
Wiley, New York.

\noindent M\'etivier, M., Costabel, P., Dugac, P. (dir.) (1981). {\it
Sim\'eon-Denis Poisson et la science de son temps}, {\'Ecole polytechnique,
Palaiseau.

\noindent Sheynin, O.B. (1978). S.D. Poisson's work in probability.
{\it Archive for the History of Exact Sciences}, {\bf 18}, 245-300.

\noindent Stigler, S. (1986). {\it The History of Statistics}. Belknap,
Harvard, pp. 182-194.
\vspace{1cm}

\hfill{Bernard Bru}


\end{document}

