Siméon Denis Poisson
Born: 21 June 1781 in Pithiviers, France
Died: 25 April 1840 in Sceaux (near Paris), France
Siméon-Denis Poisson's parents were not from
the nobility and, although it was becoming increasingly difficult to
distinguish between the nobility and the bourgeoisie in France in the years
prior to the Revolution, nevertheless the French class system still had a major
influence on his early years. The main reason for this was that the army was
one of the few occupations where the nobility enjoyed significant institutional
privileges and Poisson's father had been a soldier. Certainly Poisson's father
was discriminated against by the nobility in the upper ranks of the army and
this made a large impression on him. After retiring from active service he was
appointed to a lowly administrative post which he held at the time that his son
Siméon-Denis was born. There is no doubt that Siméon-Denis's
family put a great deal of energy into helping him have a good start in life.
Now Siméon-Denis was not the first of his
parents children but several of his older brothers and sisters had failed to
survive. Indeed his health was also very fragile as a child and he was
fortunate to pull through. This may have been because his mother, fearing that
her young child would die, entrusted him to the care of a nurse to bring him
through the critical period. His father had a large influence on his young son,
devoting time to teach him to read and write.
Siméon-Denis was eight years old when the
Parisian insurrection of 14 July 1789 heralded the start of the French
Revolution. As might be expected of someone who had suffered discrimination at
the hands of the nobility, Poisson senior was enthusiastic about the political
turn of events. One immediate consequence for his support of the Revolution was
the fact that he became president of the district of Pithiviers which is in
central France, about 80 km south of Paris. From this position he was able to
influence the future career of his son.
Poisson's father decided that the medical profession
would provide a secure future for his son. An uncle of Poisson's was a surgeon
in Fontainebleau and Poisson was sent there to become an apprentice surgeon.
However, Poisson found that he was ill suited to be a surgeon. Firstly he
lacked coordination to quite a large degree which meant that he completely
failed to master the delicate movements required. Secondly it was quickly
evident that, although he was a talented child, he had no interest in the
medical profession. Poisson returned home from Fontainebleau having essentially
failed to make the grade in his apprenticeship and his father had to think again
to find a career for him.
Times were changing quite quickly in France which was
by this time a republic. No longer were certain professions controlled by the
nobility as they had been and there had been moves towards making education
available to everyone. In 1796 Poisson was sent back to Fontainebleau by his
father, this time to enrol in the École Centrale there. On the one hand
he had shown a great lack of manual dexterity, but he now showed that he had
great talents for learning, especially mathematics. His teachers at the
École Centrale were extremely impressed and encouraged him to sit the
entrance examinations for the École Polytechnique in Paris. He sat these
examinations and proved his teachers right, for although he had far less formal
education than most of the young men taking the examinations he achieved the
top place.
Few people can have achieved academic success as
quickly as Poisson did. When he began to study mathematics in 1798 at the
École Polytechnique he was therefore in a strong position to cope with
the rigours of a hard course, yet overcome the deficiencies of his early
education. There were certainly problems for him to overcome for he had little
experience of the social or academic environment into which he was suddenly
thrust. It was therefore to his credit that he was able to undertake his
academic studies with great enthusiasm and diligence, yet find time to enjoy
the theatre and other social activities in Paris. His only weakness was the
lack of coordination which had made a career as a surgeon impossible. This was
still a drawback to him in some respects for drawing mathematical diagrams was
quite beyond him.
His teachers
Laplace and Lagrange quickly saw
his mathematical talents. They were to become friends for life with their
extremely able young student and they gave him strong support in a variety of
ways. A memoir on finite differences, written when Poisson was 18, attracted
the attention of Legendre. However,
Poisson found that descriptive geometry, an important topic at the École
Polytechnique because of Monge, was
impossible for him to succeed with because of his inability to draw diagrams.
