Pierre-Simon Laplace
by: J J O'Connor and E F Robertson.
Pierre-Simon Laplace's father, Pierre
Laplace,
was comfortably well off in the cider
trade.
Laplace's mother, Marie-Anne Sochon,
came
from a fairly prosperous farming family
who
owned land at Tourgéville. Many accounts
of Laplace say his family were 'poor
farming
people' or 'peasant farmers' but these
seem
to be rather inaccurate although there
is
little evidence of academic achievement
except
for an uncle who is thought to have
been
a secondary school teacher of mathematics.
This is stated in [1] in these terms:-
There is little record of intellectual
distinction
in the family beyond what was to be
expected
of the cultivated provincial bourgeoisie
and the minor gentry.
Laplace attended
a Benedictine
priory school in Beaumont-en-Auge,
as a day
pupil, between the ages of 7 and 16.
His
father expected him to make a career
in the
Church and indeed either the Church
or the
army were the usual destinations of
pupils
at the priory school. At the age of
16 Laplace
entered Caen University. As he was
still
intending to enter the Church, he enrolled
to study theology. However, during
his two
years at the University of Caen, Laplace
discovered his mathematical talents
and his
love of the subject. Credit for this
must
go largely to two teachers of mathematics
at Caen, C Gadbled and P Le Canu of
whom
little is known except that they realised
Laplace's great mathematical potential.
Once
he knew that mathematics was to be
his subject,
Laplace left Caen without taking his
degree,
and went to Paris. He took with him
a letter
of introduction to d'Alembert from
Le Canu,
his teacher at Caen. Although Laplace
was
only 19 years old when he arrived in
Paris
he quickly impressed d'Alembert. Not
only
did d'Alembert begin to direct Laplace's
mathematical studies, he also tried
to find
him a position to earn enough money
to support
himself in Paris. Finding a position
for
such a talented young man did not prove
hard,
and Laplace was soon appointed as professor
of mathematics at the Ecole Militaire.
Gillespie
writes in [1]:-
Imparting geometry, trigonometry, elementary
analysis, and statics to adolescent
cadets
of good family, average attainment,
and no
commitment to the subjects afforded
little
stimulus, but the post did permit Laplace
to stay in Paris.
He began producing a steady stream
of remarkable
mathematical papers, the first presented
to the Académie des Sciences in Paris
on
28 March 1770. This first paper, read
to
the Society but not published, was
on maxima
and minima of curves where he improved
on
methods given by Lagrange. His next
paper
for the Academy followed soon afterwards,
and on 18 July 1770 he read a paper
on difference
equations. Laplace's first paper which
was
to appear in print was one on the integral
calculus which he translated into Latin
and
published at Leipzig in the Nova acta
eruditorum
in
1771. Six years later Laplace republished
an improved version, apologising for
the
1771 paper and blaming errors contained
in
it on the printer. Laplace also translated
the paper on maxima and minima into
Latin
and published it in the Nova acta eruditorum
in 1774. Also in 1771 Laplace sent
another
paper Recherches sur le calcul intégral
aux
différences infiniment petites, et
aux différences
finies to the Mélanges de Turin. This
paper
contained equations which Laplace stated
were important in mechanics and physical
astronomy.
The year 1771 marks Laplace's first
attempt
to gain election to the Académie des
Sciences
but Vandermonde was preferred. Laplace
tried
to gain admission again in
1772 but this time Cousin was elected.
Despite
being only 23 (and Cousin 33) Laplace
felt
very angry at being passed over in
favour
of a mathematician who was so clearly
markedly
inferior to him. D'Alembert also must
have
been disappointed for, on 1 January
1773,
he wrote to Lagrange, the Director
of Mathematics
at the Berlin Academy of Science, asking
him whether it might be possible to
have
Laplace elected to the Berlin Academy
and
for a position to be found for Laplace
in
Berlin.
Before Lagrange could act on d'Alembert's
request, another chance for Laplace
to gain
admission to the Paris Academy arose.
