Pierre-Simon Laplace was a French mathematician and astronomer. He contributed greatly to pure mathematics, probability theory, and dynamical astronomy. Sometimes referred to as the French Newton or Newton of France, he was one of the outstanding minds of his century.
Background
Pierre Simon Laplace was born on March 23, 1749, at Beaumont-en-Auge in Normandy. Laplace’ father, Pierre, was a syndic of the Parish, probably in the cider business and certainly in comfortable circumstances. The family of his mother, Marie-Anne Sochon, were well-to-do farmers of Tourgéville. He had one elder sister, also called Marie-Anne, born in 1745. There is no record of intellectual distinction in the family beyond what was to be expected of the cultivated provincial bourgeoisie and the minor gentry. One paternal uncle, Louis, an abbé, although not was probably a teacher at the collège, kept at Beaumont-en-Auge by the Benedictines.
Education
Little is known of Laplace's early life except that he quickly showed his mathematical ability at the military academy at Beaumont. 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. In 1766 he went up to the University of Caen and matriculated in the Faculty of Arts, still formally a cleric. 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, Christophe Gadbled and Pierre Le Canuof whom little is known except that they realised Laplace's great mathematical potential.
Pierre-Simon Laplace arrived in Paris with a letter of recommendation to the mathematician Jean d’Alembert, who helped him secure a professorship at the École Militaire, where he taught from 1769 to 1776.
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. Before Lagrange could act on d'Alembert's request, another chance for Laplace to gain admission to the Paris Académie 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 Académie in less than three years. Condorcet, who was permanent secretary to the Académie, remarked on this great number of quality papers on a wide range of topics.
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 Académie 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.
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.
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 an 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.
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. Later Laplace wrote up the lectures of his course at the École Normale as Essai philosophique sur les probabilités published in 1814.
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 criticized him for being too theoretical.
Laplace presented his famous nebular hypothesis in 1796 in Exposition du systeme du monde. Exposition du systeme du monde was written as a non-mathematical introduction to Laplace's most important work Traité de 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 de Mécanique Céleste published in 5 volumes, the first two in 1799.
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. 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 percent.
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 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 contain 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.
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.
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.
On March 5, 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 French Academy of Sciences 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.
Achievements
Laplace successfully accounted for all the observed deviations of the planets from their theoretical orbits by applying Sir Isaac Newton’s theory of gravitation to the solar system, and he developed a conceptual view of evolutionary change in the structure of the solar system. He also demonstrated the usefulness of probability for interpreting scientific data.
Laplace formulated Laplace's equation and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplacian differential operator, widely used in mathematics, is also named after him.
Laplace's Mécanique Céleste (Celestial Mechanics) was the most important work in mathematical astronomy since Isaac Newton. His Théorie Analytique des Probabilités (Analytical Theory of Probability) influenced work on statistical probability for most of the nineteenth century. These two works alone guaranteed Laplace's place among the great scientists of the age.
Laplace became Count of the Empire in 1806 and he was named a marquis in 1817 after the restoration of the Bourbons.
His name is one of the 72 names of influential scientists inscribed on the Eiffel Tower. Promontorium Laplace and asteroid 4628 Laplace were named after him.
Laplace was born to a Catholic family. Laplace appears for most of his life to have veered between deism (presumably his considered position, since it is the only one found in his writings) and atheism. Sometimes he is described as an agnostic.
When presented a copy of Mécanique Céleste, Napoleon asked Laplace why God was never mentioned in his book. Laplace replied, "I had no need of that hypothesis."
Politics
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 favor. In 1814 Laplace supported the restoration of the Bourbon monarchy and cast 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 of Sciences supporting freedom of the press in 1826, he lost the remaining friends he had in politics.
