Search Results for Laplace

Biographies

1. Laplace biography
   
   • Pierre-Simon Laplace .
     
   • 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 Tourgeville.
     
   • 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.
     
   • 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 Ecole Militaire.
     
   • 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.
     
   • 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 integral aux differences infiniment petites, et aux differences finies to the Melanges 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 Academie 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 Academie 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 protege, 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 Academie 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 Academie.
     
   • It was while Lexell was in Paris that Laplace made an excursion into a new area of science [Encyclopaedia Britannica.
     
   • 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 Academie des Sciences, for example Lagrange wrote to him in 1782 saying that work on his Traite de mecanique analytique was almost complete and a committee of the Academie 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 Academie des Sciences in 1785.
     
   • Two years later Lagrange left Berlin to join Laplace as a member of the Academie des Sciences in Paris.
     
   • Laplace married on 15 May 1788.
     
   • 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 Academie des Sciences to standardise weights and measures in May 1790.
     
   • 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:- .
     
   • Before the 1793 Reign of Terror Laplace together with his wife and two children left Paris and lived 50 km southeast of Paris.
     
   • 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 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.
     
   • Later Laplace wrote up the lectures of his course at the Ecole Normale as Essai philosophique sur les probabilites 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.
     
   • 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.
     
   • Laplace states his philosophy of science in the Exposition as follows:- .
     
   • 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:- .
     
   • Exposition du systeme du monde was written as a non-mathematical introduction to Laplace's most important work Traite de Mecanique Celeste 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.
     
   • 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 Mecanique Celeste which contains the theory of tides is perhaps on the whole more obscure than any other part..
     
   • In the Mecanique Celeste 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 Mecanique Celeste 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 Helene, 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 Theorie Analytique des Probabilites was published in 1812.
     
   • The second book contains Laplace's definition of probability, Bayes's rule (so named by Poincare 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 Theorie Analytique.
     
   • 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:- .
     
   • 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 Societe 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 Ecole Polytechnique and the courses that the students studied there.
     
   • After the publication of the fourth volume of the Mecanique Celeste, 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.
     
   • 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.
     
   • 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.
     
   • Laplace's Mechanique Celeste/a> .
     
   • Laplace on "new stars" .
     
   • Laplace: Essay on probabilities .
     
   • Honours awarded to Pierre-Simon Laplace .
     
   • Lunar featuresPromontorium Laplace .
     
   • Paris street namesRue Laplace (5th Arrondissement) .
     
   • http://www-history.mcs.st-andrews.ac.uk/Biographies/Laplace.html .
     

2. Fourier biography
   
   • and also by Laplace, who Fourier rated less highly, and by Monge who Fourier described as .
     
   • Fourier began teaching at the College de France and, having excellent relations with Lagrange, Laplace and Monge, began further mathematical research.
     
   • His release has been put down to a variety of different causes, pleas by his pupils, pleas by Lagrange, Laplace or Monge or a change in the political climate.
     
   • The memoir was read to the Paris Institute on 21 December 1807 and a committee consisting of Lagrange, Laplace, Monge and Lacroix was set up to report on the work.
     
   • The first objection, made by Lagrange and Laplace in 1808, was to Fourier's expansions of functions as trigonometrical series, what we now call Fourier series.
     
   • All these are written with such exemplary clarity - from a logical as opposed to calligraphic point of view - that their inability to persuade Laplace and Lagrange ..
     
   • Laplace, and later Poisson, had similar objections.
     
   • Only one other entry was received and the committee set up to decide on the award of the prize, Lagrange, Laplace, Malus, Hauy and Legendre, awarded Fourier the prize.
     

3. Bowditch biography
   
   • On his voyage of 1802-03 he read the first volume of Laplace's Traite de mecanique celeste which had been published in 1798.
     
   • By June 1806 Bowditch had read the first four of Laplace's five volumes (the fifth volume was not published by Laplace until 1825).
     
   • Bowditch's translation of the first four volumes of Laplace's Traite de mecanique celeste was completed by 1818 but he would not publish it for many years.
     
   • to supply steps omitted in the original text; to incorporate later results into the translation; and to give credits omitted by Laplace.
     
   • As president of the Massachusetts Hospital Life Insurance Company, he enjoyed enough material success so that he could afford the $12,000 it cost to have his translation of Laplace published (1829-1839).
     
   • In 1969 by the Chelsea Publishing Company published [4] which is a reprint of the French original of Laplace's fifth volume.
     
   • Laplace's Mechanique Celeste .
     

4. Poisson biography
   
   • His teachers Laplace and Lagrange quickly saw his mathematical talents.
     
   • He proceeded immediately to the position of repetiteur in the Ecole Polytechnique, mainly on the strong recommendation of Laplace.
     
   • 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.
     
   • In the first Sur les inegalites des moyens mouvements des planetes he looked at the mathematical problems which Laplace and Lagrange had raised about perturbations of the planets.
     
   • 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.
     
   • 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.
     
   • 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:- .
     

5. Delaunay biography
   
   • Mme la Marquise de Laplace donated a new annual prize, the Laplace Prize, to be given to the student who was ranked top in his year at the Ecole Polytechnique.
     
   • Delaunay had graduated before the prize was instituted but Mme de Laplace requested that he become the first recipient of the prize which consisted of the complete works of Laplace.
     
   • It turned out to be a decision which changed the course of Delaunay's career, for reading Laplace's great works gave him a passion for celestial mechanics and he decided that he would make a career in that subject.
     
   • Mme la Marquise de Laplace was delighted with the first winner of the prize and she called him "her eldest son".
     

6. Plana biography
   
   • In 1818 Laplace proposed that the Academie des Sciences in Paris set up a prize to be awarded to whoever succeeded in constructing lunar tables based solely on the law of universal gravity.
     
   • In 1820 the prize was awarded to Carlini and Plana and to Damoiseau by a committee of which Laplace was a member.
     
   • But Laplace strongly criticised the Carlini-Plana approach to lunar theory.
     
   • letters [were] exchanged between Carlini-Plana and Laplace, and ..
     
   • After the exchanges, public and private, between Carlini-Plana and Laplace, the latter concluded that the results of the Italian astronomers and those arrived at by Damoiseau following the method of Laplace's Mecanique celeste were fairly close, and that the purpose of the Academie in establishing the prize had been reasonably fulfilled.
     

7. Newcomb biography
   
   • He was able to borrow a copy of Bowditch's translation of Laplace's Mecanique celeste from the library of the Smithsonian Institution but found that the mathematics which the book contained was rather beyond his current knowledge.
     
   • Laplace had devised a method involving cosine series for computing the perturbing force on a planet caused by other planets.
     
   • The coefficients in the series were known as 'Laplace coefficients' but the drawback of the method was that it only worked for circular orbits.
     
   • Newcomb showed how to extend Laplace's series to give a perturbing function in the case of elliptical orbits by introducing differential operators which act on the Laplace coefficients.
     

8. Petzval biography
   
   • Petzval worked for much of his life on the Laplace transform.
     
   • He was influenced by the work of Liouville and wrote both a long paper and a two volume treatise on the Laplace transform and its application to ordinary linear differential equations.
     
   • But for a student of Petzval we might today call the Laplace transform the Petzval transform.
     
   • Petzval fell out with this student who then accused Petzval of plagiarising Laplace's work.
     
   • Although this was untrue, Boole and Poincare, influenced no doubt by the quarrel, called the transformation the Laplace transform.
     

9. Ferrel biography
   
   • He sent to Philadelphia for a copy of Bowditch's translation of Laplace's Mecanique Celeste which he also studied.
     
   • This conclusion contradicted that which Laplace had come to and Ferrel decided that Laplace had made an error in neglecting second order terms.
     
   • We have seen above how Ferrel's early work on tides sought to correct some problems which were in Laplace's treatment.
     
   • When Laplace studied the tides he had ignored fluid friction because no good mathematical treatment existed at that time.
     

10. Bienayme biography
    
    • In fact the jury system in France at that time was based on Laplace's conclusions but it was under attack by Poisson.
      
    • Bienayme supported Laplace on this issue.
      
    • In fact Bienayme supported Laplace in general since it was Laplace's Theorie analytique des probabilites (1812) that was the biggest influence on Bienayme's scientific thinking throughout his life.
      
    • One of his many contributions was to generalise the Laplace method of least squares.
      