On
31 March 1773 he was elected an adjoint
in
the Académie des Sciences. By the time
of
his election he had read 13 papers
to the
Academy in less than three years. Condorcet,
who was permanent secretary to the
Academy,
remarked on this great number of quality
papers on a wide range of topics.
We have already mentioned some of Laplace's
early work. Not only had he made major
contributions
to difference equations and differential
equations but he had examined applications
to mathematical astronomy and to the
theory
of probability, two major topics which
he
would work on throughout his life.
His work
on mathematical astronomy before his
election
to the Academy included work on the
inclination
of planetary orbits, a study of how
planets
were perturbed by their moons, and
in a paper
read to the Academy on 27 November
1771 he
made a study of the motions of the
planets
which would be the first step towards
his
later masterpiece on the stability
of the
solar system.
Laplace's reputation steadily increased
during
the 1770s. It was the period in which
he
[1]:-
... established his style, reputation,
philosophical
position, certain mathematical techniques,
and a programme of research in two
areas,
probability and celestial mechanics,
in which
he worked mathematically for the rest
of
his life.
The 1780s were the period in which
Laplace
produced the depth of results which
have
made him one of the most important
and influential
scientists that the world has seen.
It was
not achieved, however, with good relationships
with his colleagues. Although d'Alembert
had been proud to have considered Laplace
as his protégé, he certainly began
to feel
that Laplace was rapidly making much
of his
own life's work obsolete and this did
nothing
to improve relations. Laplace tried
to ease
the pain for d'Alembert by stressing
the
importance of d'Alembert's work since
he
undoubtedly felt well disposed towards
d'Alembert
for the help and support he had given.
It
does appear that Laplace was not modest
about
his abilities and achievements, and
he probably
failed to recognise the effect of his
attitude
on his colleagues. Lexell visited the
Académie
des Sciences in Paris in 1780-81 and
reported
that Laplace let it be known widely
that
he considered himself the best mathematician
in France. The effect on his colleagues
would
have been only mildly eased by the
fact that
Laplace was right! Laplace had a wide
knowledge
of all sciences and dominated all discussions
in the Academy. As Lexell wrote:-
... in the Academy he wanted to pronounce
on everything.
It was while Lexell was in Paris that
Laplace
made an excursion into a new area of
science
[2]:-
Applying quantitative methods to a
comparison
of living and nonliving systems, Laplace
and the chemist Antoine Lavoisier in
1780,
with the aid of an ice calorimeter
that they
had invented, showed respiration to
be a
form of combustion.
Although Laplace soon returned to his
study
of mathematical astronomy, this work
with
Lavoisier marked the beginning of a
third
important area of research for Laplace,
namely
his work in physics particularly on
the theory
of heat which he worked on towards
the end
of his career. In 1784 Laplace was
appointed
as examiner at the Royal Artillery
Corps,
and in this role in 1785, he examined
and
passed the 16 year old Napoleon Bonaparte.
In fact this position gave Laplace
much work
in writing reports on the cadets that
he
examined but the rewards were that
he became
well known to the ministers of the
government
and others in positions of power in
France.
Laplace served on many of the committees
of the Académie des Sciences, for example
Lagrange wrote to him in 1782 saying
that
work on his Traité de mécanique analytique
was almost complete and a committee
of the
Académie des Sciences comprising of
Laplace,
Cousin, Legendre and Condorcet was
set up
to decide on publication. Laplace served
on a committee set up to investigate
the
largest hospital in Paris and he used
his
expertise in probability to compare
mortality
rates at the hospital with those of
other
hospitals in France and elsewhere.
Laplace was promoted to a senior position
in the Académie des Sciences in 1785.
Two
years later Lagrange left Berlin to
join
Laplace as a member of the Académie
des Sciences
in Paris. Thus the two great mathematical
geniuses came together in Paris and,
despite
a rivalry between them, each was to
benefit
greatly from the ideas flowing from
the other.
Laplace married on 15 May 1788. His
wife,
Marie-Charlotte de Courty de Romanges,
was
20 years younger than the 39 year old
Laplace.