Views
Laplace's lifelong work was the successful application of Newtonian gravitation to the entire solar system, accounting for all the observed deviations of the planets and satellites from their theoretical orbits. In 1773 he began his major lifework - applying Newtonian gravitation to the entire solar system - by taking up a particularly troublesome problem: why Jupiter’s orbit appeared to be continuously shrinking while Saturn’s continually expanded. The mutual gravitational interactions within the solar system were so complex that mathematical solution seemed impossible; indeed, Newton had concluded that divine intervention was periodically required to preserve the system in equilibrium. Laplace announced the invariability of planetary mean motions (average angular velocity). This discovery in 1773, the first and most important step in establishing the stability of the solar system, was the most important advance in physical astronomy since Newton. It won him associate membership in the French Academy of Sciences the same year.
Applying quantitative methods to a comparison of living and nonliving systems, Laplace and the chemist Antoine-Laurent Lavoisier in 1780, with the aid of an ice calorimeter that they had invented, showed respiration to be a form of combustion. Returning to his astronomical investigations with an examination of the entire subject of planetary perturbations - mutual gravitational effects - Laplace in 1786 proved that the eccentricities and inclinations of planetary orbits to each other will always remain small, constant, and self-correcting. The effects of perturbations were therefore conservative and periodic, not cumulative and disruptive.
During 1784-85 Laplace worked on the subject of attraction between spheroids; in this work, the potential function of later physics can be recognized for the first time. Laplace explored the problem of the attraction of any spheroid upon a particle situated outside or upon its surface. Through his discovery that the attractive force of a mass upon a particle, regardless of direction, can be obtained directly by differentiating a single function, Laplace laid the mathematical foundation for the scientific study of heat, magnetism, and electricity.
Laplace removed the last apparent anomaly from the theoretical description of the solar system in 1787 with the announcement that lunar acceleration depends on the eccentricity of the Earth’s orbit. Although the mean motion of the Moon around the Earth depends mainly on the gravitational attraction between them, it is slightly diminished by the pull of the Sun on the Moon. This solar action depends, however, on changes in the eccentricity of the Earth’s orbit resulting from perturbations by the other planets. As a result, the Moon’s mean motion is accelerated as long as the Earth’s orbit tends to become more circular; but, when the reverse occurs, this motion is retarded. The inequality is therefore not truly cumulative, Laplace concluded, but is of a period running into millions of years. The last threat of instability thus disappeared from the theoretical description of the solar system.
In 1796 Laplace published Exposition du système du monde (The System of the World), a semi-popular treatment of his work in celestial mechanics and a model of French prose. The book included his “nebular hypothesis” - attributing the origin of the solar system to cooling and contracting of a gaseous nebula - which strongly influenced future thought on planetary origin. His Traité de mécanique céleste (Celestial Mechanics), appearing in five volumes between 1798 and 1827, summarized the results obtained by his mathematical development and application of the law of gravitation. He offered a complete mechanical interpretation of the solar system by devising methods for calculating the motions of the planets and their satellites and their perturbations, including the resolution of tidal problems.
Laplace also propounded the existence of black holes. He described the idea of massive stars from which no light could escape; this light consisted of corpuscles, very small particles, according to the generally accepted theory of Isaac Newton. Laplace called such an object corps obscur, i.e. dark body.
In his Théorie analytique des probabilités Laplace set out a mathematical system of inductive reasoning based on probability, which we would today recognize as Bayesian. Laplace described many of the tools he invented for mathematically predicting the probabilities that particular events will occur in nature. He applied his theory not only to the ordinary problems of chance but also to the inquiry into the causes of phenomena, vital statistics, and future events while emphasizing its importance for physics and astronomy. The book is notable also for including a special case of what became known as the central limit theorem. Laplace proved that the distribution of errors in large data samples from astronomical observations can be approximated by a Gaussian or normal distribution.
Laplace was a supporter of absolute determinism. He argued that if any intelligent creature could find out the positions and speeds of all particles in the world at some point, it would be able to predict accurately all world events. Such a hypothetical creature was later called the Laplace's demon.