11. Bateman biography
    
    • My own interest in the integrals of the Euler-Laplace type dates, I think, from the time when Sir Edmund Whittaker gave some properties of the Laplace transformation in his lectures at Cambridge in 1903 or 1904.
      
    • I made some use of the method of the inverse Laplace transformation in the Smith's prize essay and fellowship dissertation partly published in modified form in 1909 and 1910.
      
    • Bateman was one of the first to apply Laplace transforms to integral equations in 1906.
      
    • Bateman's method was the now familiar one of applying the complex inversion formula of the Laplace transform.
      

12. Ivory biography
    
    • During these years he had spent much of his spare time in studying the works of Lagrange and Laplace on his own.
      
    • Ivory and Wallace were early supporters of the work of the French analysts, especially Lagrange and Laplace.
      
    • Ivory's critical commentary of Laplace's Mecanique celeste was praised by Laplace.
      
    • His work on the ellipsoidal equilibrium configuration of self-gravitating fluids was an extension of that of Laplace, and it influenced the achievements of Jacobi and Liouville which followed.
      

13. Legendre biography
    
    • From 1775 to 1780 he taught with Laplace at Ecole Militaire where his appointment was made on the advice of d'Alembert.
      
    • He wrote to Laplace asking for more information about the prize winning young mathematician.
      
    • Legendre submitted his results to the Academie des Sciences in Paris in January 1783 and these were highly praised by Laplace in his report delivered to the Academie in March.
      
    • Within a few days, on 30 March, Legendre was appointed an adjoint in the Academie des Sciences filling the place which had become vacant when Laplace was promoted from adjoint to associe earlier that year.
      

14. Adams biography
    
    • Adams spent much effort on the complex problem of a description of the motion of the Moon, giving a theory which was more accurate than that of Laplace.
      
    • He began this work in 1851 when elected as President of the Royal Astronomical Society and he presented a paper to the Royal Society in 1853 in which he showed that Laplace had omitted terms from his equations which were not negligible.
      
    • His corrections to Laplace's work reduced by half the discrepancy between the observed orbit and the predicted one.
      
    • It is fair to say that the French were not pleased to see Adams correcting Laplace, particularly since they had reacted angrily a few years earlier when they saw him as attempting to detract from Le Verrier's glory.
      

15. Somerville biography
    
    • At this time Mary also read Newton's Principia and, at Wallace's suggestion, Laplace's Mecanique Celeste and many other mathematical and astronomical texts.
      
    • Mary met Laplace, Poisson, Poinsot, Emile Mathieu and many others.
      
    • In 1827 Lord Brougham made a request on behalf of the Society for the Diffusion of Useful Knowledge for Mary Somerville to translate Laplace's Mecanique Celeste.
      
    • However Mary went far beyond a translation, for she explained in detail the mathematics used by Laplace which was unfamiliar to most mathematicians in England at that time.
      

16. Delambre biography
    
    • At the same meeting Laplace presented a paper on his mathematical results which allowed the perturbations produce by one planet on the orbit of another to be calculated.
      
    • Delambre was very impressed and decided to make observations of the orbit of Uranus in order to verify Laplace's theoretical results.
      
    • The topic had been suggested by Laplace and Lalande with Delambre in mind, and the committee consisting of Dominique Cassini, Lalande and Mechain duly awarded him the prize, declaring him to be:- .
      
    • The Academie had already set up a Commission of Weights and Measures in 1790 consisting of Borda, Condorcet, Laplace, Legendre and Lavoisier to advise on a metric system of weights and measures.
      

17. Adrain biography
    
    • In this paper Adrain gave 1/319 as the ellipticity of the Earth, a figure better than that given by Laplace (he gave 1/336), and about halfway between Laplace's figure and the accepted value today of 1/297.
      
    • Adrain's improvement on Laplace's value was, of course, made because Adrain had been inspired to work on the topic because of the contributions of Laplace.
      

18. Church biography
    
    • For example he published Remarks on the elementary theory of differential equations as area of research in 1965 and A generalization of Laplace's transformation in 1966.
      
    • The paper includes a discussion of a generalization the Laplace transform which he extends to non-linear partial differential equations.
      
    • This generalization of the Laplace transform is the topic of study of the second paper, again using the method to obtain solutions of second-order partial differential equations.
      

19. Chebyshev biography
    
    • Legendre and Laplace had encountered the Legendre polynomials in their work on celestial mechanics in the late eighteenth century.
      
    • Laplace had found and studied the Hermite polynomials in the course of his discoveries in probability theory during the early nineteenth century.
      
    • Twenty years later Chebyshev published On two theorems concerning probability which gives the basis for applying the theory of probability to statistical data, generalising the central limit theorem of de Moivre and Laplace.
      

20. Peirce Benjamin biography
    
    • Bowditch's translation of the first four volumes of Laplace's Traite de mecanique celeste had been completed by 1818 but he had still not published it during the years that Peirce was an undergraduate.
      
    • The course he set up was impressive, including the study of works of Lacroix, Cauchy, Monge, Biot, Hamilton, Laplace, Poisson, Gauss, Le Verrier, Bessel, Adams, Airy, MacCullagh and Franz Neumann.
      
    • He also revised and wrote a commentary on Bowditch's translation of the first four volumes of Laplace's Traite de mecanique celeste which he had himself had proof-read as an undergraduate student.
      

21. Carslaw biography
    
    • 24 (1) (1997), 4-16.',4)">4] claims it to be his later work on Laplace transforms.
      
    • The fact that Jaeger himself collaborated with Carslaw on the Laplace transform work may explain why there are differing opinions here.
      
    • In 1935, the Laplace transform was a topic of frontline research, by 1955 it was standard fare in undergraduate courses.
      

22. Arago biography
    
    • Laplace asked Poisson to find someone who would continue the work, and Poisson proposed his young friend Arago.
      
    • We should also note that he used his political positions to advance science, such as obtaining money to fund the publication of the works of Fermat and Laplace, supporting the development of railways and of the telegraph.
      
    • Arago smiled at the beautiful experiment [of Fizeau and Foucault] which, with its well deserved praise, brought back pleasant memories of his own glory days when he beat Laplace, Poisson, and Biot, to gain his place in the Academy of Sciences.
      

23. Sneddon biography
    
    • The book discusses applications of Fourier, Mellin, Laplace and Hankel transforms to the solution of problems in physics and engineering.
      
    • It does not confine itself merely to the Laplace transform, and many of the applications are of a more advanced nature than is usual - the later chapters are based almost entirely on work published within the last ten years.
      
    • The book deals with, among other topics, Laplace's equation, mixed boundary value problems, the wave equation, and the heat equation.
      

24. Bouvard biography
    
    • In 1794 Bouvard met Laplace who was at that time working on his great master-piece Mechanique celeste.
      
    • Laplace recognised Bouvard's computing skills and soon had him carrying out the complex calculations required for his theory.
      
    • Realising Bouvard's potential, Laplace arranged for him to be offered a position in the important Bureau de longitudes in 1794.
      

25. Lagrange biography
    
    • He decided to write a definitive work incorporating his contributions and wrote to Laplace on 15 September 1782:- .
      
    • It had been approved for publication by a committee of the Academie des Sciences comprising of Laplace, Cousin, Legendre and Condorcet.
      
    • The weights and measures commission was the only one allowed to continue and Lagrange became its chairman when others such as the chemist Lavoisier, Borda, Laplace, Coulomb, Brisson and Delambre were thrown off the commission.
      

26. Doetsch biography
    
    • Also in the 1920s Doetsch collaborated with Felix Bernstein on what is considered today to be the modern version of the Laplace transform.
      
    • Doetsch had collaborated with a number of Jewish mathematicians; his doctoral supervisor was Edmund Landau and his collaborator on the Laplace transform was Felix Bernstein, both Jewish mathematicians.
      
    • His most important mathematical contribution during this time was his major text on the Laplace transform and its applications to engineering published in 1937, the first such text to be written.
      

27. Mathieu Claude biography
    
    • Mathieu was one of the two enthusiasts who did most to have the legislation to revive the metric system brought in, the other being Charles-Emile Laplace, the son of Pierre-Simon Laplace.
      

28. Hamilton biography
    
    • At age 15 he started studying the works of Newton and Laplace.
      