They had two children, their son Charles-Emile
who was born in 1789 went on to a military
career.
Laplace was made a member of the committee
of the Académie des Sciences to standardise
weights and measures in May 1790. This
committee
worked on the metric system and advocated
a decimal base. In 1793 the Reign of
Terror
commenced and the Académie des Sciences,
along with the other learned societies,
was
suppressed on 8 August. The weights
and measures
commission was the only one allowed
to continue
but soon Laplace, together with Lavoisier,
Borda, Coulomb, Brisson and Delambre
were
thrown off the commission since all
those
on the committee had to be worthy:-
... by their Republican virtues and
hatred
of kings.
Before the 1793 Reign of Terror Laplace
together
with his wife and two children left
Paris
and lived 50 km southeast of Paris.
He did
not return to Paris until after July
1794.
Although Laplace managed to avoid the
fate
of some of his colleagues during the
Revolution,
such as Lavoisier who was guillotined
in
May 1794 while Laplace was out of Paris,
he did have some difficult times. He
was
consulted, together with Lagrange and
Laland,
over the new calendar for the Revolution.
Laplace knew well that the proposed
scheme
did not really work because the length
of
the proposed year did not fit with
the astronomical
data. However he was wise enough not
to try
to overrule political dogma with scientific
facts. He also conformed, perhaps more
happily,
to the decisions regarding the metric
division
of angles into 100 subdivisions. In
1795
the Ecole Normale was founded with
the aim
of training school teachers and Laplace
taught
courses there including one on probability
which he gave in 1795. The Ecole Normale
survived for only four months for the
1200
pupils, who were training to become
school
teachers, found the level of teaching
well
beyond them. This is entirely understandable.
Later Laplace wrote up the lectures
of his
course at the Ecole Normale as Essai
philosophique
sur les probabilités published in 1814.
A
review of the Essai states:-
... after a general introduction concerning
the principles of probability theory,
one
finds a discussion of a host of applications,
including those to games of chance,
natural
philosophy, the moral sciences, testimony,
judicial decisions and mortality.
In 1795 the Académie des Sciences was
reopened
as the Institut National des Sciences
et
des Arts. Also in 1795 the Bureau des
Longitudes
was founded with Lagrange and Laplace
as
the mathematicians among its founding
members
and Laplace went on to lead the Bureau
and
the Paris Observatory. However although
some
considered he did a fine job in these
posts
others criticised him for being too
theoretical.
Delambre wrote some years later:-
... never should one put a geometer
at the
head of an observatory; he will neglect
all
the observations except those needed
for
his formulas.
Delambre also wrote concerning Laplace's
leadership of the Bureau des Longitudes:-
One can reproach [Laplace] with the
fact
that in more than 20 years of existence
the
Bureau des Longitudes has not determined
the position of a single star, or undertaken
the preparation of the smallest catalogue.
Laplace presented his famous nebular
hypothesis
in 1796 in Exposition du systeme du
monde,
which viewed the solar system as originating
from the contracting and cooling of
a large,
flattened, and slowly rotating cloud
of incandescent
gas. The Exposition consisted of five
books:
the first was on the apparent motions
of
the celestial bodies, the motion of
the sea,
and also atmospheric refraction; the
second
was on the actual motion of the celestial
bodies; the third was on force and
momentum;
the fourth was on the theory of universal
gravitation and included an account
of the
motion of the sea and the shape of
the Earth;
the final book gave an historical account
of astronomy and included his famous
nebular
hypothesis. Laplace states his philosophy
of science in the Exposition as follows:-
If man were restricted to collecting
facts
the sciences were only a sterile nomenclature
and he would never have known the great
laws
of nature. It is in comparing the phenomena
with each other, in seeking to grasp
their
relationships, that he is led to discover
these laws...
In view of modern theories of impacts
of
comets on the Earth it is particularly
interesting
to see Laplace's remarkably modern
view of
this:-
... the small probability of collision
of
the Earth and a comet can become very
great
in adding over a long sequence of centuries.