This would have been an insurmountable problem had he been going into public
service, but those aiming at a career in pure science could be excused the
drawing requirements, and Poisson was not held back. In his final year of study
he wrote a paper on the theory of equations and Bezout's theorem, and this was of such quality that he was allowed
to graduate in 1800 without taking the final examination. He proceeded
immediately to the position of répétiteur in the École
Polytechnique, mainly on the strong recommendation of Laplace. It was quite unusual for anyone to gain their first
appointment in Paris, most of the top mathematicians having to serve in the
provinces before returning to Paris.
Poisson was named deputy professor at the École
Polytechnique in 1802, a position he held until 1806 when he was appointed to
the professorship at the École Polytechnique which Fourier had vacated when he had been sent by
Napoleon to Grenoble. In fact Poisson had little time for politics for rather
his whole energies were directed to support mathematics, science, education and
the École Polytechnique. When the students at the École had been
about to publish an attack on Napoleon's ideas for the Grand Empire in 1804,
Poisson had managed to stop them, not because he supported Napoleon's views but
rather because he saw that the students would damage the École
Polytechnique by their actions. Poisson's motives were not understood by
Napoleon's administration, however, and they saw Poisson as a supporter which
did his career no harm at all.
During this period Poisson studied problems relating
to ordinary differential equations
and partial differential equations. In
particular he studied applications to a number of physical problems such as the
pendulum in a resisting medium and the theory of sound. His studies were purely
theoretical, however, for as we mentioned above, he was extremely clumsy with his
hands :-
Poisson ... was content to remain totally unfamiliar
with the vicissitudes of experimental research. It is quite unlikely that he
ever attempted an experimental measurement, nor did he try his hand at drafting
experimental designs.
His first attempt to be elected to the Institute was
in 1806 when he was backed by
Laplace, Lagrange, Lacroix,
Legendre and Biot for a place in
the Mathematics Section. Bossut was 76
years old at the time and, had he died, Poisson would have gained a place. However Bossut lived for another seven years so
there was no route into the mathematics section for Poisson. He did, however,
gain further prestigious posts. In addition to his professorship at the
École Polytechnique, in 1808 Poisson became an astronomer at Bureau des
Longitudes. In 1809 he added another appointment, namely that of the chair of
mechanics in the newly opened Faculté des Sciences.
In 1808 and 1809 Poisson published three important
papers with the Academy of Sciences. In the first Sur les inégalités
des moyens mouvement des planètes he looked at the mathematical problems
which Laplace and Lagrange had raised about perturbations of
the planets. His approach to these problems was to use series expansions to
derive approximate solutions. This was typical of the type of problem which he
found interesting. Libri wrote []:-
... he especially liked unresolved questions that had
been treated by others or areas in which there was still work to be done.
In 1809 he published two papers, the first Sur le
mouvement de rotation de la terre and the second, Sur la variation des
constantes arbitraires dans les questions de méchanique was a direct
consequence of developments in
Lagrange's method of variation of arbitrary constants which had been
inspired by Poisson's 1808 paper. In addition he published a new edition
of Clairaut's Théorie de la
figure de la terre in 1808. The work had been first published by Clairaut in 1743 and it confirmed the Newton- Huygens belief that the Earth was
flattened at the poles. In 1811 Poisson published his two volume treatise
Traité de mécanique which was an exceptionally clear treatment
based on his course notes at the École Polytechnique.
Malus was
known to have a terminal illness by 1811 and his death would leave a vacancy in
the physics section of the Institute. The mathematicians, aiming to have
Poisson fill that vacancy when it occurred, set the topic for the Grand Prix on
electricity so as to maximise Poisson's chances. The topic for the prize was as
follows (see for example ):-
To determine by calculation and to confirm by
experiment the manner in which electricity is distributed at the surface of
electrical bodies considered either in isolation or in the presence of each
other - for example at the surface of two electrified spheres in the presence
of each other. In order to simplify the problem, the Class asks only for an
examination of cases where the electricity spread on each surface remains
always of the same kind.
Poisson had made considerable progress with the
problem before Malus died on 24
February 1812. Poisson submitted the first part of his solution to the Academy
on 9 March entitled Sur la distribution de l'électricité à
la surface des corps conducteurs. As the mathematicians had intended, this was
the deciding factor in Poisson being elected to the physics section of the
Institute to replace Malus. It also
marked a move away from experimental research towards theoretical research in
what was considered to constitute physics, and in this the Institute was
following the lead given by Laplace.