    • In 1822 Hamilton found an error in Laplace's Mecanique celeste and, as a result of this, he came to the attention of John Brinkley, the Royal Astronomer of Ireland, who said:- .
      

29. Van der Pol biography
    
    • Let us look first at the last of these topics on which Bremmer and van der Pol collaborated in writing the classic text Operational Calculus: Based on the Two-Sided Laplace Integral.
      
    • This 1950 book was not the first joint work of van der Pol and Bremmer on the operational calculus, for example they published two papers with the title Modern operational calculus based on the two-sided Laplace integral in 1948.
      

30. Krylov Aleksei biography
    
    • In 1931 he found a new method of solving the secular equation determining the frequency of vibrations in mechanical systems which is better than methods due to Lagrange, Laplace, Jacobi and Le Verrier.
      
    • Before we describe these methods, it is good to return a bit back and consider how the first creators of these methods, Lagrange and Laplace, and then such a great astronomer as Le Verrier and such a great mathematician as Jacobi proceeded ..
      

31. Mechain biography
    
    • The Commission of Weights and Measures, which had as its members Condorcet, Lavoisier, Laplace and Legendre, was set up by the Academie des Sciences in 1790 to bring in a uniform system of measurement.
      
    • Napoleon, after taking advice from Delambre and Laplace, approved the mission.
      

32. Bayes biography
    
    • Bayes's conclusions were accepted by Laplace in a 1781 memoir, rediscovered by Condorcet (as Laplace mentions), and remained unchallenged until Boole questioned them in the Laws of Thought .
      

33. Cauchy biography
    
    • Laplace and Lagrange were visitors at the Cauchy family home and Lagrange in particular seems to have taken an interest in young Cauchy's mathematical education.
      
    • He took a copy of Laplace's Mecanique Celeste and one of Lagrange's Theorie des Fonctions with him.
      

34. Green biography
    
    • He translated the first volume of Laplace's Mecanique celeste into English and he published this in Nottingham in 1814.
      
    • Among them are Cavendish's single-fluid theoretical study of electricity of 1771, two memoirs by Poisson of 1812 on surface electricity and three on magnetism (1821-1823), and contributions by Arago, Laplace, Fourier, Cauchy, and T Young.
      

35. Dionis biography
    
    • However, he wrote extensively on applications of mathematics to astronomy, in particular planetary orbits, and his work was highly regarded by Lagrange, Laplace and Condorcet.
      
    • With Condorcet and Laplace he undertook a determination of the population of France [Dictionary of Scientific Biography (New York 1970-1990).',1)">1]:- .
      

36. Clerke biography
    
    • She wrote famous biographies of Galileo, Huygens, Kepler, Lagrange, Laplace, and other scientists for the ninth edition of Encyclopaedia Britannica.
      
    • The article on Laplace is particularly interesting since it discusses his mathematics in considerable depth.
      

37. Herschel biography
    
    • These trips included visits to other scientist, for example while in Paris Herschel and Babbage had discussed topics of common interest with Arago, Laplace and Biot.
      
    • Biot considered him the natural successor to Laplace when he died in 1827.
      

38. Murnaghan biography
    
    • After he retired from his position in Brazil and returned to the United States he published The calculus of variations and The Laplace transformation , both in 1962.
      
    • The first of these is a short book of less that 100 pages written for engineers and scientists, while the second consists of 19 lectures on such topics as: the Fourier integral; the Laplace integral transformation; the differential equations of Laguerre and Bessel; properties of special functions; asymptotic series for an error function, and for certain Bessel functions.
      

39. Thomson biography
    
    • In particular the works of Lagrange, Laplace, Legendre, Fresnel and Fourier were treated with "reverence" to use a word which Thomson himself would later use to describe the attitude that his lecturers had towards these French mathematicians.
      
    • In fact Thomson also read Laplace's Mecanique celeste in session 1839-40 and visited Paris during this session.
      

40. Jeffery biography
    
    • He did one years teacher training in 1911 but he was already undertaking research and his first paper On a form of the solution of Laplace's equation suitable for problems relating to two spheres was read to the Royal Society in 1912.
      
    • He made effective use of Whittaker's general solution to Laplace's equation which Whittaker found in 1903.
      

41. Borda biography
    
    • When Borda was made Chairman of the Commission of Weights and Measures, which had as its members Condorcet, Lavoisier, Laplace and Legendre, he soon put his accurate surveying instrument to good use.
      
    • In early 1793 it looked as though political events would prevent the project being completed and Borda, Lagrange and Laplace made a provisional estimate of the metre based on a survey previously carried our by Cassini de Thury.
      

42. Ampere biography
    
    • Laplace noticed an error, explaining the error to Ampere in a letter, which Ampere was able to correct and the treatise was reprinted.
      
    • By 1816 he was a strong advocate of a wave theory of light, agreeing with Fresnel and opposed to Biot and Laplace who advocated a corpuscular theory.
      

43. Jeffrey biography
    
    • He did one years teacher training in 1911 but he was already undertaking research and his first paper On a form of the solution of Laplace's equation suitable for problems relating to two spheres was read to the Royal Society in 1912.
      
    • He made effective use of Whittaker's general solution to Laplace's equation which Whittaker found in 1903.
      

44. Ohm biography
    
    • Langsdorf, however, advised Ohm to continue with his studies of mathematics on his own, advising Ohm to read the works of Euler, Laplace and Lacroix.
      
    • As he had done for so much of his life, Ohm continued his private studies reading the texts of the leading French mathematicians Lagrange, Legendre, Laplace, Biot and Poisson.
      

45. Quetelet biography
    
    • He learnt astronomy from Arago and Bouvard and the theory of probability under Joseph Fourier and Pierre Laplace.
      
    • Influenced by Laplace and Fourier, Quetelet was the first to use the normal curve other than as an error law.
      

46. Dirichlet biography
    
    • He had some of the leading mathematicians as teachers and he was able to profit greatly from the experience of coming in contact with Biot, Fourier, Francoeur, Hachette, Laplace, Lacroix, Legendre, and Poisson.
      
    • He turned to Laplace's problem of proving the stability of the solar system and produced an analysis which avoided the problem of using series expansion with quadratic and higher terms disregarded.
      

47. Puissant biography
    
    • On 3 November 1828 Puissant was elected to the Academy of Sciences to fill the vacancy caused by the death of Laplace in the previous year.
      

48. Cournot biography
    
    • After leaving school he spent four years in a lawyer's office but after he had read Laplace and the correspondence between Leibniz and Clarke he decided to enter university.
      

49. Friedmann biography
    
    • In his last year at the University he was working on an essay on the subject I assigned: 'Find all orthogonal substitutions such that the Laplace equation, transformed for the new variables, admits particular solutions in the form of a product of two functions, one of which depends only on one, and the other on the other two variables'.
      

50. Coulomb biography
    
    • Coulomb worked closely with Bossut, Borda, de Prony, and Laplace over this period.
      

51. Blades Edward biography
    
    • For example, he communicated On Spheroidal Harmonics and Allied Functions, by Mr G B Jeffery to the meeting on Friday 11 June 1915 and Transformations of Axes for Whittaker's Solution of Laplace's Equation, by Dr G B Jeffery to the meeting on Friday 9 March 1917.
      

52. Malus biography
    
    • In 1811 Malus served, along with Lagrange, Legendre, Laplace and Hauy, on the committee to decide on who to award the prize to for the best work on the propagation of heat in solid bodies.
      

53. Knopp biography
    
    • After he retired Knopp continued to publish interesting papers such as Zwei Abelsche Satze (1952) in which he proved abelian theorems for Laplace and Abel transforms which are closely related to the well-known Tauberian theorems of Karamata.
      

54. Euler biography
    
    • He published a number of major pieces of work through the 1750s setting up the main formulae for the topic, the continuity equation, the Laplace velocity potential equation, and the Euler equations for the motion of an inviscid incompressible fluid.
      

55. Hill biography
    
    • These texts included Lacroix' Traite du calcul differentiel et integral, Lagrange's Mechanique analytique, Laplace's Mechanique celeste and Legendre's Fonctions elliptiques.
      

56. Haret biography
    
    • "Spiru Haret's theorem" is to be naturally added to the logical succession of theorems with respect to this problem known as "Laplace-Lagrange theorem" and "Poisson's theorem".
      