It is easy to picture the effects of
this
impact on the Earth. The axis and the
motion
of rotation have changed, the seas
abandoning
their old position..., a large part
of men
and animals drowned in this universal
deluge,
or destroyed by the violent tremor
imparted
to the terrestrial globe.
Exposition du systeme du monde was
written
as a non-mathematical introduction
to Laplace's
most important work Traité du Mécanique
Céleste
whose first volume appeared three years
later.
Laplace had already discovered the
invariability
of planetary mean motions. In 1786
he had
proved that the eccentricities and
inclinations
of planetary orbits to each other always
remain small, constant, and self-correcting.
These and many other of his earlier
results
formed the basis for his great work
the Traité
du Mécanique Céleste published in 5
volumes,
the first two in 1799. The first volume
of
the Mécanique Céleste is divided into
two
books, the first on general laws of
equilibrium
and motion of solids and also fluids,
while
the second book is on the law of universal
gravitation and the motions of the
centres
of gravity of the bodies in the solar
system.
The main mathematical approach here
is the
setting up of differential equations
and
solving them to describe the resulting
motions.
The second volume deals with mechanics
applied
to a study of the planets. In it Laplace
included a study of the shape of the
Earth
which included a discussion of data
obtained
from several different expeditions,
and Laplace
applied his theory of errors to the
results.
Another topic studied here by Laplace
was
the theory of the tides but Airy, giving
his own results nearly 50 years later,
wrote:-
It would be useless to offer this theory
in the same shape in which Laplace
has given
it; for that part of the Mécanique
Céleste
which contains the theory of tides
is perhaps
on the whole more obscure than any
other
part...
In the Mécanique Céleste Laplace's
equation
appears but although we now name this
equation
after Laplace, it was in fact known
before
the time of Laplace. The Legendre functions
also appear here and were known for
many
years as the Laplace coefficients.
The Mécanique
Céleste does not attribute many of
the ideas
to the work of others but Laplace was
heavily
influenced by Lagrange and by Legendre
and
used methods which they had developed
with
few references to the originators of
the
ideas. Under Napoleon Laplace was a
member,
then chancellor, of the Senate, and
received
the Legion of Honour in 1805. However
Napoleon,
in his memoirs written on St Hélène,
says
he removed Laplace from the office
of Minister
of the Interior, which he held in 1799,
after
only six weeks:-
... because he brought the spirit of
the
infinitely small into the government.
Laplace became Count of the Empire
in 1806
and he was named a marquis in 1817
after
the restoration of the Bourbons. The
first
edition of Laplace's Théorie Analytique
des
Probabilités was published in 1812.
This
first edition was dedicated to Napoleon-le-Grand
but, for obvious reason, the dedication
was
removed in later editions! The work
consisted
of two books and a second edition two
years
later saw an increase in the material
by
about an extra 30 per cent.
The first book studies generating functions
and also approximations to various
expressions
occurring in probability theory. The
second
book contains Laplace's definition
of probability,
Bayes's rule (so named by Poincaré
many years
later), and remarks on moral and mathematical
expectation. The book continues with
methods
of finding probabilities of compound
events
when the probabilities of their simple
components
are known, then a discussion of the
method
of least squares, Buffon's needle problem,
and inverse probability. Applications
to
mortality, life expectancy and the
length
of marriages are given and finally
Laplace
looks at moral expectation and probability
in legal matters.
Later editions of the Théorie Analytique
des Probabilités also contains supplements
which consider applications of probability
to: errors in observations; the determination
of the masses of Jupiter, Saturn and
Uranus;
triangulation methods in surveying;
and problems
of geodesy in particular the determination
of the meridian of France. Much of
this work
was done by Laplace between 1817 and
1819
and appears in the 1820 edition of
the Théorie
Analytique. A rather less impressive
fourth
supplement, which returns to the first
topic
of generating functions, appeared with
the
1825 edition. This final supplement
was presented
to the Institute by Laplace, who was
76 years
old by this time, and by his son.
We mentioned briefly above Laplace's
first
work on physics in 1780 which was outside
the area of mechanics in which he contributed
so much. Around 1804 Laplace seems
to have
developed an approach to physics which
would
be highly influential for some years.
