Pierre-Simon Laplace
Born: 23 March 1749 in Beaumont-en-Auge, Normandy,
France
Died: 5 March 1827 in Paris, France
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 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 École Militaire. Gillespie writes in:-
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:-
... 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:-
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 École 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 École 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
École 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 École 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.
J J O'Connor and E F Robertson
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