57. Clausius biography
    
    • Laplace, Poisson, Sadi Carnot and Clapeyron had all developed the subject using this caloric theory as a basis.
      

58. Vandermonde biography
    
    • His friend Monge was also involved with the Ecole Normale as were Lagrange and Laplace.
      

59. Hertz Heinrich biography
    
    • He was advised by von Jolly to read works of Lagrange, Laplace and Poisson [Dictionary of Scientific Biography (New York 1970-1990).',1)">1]:- .
      

60. Schwarzschild biography
    
    • His dissertation, on an application of Poincare's theory of stable configurations of rotating bodies to tidal deformation of moons and to Laplace's origin of the solar system, was supervised by Hugo von Seeliger.
      

61. Subbotin biography
    
    • Subbotin not only showed the possibility of improving the convergence of the trigonometric series by which the behaviour of perturbing forces is represented, but also gave an expression for determining Laplace coefficients and presented formulas for computing the coefficients of the necessary members of the trigonometric series.
      

62. Todhunter biography
    
    • Among his books on the history of mathematics are A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace (1865, reprinted 1965) and History of the Mathematical Theories of Attraction (1873).
      

63. Ruffini biography
    
    • He wrote several works on philosophy, one of which argues against some of Laplace's philosophical ideas.
      

64. FitzGerald biography
    
    • He studied the works of Lagrange, Laplace, Franz Neumann, and those of his own countrymen Hamilton and MacCullagh.
      

65. Strong biography
    
    • The use of Leibniz's approach, as developed by Laplace and Lagrange, was used by Strong in his papers from about 1825 onwards so he participated actively in the introduction of the continental approach to differential and integral calculus into America.
      

66. Rayleigh biography
    
    • Among the publications devoted to mathematics, rather than to its applications, are papers on Bessel functions, the relationship between Laplace functions and Bessel functions, and Legendre functions.
      

67. Bernstein Felix biography
    
    • His range of interests were remarkable and he worked on convex functions, isoperimetric problems, the Laplace transform, number theory (including Fermat's Last Theorem), differential equations and the mathematical theory of genetics.
      

68. Pratt biography
    
    • He revised the work in 1842, then expanded and republished it under the title On attractions, Laplace's functions and the figure of the Earth in 1860.
      

69. Lions Jacques-Louis biography
    
    • Evolution: Fourier, Laplace.
      

70. Sturm biography
    
    • As for M Arago, I have two or three times been among the group of scientists he invites to his house every Thursday, and there I have seen the leading scientists, Laplace, Poisson, Fourier, Gay-Lussac, Ampere, etc.
      

71. Bellman biography
    
    • However he also wrote Analytic number theory (1980), Mathematical methods in medicine (1983), and The Laplace transform (1984).
      

72. Eells biography
    
    • This he did with "Global Analysis" in 1971-72, "Geometry of the Laplace Operator" in 1976-77, and "Partial Differential Equations in Differential Geometry", in 1989-90.
      

73. Gauss biography
    
    • Gauss used the Laplace equation to aid him with his calculations, and ended up specifying a location for the magnetic South pole.
      

74. Bunyakovsky biography
    
    • Bunyakovskii's book also attempts to make Laplace's Theorie analytique des probabilites (1812) more accessible.
      

75. Patodi biography
    
    • Patodi's first paper Curvature and the eigenforms of the Laplace operator was part of his thesis and the contents of this paper are described in [Geometry and analysis : papers dedicated to the memory of V K Patodi (Bangalore, 1980), i-iii.',2)">2]:- .
      

76. Osipovsky biography
    
    • He also translated Laplace's Mechanique celeste into Russian.
      

77. Darwin biography
    
    • In particular, using methods introduced by Laplace and Thomson, he discussed the effects of tidal action on the Sun-Earth-Moon system.
      

78. Whittaker biography
    
    • His results in partial differential equations (described as 'most sensational' by Watson) included a general solution of the Laplace equation in three dimensions in a particular form and the solution of the wave equation.
      

79. Korkin biography
    
    • He had read, and with his wonderful memory could then recall, most works by Abel, Dirichlet, Euler, Fourier, Gauss, Jacobi, Lagrange, Laplace, Legendre, Monge, and Poisson.
      

80. West biography
    
    • These show West to have been familiar with the works of Lagrange, Laplace and Arbogast and, had they been published promptly, would have established him as a leading British exponent of Continental analysis and its applications.
      

81. Ritt biography
    
    • Among his heroes were Niels Henrik Abel, Augustin Louis Cauchy, David Hilbert, Carl G J Jacobi, Joseph-Louis Lagrange, the marquis Pierre Simon de Laplace, Joseph Liouville and Jules Henri Poincare.
      

82. Ptolemy biography
    
    • After comments by Laplace and Lalande, the next to attack Ptolemy vigorously was Delambre.
      

83. De Moivre biography
    
    • owes more to [de Moivre] than any other mathematician, with the single exception of Laplace.
      

84. Helmholtz biography
    
    • However he did not, rather he studied mathematics on his own, reading works by Laplace, Biot and Daniel Bernoulli.
      

85. Lacroix biography
    
    • Laplace had been an examiner at the Royal Artillery Corps since 1784, but before the Reign of Terror he left Paris with his family.
      

86. Doob biography
    
    • The first half concerns the potential theory of the Laplace operator (i.e.
      

87. Jeffreys biography
    
    • In pure mathematics he studied operational methods (where he improved on Heaviside's operational calculus and Laplace transforms), cartesian tensors and asymptotic approximations.
      

88. Fresnel biography
    
    • In 1819 the committee to judge the Grand Prix of the Academie des Sciences, with Arago as chairman, and including Poisson, Biot and Laplace, met to consider Fresnel's submission.
      

89. Libri biography
    
    • The following year, being now in the fortunate position of having the title of Professor, being paid a professorial salary but having no commitments, he visited Paris and was well received by the top mathematicians of the day including Laplace, Poisson, Ampere, Fourier and Arago.
      

90. Steklov biography
    
    • In addition to the work for his master's thesis and his doctoral thesis referred to above, he reduced problems to boundary value problems of Dirichlet type where Laplace's equation must be solved on a surface.
      

91. Dougall biography
    
    • The author's ingenious proof is based on the repeated application of Laplace's operator to homogeneous harmonic polynomials.
      

92. Stokes biography
    
    • With Green, who in turn had influenced him, Stokes followed the work of the French, especially Lagrange, Laplace, Fourier, Poisson, and Cauchy.
      

93. Lame biography
    
    • He used them to transform Laplace's equation into ellipsoidal coordinates and so separate the variables and solve the resulting equation.
      

94. Gronwall biography
    
    • Gronwall's work contains classical analysis (Fourier series, Gibbs phenomenon, summability theory, Laplace and Legendre series), differential and integral equations, analytic number theory (transcendental numbers, divisor function, L-function of Dirichlet), complex function theory (Dirichlet L-series, conformal mappings, univalent functions), differential geometry, mathematical physics (problems of elasticity, ballistics, induction, potential theory, kinetic theory of gases, optics), nomography, atomic physics (wave mechanics of hydrogen and helium atom, lattice theory of crystals) and physical chemistry where he is especially known as a very important contributor.
      

95. Poincare biography
    
    • He also showed that series expansions previously used in studying the 3-body problem were convergent, but not in general uniformly convergent, so putting in doubt the stability proofs of Lagrange and Laplace.
      

96. Tamarkin biography
    
    • Five papers were published in these journals in 1926 and 1927: On Laplace's integral equations; On Volterra's integro-functional equation; A new proof of Parseval's identity for trigonometric functions; On Fredholm's integral equations, whose kernels are analytic in a parameter; and The notion of the Green's function in the theory of integro-differential equations.
      

97. Weierstrass biography
    
    • He did study mathematics on his own, however, reading Laplace's Mecanique celeste and then a work by Jacobi on elliptic functions.
      

98. Titeica biography
    
    • It describes the work he did on the lattice of mutually conjugated lines on a surface and the Laplace sequence of such lattices [Balkan J.
      

99. Tisserand biography
    
    • Tisserand is especially remembered for his four volume textbook which is an update of Laplace's work.
      

100. Boscovich biography
     
     • Now the young ambitious Laplace attacked his methods.
       

101. Levy Paul biography
     
     • In 1926 he extended Laplace transforms to broader function classes.
       