Laplace also reflected on the field of erroneous human decisions, such as testimonies or verdicts, within the framework of urn models. In view of the oversimplified models Laplace expressed certain reservations, but he emphasized at the same time the advantages of probabilistic "estimations." In the first supplement of his Théorie analytique, Laplace calculated the a posteriori probability that the defendant is actually guilty, if n votes have been cast against him, under the double presupposition that among n members of a jury the same probability x of a correct decision in the case of guilt can be assigned to all of them, and that all values x are a priority uniformly distributed between 1/2 and 1. On the basis of these calculations, Laplace gave recommendations for the composition of, and the majority within, Juries, which he also published in a pamphlet in 1816.
Quotations:
"What we know is not much. What we don't know is enormous."
"Read Euler, read Euler, he is the master of us all."
"Nature laughs at the difficulties of integration."
"The most important questions of life... are indeed for the most part only problems of probability."
"Man follows only phantoms."
"All the effects of Nature are only the mathematical consequences of a small number of immutable laws."
"It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge."
"The word “chance” then expresses only our ignorance of the causes of the phenomena that we observe to occur and to succeed one another in no apparent order. Probability is relative in part to this ignorance, and in part to our knowledge."
Membership
Besides membership in several scientific societies, Laplace was one of the prominent figures in French Freemasonry. He was an honored Grand Master of the Grand Orient de France.
French Academy of Sciences
,
France
1773
Royal Society
,
United Kingdom
1789
Société d'Arcueil
,
France
1805
Royal Swedish Academy of Sciences
,
Sweden
1806
Royal Society of Edinburgh
1813
American Academy of Arts and Sciences
,
United States
1822
Grand Orient de France
,
France
Personality
It does appear that Laplace was not modest about his abilities and achievements, and he probably failed to recognize 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.
Contemporaries noted the kindness of Laplace in relation to young scientists, the continued willingness to help.
Quotes from others about the person
"Laplace made many important discoveries in mathematical physics... Indeed, he was interested in anything that helped to interpret nature. He worked on hydrodynamics, the wave propagation of sound, and the tides. In the field of chemistry, his work on the liquid state of matter is classic. His studies of the tension in the surface layer of water, which accounts for the rise of liquids inside a capillary tube, and of the cohesive forces in liquids, are fundamental. Laplace and Lavoisier designed an ice calorimeter (1784) to measure heat and measured the specific heat of numerous substances; heat, to them, was still a special kind of matter. Most of Laplace's life was, however, devoted to celestial mechanics." - Morris Kline
"Laplace created a number of new mathematical methods that were subsequently expanded into branches of mathematics, but he never cared for mathematics except as it helped him to study nature." - Morris Kline
"Laplace had taken Newton's science and turned it into philosophy. The universe was a piece of machinery, its history was predetermined, there was no room for chance or for free will. The cosmos was indeed an ice-cold clock." - Brian L. Silver
Connections
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-Émile who was born in 1789 went on to a military career.
Pierre-Simon Laplace and Antoine Lavoisier carried out together several experiments. The two also designed an ice calorimeter to measure the heat released during various chemical reactions.
Marie-Joseph Lagrange and Pierre-Simon Laplace were collagues at the École normale supérieure.
Academic advisor:
Jean le Rond d'Alembert
Laplace was not more than eighteen when, armed with letters of recommendation, he approached J. B. d'Alembert, then at the height of his fame, in the hope of finding a career in Paris. The letters remained unnoticed, but Laplace was not crushed by the rebuff. He wrote to the great geometer a letter on the principles of mechanics, which evoked an immediate and enthusiastic response. “You,” said d'Alembert to him, “needed no introduction; you have recommended yourself; my support is your due.” He accordingly obtained for him an appointment as a professor of mathematics in the Ecole Militaire of Paris and continued zealously to forward his interests.
During the later years of his life, Laplace lived much at Arcueil, where he had a country-place adjoining that of his friend C. L. Berthollet. With his co-operation, the Société d'Arcueil was formed, and he occasionally contributed to its Memoirs.
