**Pierre-Simon Laplace** proved the stability of the solar system. In analysis Laplace introduced the potential function and Laplace coefficients. He also put the theory of mathematical probability on a sound footing.

- Laplace attended a Benedictine priory school in Beaumont-en-Auge, as a day pupil, between the ages of 7 and 16.
- At the age of 16 Laplace entered Caen University.
- 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.
- 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.
- 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 Ⓣ(Research on the calculus of infinitely small differences, and finite difference) 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 Académie arose.
- We have already mentioned some of Laplace's early work.
- Laplace's reputation steadily increased during the 1770s.
- 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.
- 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 Académie.
- 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.
- 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 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.
- His wife, Marie-Charlotte de Courty de Romanges, was 20 years younger than the 39 year old Laplace.
- Laplace was made a member of the committee of the Académie des Sciences to standardise weights and measures in May 1790.
- 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.
- 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.
- 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.
- Later Laplace wrote up the lectures of his course at the École Normale as Essai philosophique sur les probabilités published in 1814.
- 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.
- Laplace presented his famous nebular hypothesis in 1796 in Exposition du systeme du monde Ⓣ(Exposition of the system of the world), which viewed the solar system as originating from the contracting and cooling of a large, flattened, and slowly rotating cloud of incandescent gas.
- Exposition du systeme du monde Ⓣ(Exposition of the system of the world) was written as a non-mathematical introduction to Laplace's most important work Traité de Mécanique Céleste Ⓣ(Treatise on celestial mechanics) whose first volume appeared three years later.
- Laplace had already discovered the invariability of planetary mean motions.
- 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.
- In the Mécanique Céleste Ⓣ(Treatise on celestial mechanics) 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 Ⓣ(Treatise on celestial mechanics) 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.
- 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 Ⓣ(Analytic theory of probability) was published in 1812.
- 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.
- Applications to mortality, life expectancy and the length of marriages are given and finally Laplace looks at moral expectation and probability in legal matters.
- Much of this work was done by Laplace between 1817 and 1819 and appears in the 1820 edition of the Théorie Analytique Ⓣ(Analytic theory).
- 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.
- 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.
- 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 Ⓣ(Celestial mechanics), 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).
- 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.
- In 1814 Laplace supported the restoration of the Bourbon monarchy and cast his vote in the Senate against Napoleon.
- On the morning of Monday 5 March 1827 Laplace died.
- 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.

Born 23 March 1749, Beaumont-en-Auge, Normandy, France. Died 5 March 1827, Paris, France.

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