102. Price biography
     
     • This is not Laplace's rule of succession, but rather a calculation of the posterior probability that the unknown chance x of the event exceeds 1/2 , based on Bayes's assumption that all values of x are a priori equally likely.
       

103. Meissel biography
     
     • Meissel must be judged as a classical mathematician, continuing a tradition from an earlier epoch associated with names like Euler, Laplace, Legendre, Gauss, Jacobi, and Dirichlet.
       

104. Beltrami biography
     
     • He gave a generalised form of the Laplace operator.
       

105. Schmidt biography
     
     • We should note, however, that Laplace presented the Gram-Schmidt process before either Gram or Schmidt.
       

106. Lewy biography
     
     • The solution is given by the sum of two integrals of Laplace type taken over a complex path of integration.
       

107. Puiseux biography
     
     • Laplace's theory of the Moon, presented in 1787, had been shown to be inadequate by Adams in 1853.
       

108. Bosanquet biography
     
     • His later work on integrals include two major papers on the Laplace-Stieltjes integral published in 1953 and 1961.
       

109. Arbogast biography
     
     • The formal algebraic manipulation of series investigated by Lagrange and Laplace in the 1770s was put in the form of operator equalities by Arbogast in 1800 in Calcul des derivations.
       

110. Gelfond biography
     
     • The chapter titles of this book are: Residues; Singular points and series representations of a function; Expansion of a function in a series and properties of the gamma function; Some functional identities and asymptotic estimates; and Laplace transformation and some problems which are solved by the use of residue theory.
       

111. Pincherle biography
     
     • Although his efforts did not prove very fruitful, he was able to study in depth the Laplace transform, iteration problems, and series of generalised factors.
       

112. Jeans biography
     
     • Jeans' work in fluids led him to believe that Laplace's nebular hypothesis for the creation of the solar system was incorrect.
       

113. Boole biography
     
     • At this time Boole was studying the works of Laplace and Lagrange, making notes which would later be the basis for his first mathematics paper.
       

114. Gram biography
     
     • The process seems to be a result of Laplace and it was essentially used by Cauchy in 1836.
       

115. Blades biography
     
     • For example, he communicated On Spheroidal Harmonics and Allied Functions, by Mr G B Jeffery to the meeting on Friday 11 June 1915 and Transformations of Axes for Whittaker's Solution of Laplace's Equation, by Dr G B Jeffery to the meeting on Friday 9 March 1917.
       

116. Biot biography
     
     • Three years later he became Professor of Mathematical Physics at the College de France, an appointment which was due to the influence of Laplace.
       

117. Grassmann biography
     
     • He took the basic theory from Laplace's Mechanique celeste and from Lagrange's Mechanique analytique but he realised that he was able to apply the vector methods which he had been developing since 1832 (described in the preface to Die Lineale Ausdehnungslehre) to produce an original and simplified approach.
       

118. Germain biography
     
     • Germain attempted to extend her research, in a paper submitted in 1825 to a commission of the Institut de France, whose members included Poisson, Gaspard de Prony and Laplace.
       

119. Post biography
     
     • It does contain a really important idea, for in the paper Post proves an important result about inverting the Laplace transform.
       

120. Abel biography
     
     • Holmboe was convinced that Abel had great talent and encouraged him greatly taking him on to study the works of Lagrange and Laplace.
       

121. Ostrogradski biography
     
     • Here between 1822 and 1827 he attended lectures by Laplace, Fourier, Legendre, Poisson, Binet and Cauchy.
       

122. Bertrand biography
     
     • Bertrand mentioned some of his predecessors (De Moivre, Laplace, Bienayme), but did not refer to other scholars, notably to Chebyshev.
       

123. Picard Emile biography
     
     • Starting in 1890, he extended properties of the Laplace equation to more general elliptic equations.
       

124. Napier biography
     
     • Laplace, 200 year later, agreed, saying that logarithms:- .
       

History Topics

1. Matrices and determinants
   
   • He also knew that a determinant could be expanded using any column - what is now called the Laplace expansion.
     Go directly to this paragraph
     
   • In 1772 Laplace claimed that the methods introduced by Cramer and Bezout were impractical and, in a paper where he studied the orbits of the inner planets, he discussed the solution of systems of linear equations without actually calculating it, by using determinants.
     Go directly to this paragraph
     
   • Rather surprisingly Laplace used the word 'resultant' for what we now call the determinant: surprising since it is the same word as used by Leibniz yet Laplace must have been unaware of Leibniz's work.
     Go directly to this paragraph
     
   • Laplace gave the expansion of a determinant which is now named after him.
     Go directly to this paragraph
     
   • However this comment is made with hindsight since Lagrange himself saw no connection between his work and that of Laplace and Vandermonde.
     

2. Orbits
   
   • Laplace, from 1774 onwards, became an important contributor to the attempt of the theoreticians to explain the observations of the observers.
     Go directly to this paragraph
     
   • Lagrange introduced the method of variation of the arbitrary constants in a paper in 1776 stating that the method was of interest in celestial mechanics and, in special cases, had been already been used by Euler, Laplace and himself.
     Go directly to this paragraph
     
   • Laplace read a memoir to the Academie des Sciences on 23 November 1785 in which he gave a theoretical explanation of all the remaining major discrepancies between theory and observation of all the planets and their moons excluding Uranus.
     Go directly to this paragraph
     
   • Laplace's work of 1787, that of Adams of 1854 and later Delaunay's work described below eventually provided solutions.
     Go directly to this paragraph
     
   • The stability proofs of Lagrange and Laplace became inconclusive after this result.
     Go directly to this paragraph
     

3. Indian numerals
   
   • It is worth beginning this article with the same quote from Laplace which we give in the article Overview of Indian mathematics.
     
   • Laplace wrote:- .
     
   • The second aspect of the Indian number system which we want to investigate here is the place value system which, as Laplace comments in the quote which we gave at the beginning of this article, seems "so simple that its significance and profound importance is no longer appreciated." We should also note the fact, which is important to both aspects, that the Indian number systems are almost exclusively base 10, as opposed to the Babylonian base 60 systems.
     
   • All that we know is that the place-value system of the Indians, however it arose, was transmitted to the Arabs and later into Europe to have, in the words of Laplace, profound importance on the development of mathematics.
     

4. Decimal time
   
   • Laplace was enthusiastic and had his watch converted to the new time.
     
   • However Laplace was one of the few to greet the changes in the units of time and angle with any enthusiasm.
     
   • Laplace, now a senator, stated that the new calendar had scientific flaws and should be scrapped.
     

5. Fund theorem of algebra
   
   • Laplace, in 1795, tried to prove the FTA using a completely different approach using the discriminant of a polynomial.
     Go directly to this paragraph
     
   • Gauss's criticisms of the Lagrange-Laplace proofs did not seem to find immediate favour in France.
     Go directly to this paragraph
     
   • Even the 1828 Edition, edited by Poinsot, still expresses complete satisfaction with the Lagrange-Laplace proofs and no mention of the Gauss criticisms.
     Go directly to this paragraph
     

6. 20th century time
   
   • By this he was thinking about Laplace's realisation that Newton's laws completely determined the future if the position, mass and movement of every particle were known.
     
   • Laplace was, of course, right, but Newton on the other hand had based his theory on absolute space and absolute time and the positions and velocities of the particles were given with respect to this absolute coordinate system.
     
   • Even in this form it has a direct consequence for aspects of time we have already discussed, for it means that Laplace's realisation that Newton's laws meant that the future was completely determined by the present would not extend to quantum theory.
     

7. Measurement
   
   • Indeed, probably Laplace and others were more interested in finding the shape of the Earth rather than the length of the metre.
     
   • However between these dates the French Revolution progressed to the stage where the Academie des Sciences was abolished in August 1793 but before that Borda, Lagrange and Laplace had computed a provisional value for the metre based on the survey carried out by Cassini de Thury in 1740.
     

8. General relativity
   
   • Newton's universal gravitation was considered proved correct, thanks to the work of Clairaut and Laplace.
     Go directly to this paragraph
     
   • Laplace looked at the stability of the solar system in Traite du Mecanique Celeste in 1799.
     Go directly to this paragraph
     

9. Classical time
   
   • There was another interesting consequence of Newton's description of the universe based on his precise mathematical laws, and this was fully understood by Laplace.
     