This
is best explained by Laplace himself:-
... I have sought to establish that
the phenomena
of nature can be reduced in the last
analysis
to actions at a distance between molecule
and molecule, and that the consideration
of these actions must serve as the
basis
of the mathematical theory of these
phenomena.
This approach to physics, attempting
to explain
everything from the forces acting locally
between molecules, already was used
by him
in the fourth volume of the Mécanique
Céleste
which appeared in 1805. This volume
contains
a study of pressure and density, astronomical
refraction, barometric pressure and
the transmission
of gravity based on this new philosophy
of
physics. It is worth remarking that
it was
a new approach, not because theories
of molecules
were new, but rather because it was
applied
to a much wider range of problems than
any
previous theory and, typically of Laplace,
it was much more mathematical than
any previous
theories. Laplace's desire to take
a leading
role in physics led him to become a
founder
member of the Société d'Arcueil in
around
1805. Together with the chemist Berthollet,
he set up the Society which operated
out
of their homes in Arcueil which was
south
of Paris. Among the mathematicians
who were
members of this active group of scientists
were Biot and Poisson. The group strongly
advocated a mathematical approach to
science
with Laplace playing the leading role.
This
marks the height of Laplace's influence,
dominant also in the Institute and
having
a powerful influence on the Ecole Polytechnique
and the courses that the students studied
there.
After the publication of the fourth
volume
of the Mécanique Céleste, Laplace continued
to apply his ideas of physics to other
problems
such as capillary action (1806-07),
double
refraction (1809), the velocity of
sound
(1816), the theory of heat, in particular
the shape and rotation of the cooling
Earth
(1817-1820), and elastic fluids (1821).
However
during this period his dominant position
in French science came to an end and
others
with different physical theories began
to
grow in importance.
The Société d'Arcueil, after a few
years
of high activity, began to become less
active
with the meetings becoming less regular
around
1812. The meetings ended completely
the following
year. Arago, who had been a staunch
member
of the Society, began to favour the
wave
theory of light as proposed by Fresnel
around
1815 which was directly opposed to
the corpuscular
theory which Laplace supported and
developed.
Many of Laplace's other physical theories
were attacked, for instance his caloric
theory
of heat was at odds with the work of
Petit
and of Fourier. However, Laplace did
not
concede that his physical theories
were wrong
and kept his belief in fluids of heat
and
light, writing papers on these topics
when
over 70 years of age.
At the time that his influence was
decreasing,
personal tragedy struck Laplace. His
only
daughter, Sophie-Suzanne, had married
the
Marquis de Portes and she died in childbirth
in 1813. The child, however, survived
and
it is through her that there are descendants
of Laplace. Laplace's son, Charles-Emile,
lived to the age of 85 but had no children.
Laplace had always changed his views
with
the changing political events of the
time,
modifying his opinions to fit in with
the
frequent political changes which were
typical
of this period. This way of behaving
added
to his success in the 1790s and 1800s
but
certainly did nothing for his personal
relations
with his colleagues who saw his changes
of
views as merely attempts to win favour.
In
1814 Laplace supported the restoration
of
the Bourbon monarchy and caste his
vote in
the Senate against Napoleon. The Hundred
Days were an embarrassment to him the
following
year and he conveniently left Paris
for the
critical period. After this he remained
a
supporter of the Bourbon monarchy and
became
unpopular in political circles. When
he refused
to sign the document of the French
Academy
supporting freedom of the press in
1826,
he lost the remaining friends he had
in politics.
On the morning of Monday 5 March 1827
Laplace
died. Few events would cause the Academy
to cancel a meeting but they did on
that
day as a mark of respect for one of
the greatest
scientists of all time. Surprisingly
there
was no quick decision to fill the place
left
vacant on his death and the decision
of the
Academy in October 1827 not to fill
the vacant
place for another 6 months did not
result
in an appointment at that stage, some
further
months elapsing before Puissant was
elected
as Laplace's successor.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/La
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