Poisson continued to add various responsibilities to
his already busy life. In 1815 he became examiner for the École
Militaire and in the following year he became an examiner for the final
examinations at the École Polytechnique.
It is remarkable how much work Poisson put in; to his
research, to his teaching and to playing an ever increasingly important role in
the organisation of mathematics in France. When he married Nancy de Bardi in
1817 he found that family life put yet another pressure on him yet somehow he
survived the pressures continuing to take on further duties. His research
contributions covered a wide range of applied mathematics topics. Although he
devised no innovative new theories, he made major contributions to further
developing the theories of others often being the first to exhibit their real
significance. We mention now just a few of the topics he studied after his
election to the Academy.
In 1813 Poisson studied the potential in the interior of attracting masses, producing results
which would find application in electrostatics. He produced major work on
electricity and magnetism, followed by work on elastic surfaces. Papers
followed on the velocity of sound in gasses, on the propagation of heat, and on
elastic vibrations. In 1815 he published a work on heat which annoyed Fourier who wrote:-
Poisson has too much talent to apply it to the work of
others. to use it to discover what is already know is to waste it ...
Fourier went
on to make valid objections to Poisson's arguments which he corrected in later
memoirs of 1820 and 1821.
In 1823 Poisson published on heat, producing results
which influenced Sadi Carnot. Much of
Poisson's work was motivated by results of
Laplace, in particular his work on the relative velocity of sound and
his work on attractive forces. This latter work was not only influenced by Laplace's work but also by the earlier
contributions of Ivory. Poisson's work
on attractive forces was itself a major influence on Green's major paper of 1828 although Poisson never seems to have
discovered that Green was inspired by
his formulations.
In Recherchés sur la probabilité des
jugements en matière criminelle et matière civile, an important
work on probability published in 1837,
the Poisson distribution first appears. The Poisson distribution describes the
probability that a random event will occur in a time or space interval under
the conditions that the probability of the event occurring is very small, but
the number of trials is very large so that the event actually occurs a few
times. He also introduced the expression "law of large numbers".
Although we now rate this work as of great importance, it found little favour
at the time, the exception being in Russia where Chebyshev developed his ideas.
It is interesting that Poisson did not exhibit the
chauvinistic attitude of many scientists of his day. Lagrange and Laplace
recognised Fermat as the inventor of
the differential and integral calculus; he was French after all while
neither Leibniz nor Newton were! Poisson, however, wrote in
1831:-
This [differential and integral] calculus consists in
a collection of rules ... rather than in the use of infinitely small quantities
... and in this regard its creation does not predate Leibniz, the author of the algorithm and of the notation that has
generally prevailed.
He published between 300 and 400 mathematical works in
all. Despite this exceptionally large output, he worked on one topic at a
time. Libri writes []:-
Poisson never wished to occupy himself with two things
at the same time; when, in the course of his labours, a research project
crossed his mind that did not form any immediate connection with what he was
doing at the time, he contented himself with writing a few words in his little
wallet. The persons to whom he used to communicate his scientific ideas know
that as soon as he had finished one memoir, he passed without interruption to
another subject, and that he customarily selected from his wallet the questions
with which he should occupy himself. To foresee beforehand in this manner the
problems that offer some chance of success, and to be able to wait before
applying oneself to them, is to show proof of a mind both penetrating and
methodical.
Poisson's name is attached to a wide variety of ideas,
for example:- Poisson's integral, Poisson's equation in potential theory,
Poisson brackets in differential equations, Poisson's ratio in elasticity, and
Poisson's constant in electricity. However, he was not highly regarded by other
French mathematicians either during his lifetime or after his death. His
reputation was guaranteed by the esteem that he was held in by foreign
mathematicians who seemed more able than his own colleagues to recognise the
importance of his ideas. Poisson himself was completely dedicated to
mathematics. Arago reported that
Poisson frequently said:-
Life is good for only two things: to study mathematics
and to teach it.
J J O'Connor and E F Robertson
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