   • Laplace correctly argued that given the laws of mechanics, the complete picture of the past and future world is encapsulated in the present world.
     

10. Classical light
    
    • Fresnel wrote a paper giving the mathematical basis for his wave theory of light and in 1819 the committee, with Arago as chairman, and including Poisson, Biot and Laplace met to consider his work.
      

11. History overview
    
    • The period around the turn of the century saw Laplace's great work on celestial mechanics as well as major progress in synthetic geometry by Monge and Carnot.
      Go directly to this paragraph
      

12. Indian mathematics
    
    • Laplace put this with great clarity:- .
      

Famous Curves

1. Lissajous
   
   • His New American Practical Navigator(1802) and his translation of Laplace's Mecanique celestegave him an international reputation.
     

2. Frequency
   
   • It was also studied with Laplace and Gauss.
     

Societies etc

1. Laplace
   
   • Pierre Simon Laplace .
     

2. Turin Mathematical Society
   
   • The same volume contains Recherches sur le calcul integral aux differences infiniment petites, et aux differences finies by Laplace showing that the journal had already gained a high reputation.
     
   • This paper contained equations which Laplace stated were important in mechanics and physical astronomy.
     

3. Paris street names
   
   • Rue Laplace ( 5th Arrondissement) WnM .
     

4. Lunar features
   

5. Lunar features
   
   • (L) Promontorium Laplace .
     

6. Lunar features
   
   • Promontorium Laplace .
     

7. International Congress Speakers
   
   • Salomon Bochner, Laplace Operator on Manifolds.
     

8. Fellows of the RSE
   
   • Pierre Simon Laplace1813More infoMacTutor biography .
     

9. Fellows of the RSE
   
   • Pierre Simon Laplace1813More infoMacTutor biography .
     

10. Fellows of the RSE
    
    • Pierre Simon Laplace1813More infoMacTutor biography .
      

11. Fellow of the Royal Society
    
    • Pierre S Laplace 1789 .
      

12. Eiffel Tower
    
    • Laplace .
      

13. AMS Steele Prize
    
    • He later extended this work to a spectral theory for the automorphic Laplace operator, relying on the Radon transform on horospheres to avoid Eisenstein series.
      

References

1. References for Laplace
   
   • References for Pierre-Simon Laplace .
     
   • H Bernhard, Laplace, in H Wussing and W Arnold, Biographien bedeutender Mathematiker (Berlin, 1983).
     
   • C C Gillispie, Pierre-Simon Laplace.
     
   • B A Vorontsov-Vel'yaminov, Laplace (Russian), 'Nauka' (Moscow, 1985).
     
   • V Banfi, The origin of the solar system according to P S Laplace (Italian), Atti Accad.
     
   • F Barone, The epistemology of Pierre-Simon de Laplace (Italian), Atti Accad.
     
   • L Brandt, Uber das Bahnbestimmungsproblem bei Gauss und Laplace.
     
   • P Brosche, Laplace schreibt nach Gotha, Ber.
     
   • B Bru, L'a-peu-pres et l'a-fort-peu-pres au temps de Laplace, in L'a-peu-pres (Paris, 1988), 87-103.
     
   • W G Cochran, Laplace's ratio estimator, in Contributions to survey sampling and applied statistics (New York, 1978), 3-10.
     
   • A I Dale, Bayes or Laplace? An examination of the origin and early applications of Bayes' theorem, Arch.
     
   • M A B Deakin, The ascendancy of the Laplace transform and how it came about, Arch.
     
   • M A B Deakin, Corrigendum: 'Operational calculus and the Laplace transform', Austral.
     
   • M A B Deakin, Euler's version of the Laplace transform, Amer.
     
   • M A B Deakin, Operational calculus and the Laplace transform, Austral.
     
   • M A B Deakin, The development of the Laplace transform, 1737-1937 I : Euler to Spitzer, 1737-1880, Arch.
     
   • M A B Deakin, The true origins of the Laplace transform, Math.
     
   • J Dhombres, La theorie de la capillarite selon Laplace : mathematisation superficielle ou etendue?, La mathematisation 1780-1830, Rev.
     
   • Les lecons de Laplace a l'ecole Normale de l'an III, Rev.
     
   • P Dupont, Laplace and the indifference principle in the 'Essai philosophique des probabilites' (Italian), Rend.
     
   • J Fourier, Eloge historique de M le Marquis de Laplace, MASIF 10 (1831).
     
   • E Frankel, The search for a corpuscular theory of double refraction : Malus, Laplace and the prize competition of 1808, Centaurus 18 (1973/74), 223-245.
     
   • H H Frisinger, Mathematicians in the history of meteorology: the pressure-height problem from Pascal to Laplace, Historia Math.
     
   • extensional probabilities from their origins to Laplace, Historia Math.
     
   • C C Gillispie, Memoires inedits ou anonymes de Laplace sur la theorie des erreurs, les polynomes de Legendre, et la philosophie des probabilites, Rev.
     
   • S Gindikin, Pierre-Simon Laplace (Russian), Kvant (12) (1977), 12-21.
     
   • F J Giron, History of probability theory: from Pascal to Laplace , in History of mathematics in the XIXth century (Spanish) 2 (Madrid, 1994), 113-133.
     
   • B V Gnedenko, Pierre Simon Laplace (1749-1827) on the 150th anniversary of his death (Bulgarian), Fiz.-Mat.
     
   • I A Golovinskii, How was the Laplace transform introduced? (Russian), Istor.-Mat.
     
   • I A Golovinskii, Laplace interpolation series (Russian), Istor.-Mat.
     
   • I A Golovinskii, The importance of the discovery of the Laplace transform to the development of interpolation methods (Russian), Voprosy Istor.
     
   • M A Gomez Villegas, The problem of inverse probability : Bayes and Laplace (Spanish), in Current perspectives in logic and philosophy of science (Spanish) (Madrid, 1994), 385-396.
     
   • I Grattan-Guinness, Before Bowditch : Henry Harte's translation of Books 1 and 2 of Laplace's Mecanique celeste, NTM Schr.
     
   • I Grattan-Guinness, Thus it mysteriously appears : impressions of Laplace's use of series, Rechnen mit dem Unendlichen (Basel, 1990), 95-102.
     
   • J Hadamard, Celebration du deuxieme centenaire de la naissance de P S Laplace, Arch.
     
   • A M Hinz, Laplace in Calvados, Math.
     
   • M Jacobsen, Laplace and the origin of the Ornstein-Uhlenbeck process, Bernoulli 2 (3) (1996), 271-286.
     
   • S L Jaki, The five forms of Laplace's cosmogony, Amer.
     
   • J Langins, Sur l'enseignement et les examens a l'Ecole polytechnique sous le Directoire: a propos d'une lettre inedite de Laplace, Rev.
     
   • B Ju Levin, On the history of the term 'Kant-Laplace hypothesis' (Russian), Voprosy Istor.
     
   • B Yu Levin, Laplace's cosmogonic hypothesis (history of its creation and publication) (Russian), Voprosy Istor.
     
   • W Lorey, Die Bedeutung von Pierre Simon Laplace (28.3.
     
   • J Merleau-Ponty, Situation et role de l'hypothese cosmogonique dans la pensee cosmologique de Laplace, Rev.
     
   • J Merleau-Ponty, Erratum: 'Situation et role de l'hypothese cosmogonique dans la pensee cosmologique de Laplace', Rev.
     
   • V V Pavlovskaja, The problem of the stability of the equilibrium of a revolving fluid in the works of d'Alembert and Laplace (Russian), in Problems in the history of mathematics and mechanics (Kiev, 1977), 58-67.
     
   • J-B Pecot, Le probleme de l'ellipsoide et l'analyse harmonique : la controverse entre Legendre et Laplace, in Analyse diophantienne et geometrie algebrique (Paris, 1993), 113-157.
     
   • S S Petrova, On the history of Laplace's method of cascades (Russian), in Studies in the history of mathematics 19 'Nauka' (Moscow, 1974), 125-131, 301.
     
   • S S Petrova, Early history of the Laplace transform (Russian), Istor.-Mat.
     
   • Newton and Laplace-their life and work (Bulgarian), Fiz.-Mat.
     
   • R L Plackett, The influence of Laplace and Gauss in Britain, Bull.
     
   • A W Richeson, Laplace's contribution to pure mathematics, Nat.
     
   • L M R Saraiva, Laplace, Lavoisier and the quantification of heat, Physis Riv.
     
   • I Schneider, Laplace and thereafter : the status of probability calculus in the nineteenth century, in The probabilistic revolution 1 (Cambridge, MA-London, 1987), 191-214.
     
   • F Sebastiani, The microscopic-caloric theories of gases of Laplace, Ampere, Poisson and Prevost (Italian), Physis - Riv.
     
   • F Sebastiani, The caloric theories of Laplace, Poisson, Sadi Carnot and Clapeyron, and the theory of thermal phenomena in gases formulated by Clausius in 1850 (Italian), Physis - Riv.
     
   • O B Sheynin, The probability theory of P-S Laplace (Russian), Istor.-Mat.
     
   • O B Sheynin, P S Laplace's work on probability, Arch.
     
   • O B Sheynin, On the history of the de Moivre-Laplace limit theorems (Russian), in History and methodology of natural sciences No.
     
   • O B Sheynin, The appearance of Dirac's delta functions in the works of P S Laplace (Russian), Istor.-Mat.
     
   • V S Sologub, On the first integration methods of the Laplace equation (Ukrainian), Istor.-Mat.
     
   • S M Stigler, Laplace's 1774 memoir on inverse probability, Statist.
     
   • S M Stigler, Studies in the history of probability and statistics XXXIV: Napoleonic statistics : the work of Laplace, Biometrika 62 (2) (1975), 503-517.
     
   • S M Stigler, Laplace's early work : chronology and citations, Isis 69 (247) (1978), 234-254.
     
   • S M Stigler, Studies in the history of probability and statistics XXXII : Laplace, Fisher, and the discovery of the concept of sufficiency, Biometrika 60 (1973), 439-445.
     
   • D van Dantzig, Laplace, probabiliste et statisticien, et ses precurseurs, Arch.
     
   • E T Whittaker, Works of Laplace, Mathematical Gazette 33 (1949), 1-12.
     
   • E T Whittaker, Laplace, Amer.
     
   • C Wilson, The great inequality of Jupiter and Saturn : from Kepler to Laplace, Arch.
     
   • S L Zabell, Buffon, Price, and Laplace : scientific attribution in the 18th century, Arch.
     
   • http://www-history.mcs.st-andrews.ac.uk/References/Laplace.html .
     

2. References for Plancherel
   
   • Sur l'application aux series de Laplace du procede de sommation de M.
     
   • Sur la sommation des series de Laplace de de Legendre.
     
   • Sur le role de la transformation de Laplace dans l'integration d'une classe de problemes mixtes du type hyperbolique et sur les developpements en series d'un couple de fonctions arbitraires.
     

3. References for Legendre
   
   • C C Gillispie, Memoires inedits ou anonymes de Laplace sur la theorie des erreurs, les polynomes de Legendre, et la philosophie des probabilites, Rev.
     
   • J-B Pecot, Le probleme de l'ellipsoide et l'analyse harmonique : la controverse entre Legendre et Laplace, in Analyse diophantienne et geometrie algebrique (Paris, 1993), 113-157.
     

4. References for Lacroix
   
   • R Taton, Laplace et Sylvestre Francois Lacroix, in Rev.
     

5. References for Craig James
   
   • S M Stigler, John Craig and the probability of history : from the death of Christ to the birth of Laplace, Journal of the American Statistical Association 81 (1986), 879-887.
     

6. References for Poincare
   
   • M A B Deakin, The development of the Laplace transform, 1737-1937.
     

7. References for Lambert
   
   • U Garibaldi and M A Penco, Probability theory and physics between Bernoulli and Laplace : the contribution of J H Lambert (1728-1777) (Italian), in Proceedings of the fifth national congress on the history of physics, Rome, 1984, Rend.
     

8. References for Pascal
   
   • H H Frisinger, Mathematicians in the history of meteorology : the pressure-height problem from Pascal to Laplace, Historia Math.
     

9. References for De Moivre
   
   • O B Sheynin, On the history of the de Moivre-Laplace limit theorems (Russian), in History and methodology of natural sciences IX : Mechanics, mathematics (Moscow, 1970), 199-211.
     

10. References for Price
    
    • S L Zabell, Buffon, Price, and Laplace : scientific attribution in the 18th century, Arch.
      

11. References for Monge
    
    • J J Bikerman, Capillarity before Laplace : Clairaut, Segner, Monge, Young, Arch.
      

12. References for Ampere
    
    • F Sebastiani, The microscopic-caloric theories of gases of Laplace, Ampere, Poisson and Prevost (Italian), Physis - Riv.
      

13. References for Clapeyron
    
    • F Sebastiani, The caloric theories of Laplace, Poisson, Sadi Carnot and Clapeyron and the theory of thermal phenomena in gases formulated by Clausius in 1850 (Italian), Physis - Riv.
      

14. References for Malus
    
    • E Frankel, The search for a corpuscular theory of double refraction : Malus, Laplace and the prize competition of 1808, Centaurus 18 (1973/74), 223-245.
      

15. References for Bayes
    
    • A I Dale, Bayes or Laplace? An examination of the origin and early applications of Bayes' theorem, Arch.
      

16. References for Buffon
    
    • S L Zabell, Buffon, Price, and Laplace : scientific attribution in the 18th century, Arch.
      

17. References for Clausius
    
    • F Sebastiani, The caloric theories of Laplace, Poisson, Sadi Carnot and Clapeyron, and the theory of thermal phenomena in gases formulated by Clausius in 1850 (Italian), Physis - Riv.
      

18. References for Segner
    
    • J J Bikerman, Capillarity before Laplace : Clairaut, Segner, Monge, Young, Arch.
      

19. References for Craig
    
    • S M Stigler, John Craig and the probability of history : from the death of Christ to the birth of Laplace, Journal of the American Statistical Association 81 (1986), 879-887.
      

20. References for Carnot Sadi
    
    • F Sebastiani, The caloric theories of Laplace, Poisson, Sadi Carnot and Clapeyron, and the theory of thermal phenomena in gases formulated by Clausius in 1850 (Italian), Physis-Riv.
      

21. References for Gauss
    
    • R L Plackett, The influence of Laplace and Gauss in Britain, Bull.
      

22. References for Bertrand
    
    • The Laplace integral and the Bertrand problem (Russian), Investigations in the history of mechanics ('Nauka', Moscow, 1981), 128-140; 311.
      

23. References for Plana
    
    • G Tagliaferri and P Tucci, Carlini and Plana on the theory of the moon and their dispute with Laplace, Ann.
      

24. References for D'Alembert
    
    • V V Pavlovskaja, The problem of the stability of the equilibrium of a revolving fluid in the works of d'Alembert and Laplace (Russian), in Problems in the history of mathematics and mechanics (Kiev, 1977), 58-67.
      

Additional material

1. Laplace: 'Méchanique Céleste
   
   • Laplace: Mechanique Celeste .
     
   • Pierre-Simon Laplace published the first two volumes of Mechanique Celeste in 1799.
     
   • Nathaniel Bowditch translated Laplace's book into English and this English translation was published in 1829.
     
   • Below we give Bowditch's translation of Laplace's Preface:- .
     
   • http://www-history.mcs.st-andrews.ac.uk/Extras/Laplace_mechanique_celeste.html .
     

2. Laplace on 'new stars
   
   • Laplace on "new stars" .
     
   • Variable stars had been known for 200 years when Laplace wrote Exposition du systeme du monde (1796).
     
   • Laplace wrote about supernovae in Exposition du systeme du monde in 1796:- .
     
   • http://www-history.mcs.st-andrews.ac.uk/Extras/Laplace_new_stars.html .
     

3. Laplace: 'Essay on probabilities
   
   • Laplace: Essay on probabilities .
     
   • Laplace wrote A philosophical essay on probabilities which was translated by F W Truscott and F L Emory and was published by Dover in 1953.
     
   • http://www-history.mcs.st-andrews.ac.uk/Extras/Laplace_Probabilities.html .
     

4. George William Hill's new theory of Jupiter and Saturn
   
   • But these terms not bringing about a reconciliation between observation and theory, Lagrange and Laplace were led to make their notable researches on the possibility of secular equations in the mean motions of the planets.
     
   • At length the whole difficulty with Jupiter and Saturn was removed by Laplace's discovery of the great inequalities in 1786.
     
   • This great success seems to have stirred up Laplace and his collaborators to pushing the approximations still further.
     
   • The results he obtained failed to satisfy an equation of condition which Laplace had employed in his investigation.
     
   • After some discussion Laplace abandoned his equation and substituted for it another, which Plana's results were as far from satisfying as before.
     
   • Pontecoulant then, taking up the subject, discovered that Laplace's results had been taken with the wrong sign, and that Plana had made errors of some importance in his investigation.
     
   • Neither Laplace's, Plana's, nor Pontecoulant's determination of these second-order terms can be regarded as anything else than a very rude and inadequate approximation.
     
   • In the Mecanique Celeste, Laplace had determined all long-period inequalities as if they were to be applied to the mean longitude, and had so directed they should, while the short-period ones were derived as if they were to be added to the true longitude.
     
   • For Laplace has nowhere shown how these two modes of application can be employed in unison.
     

5. George William Hill's new theory of Jupiter and Saturn
   
   • But these terms not bringing about a reconciliation between observation and theory, Lagrange and Laplace were led to make their notable researches on the possibility of secular equations in the mean motions of the planets.
     
   • At length the whole difficulty with Jupiter and Saturn was removed by Laplace's discovery of the great inequalities in 1786.
     
   • This great success seems to have stirred up Laplace and his collaborators to pushing the approximations still further.
     
   • The results he obtained failed to satisfy an equation of condition which Laplace had employed in his investigation.
     
   • After some discussion Laplace abandoned his equation and substituted for it another, which Plana's results were as far from satisfying as before.
     
   • Pontecoulant then, taking up the subject, discovered that Laplace's results had been taken with the wrong sign, and that Plana had made errors of some importance in his investigation.
     
   • Neither Laplace's, Plana's, nor Pontecoulant's determination of these second-order terms can be regarded as anything else than a very rude and inadequate approximation.
     
   • In the Mecanique Celeste, Laplace had determined all long-period inequalities as if they were to be applied to the mean longitude, and had so directed they should, while the short-period ones were derived as if they were to be added to the true longitude.
     
   • For Laplace has nowhere shown how these two modes of application can be employed in unison.
     

6. Andrew Forsyth addresses the British Association in 1905, Part 2
   
   • The beginnings were made by the Bernoullis (a family that must be of supreme interest to Dr Francis Galton in his latest statistical compilations, for it contained no fewer than seven mathematicians of mark, distributed over three generations), but the main achievements are due to Euler, Lagrange, and Laplace.
     
   • It was made, in the main, by Lagrange, as regards the wider theory, and by Laplace, as regards the amplitude of detailed application.
     
   • In that year Laplace published the last progressive instalment of his great treatise on Celestial Mechanics, the portion that still remained for the future being solely of an historical character; the great number of astronomical phenomena which he had been able to explain by his mathematical presentation of the consequences of the Newtonian theory would, by themselves, have been sufficient to give confidence in the validity of that theory.
     

7. R A Fisher: 'History of Statistics
   
   • Whereas Bayes excelled in logical penetration, Laplace (1820) was unrivalled for his mastery of analytic technique.
     
   • These seem to have been later discovered independently by Thiele (1889), but mathematically Laplace's methods were more powerful than Thiele's and far more influential on the development of the subject in France and England.
     
   • A direct result of Laplace's study of the distribution of the resultant of numerous independent causes was the recognition of the normal law of error, a law more usually ascribed, with some reason, to his great contemporary, Gauss.
     

8. Joseph Fourier on his teachers
   
   • Among his teachers were Laplace, Monge, and Lagrange, and Fourier gave charming descriptions of these famous mathematicians.
     
   • Laplace was 45 years old when Fourier attended his lectures:- .
     
   • Laplace seems quite young; his voice is quiet but clear, and he speaks precisely, though not very fluently; his appearance is pleasant, and he dresses very simply; he is of medium height.
     

9. Horace Lamb addresses the British Association in 1904
   
   • When he came to manhood Lagrange, Laplace, Poisson, Fourier, Fresnel, Ampere, had but lately passed away.
     
   • When the foundations of Analytical Dynamics had been laid by Euler and d'Alembert, the first important application was naturally to the problems of Gravitational Astronomy; this formed, of course, the chief work of Laplace, Lagrange, and others.
     
   • It has suggested many important analytical results, and still gives the best and simplest intuitive foundation for a whole class of theorems which are otherwise hard to comprehend in their various relations, such as Fourier's theorem, Laplace's expansion, Bessel's functions, and the like.
     

10. EMS 1938 Colloquium
    
    • He sketched the views of Laplace, de Mises, Wald and others, and described in more detail the "modernised classical definition" of Neyman and Kolmogorov.
      
    • The discussion was noteworthy for Professor Whittaker's vigorous defence of the classical (Laplace's) point of view against all comers.
      

11. Somerville's Booklist
    

12. L R Ford - Differential Equations
    
    • Subsequent chapters cover special methods for equations of first order, linear equations of any order with a brief account of the use of the Laplace transform, solution in series of the hypergeometric, Legendre's and Bessel's equations, approximate numerical solutions, and two chapters on partial differential equations.
      
    • General solutions of simple types of partial differential equations are obtained before separation of variables is used to solve problems of vibration and the Laplace equation in two dimensions.
      

13. Kelvin on the sun, Part 2
    
    • This is just the beginning postulated by Laplace for his nebular theory of the evolution of the solar system which, founded on the natural history of the stellar universe, as observed by the elder Herschel, and completed in details by the profound dynamical judgment and imaginative genius of Laplace, seems converted by thermodynamics into a necessary truth, if we make no other uncertain assumption than that the materials at present constituting the dead matter of the solar system have existed under the laws of dead matter for a hundred million years.
      

14. Thomas Muir: 'History of determinants
    
    • 2, which occurs under Laplace, is meant to show that the theorem was not then heard of for the first time, but that Laplace contributed something additional to our knowledge of it.
      

15. H S Ruse papers
    
    • General solutions of Laplace's equation in a simply harmonic manifold (1963).
      
    • T J Willmore writes: Explicit formulae are obtained for general solutions of Laplace's equation in a real n-cell equipped with a simply harmonic riemannian metric.
      

16. EMS 1938 Colloquium 4.html
    
    • He sketched the views of Laplace, de Mises, Wald and others, and described in more detail the "modernised classical definition" of Neymann and Kolmogorov.
      
    • The discussion was noteworthy for Professor Whittaker's vigorous defence of the classical (Laplace's) point of view against all comers.
      

17. EMS obituary
    
    • The Laplace transformation was applied here, as it had been by various previous writers on the theory of functions, notably by A J Macintyre.
      
    • Mrs Macintyre later devised an integral transform in which the kernel was obtained from that of the Laplace transform by a process involving fractional differentiation, and applied it to extend the theory of the Gregory-Newton and Abel interpolation series.
      

18. George Temple's Inaugural Lecture II
    
    • All our masters, from Laplace to Cauchy, have proceeded in the same way.
      

19. Whittaker RSE Prize
    
    • An early and brilliant example was his general solution of Laplace's equation, which might be considered the fundamental partial differential equation of the older physics.
      

20. R A Fisher: 'Statistical Methods' Introduction
    
    • Three of the distributions with which we shall be concerned, Bernoulli's binomial distribution, Laplace's normal distribution, and Poisson's series, were developed by writers on probability.
      

21. James Clerk Maxwell on the nature of Saturn's rings
    
    • We know, since it has been demonstrated by Laplace, that a uniform solid ring cannot revolve permanently about a planet.
      

22. Whittaker EMS Obituary.html
    
    • Then in 1902 and 1903 he published two papers on the partial differential equations of mathematical physics in which he obtained the solution of Laplace's equation with which his name is associated.
      

23. Edward Sang on his tables
    
    • Laplace had, in anticipation, reduced all his data in the Mecanique Celeste to the new system, and instruments had been graduated suitably.
      

24. Goursat: 'Cours d'analyse mathématique
    
    • - Methode de Laplace.
      

25. Zhukovsky (or Jowkowski) aerofoils
    
    • One of the curious and useful facts about differentiable complex functions is that their real and imaginary parts satisfy Laplace's Equation (a partial differential equation important in many applications from Electricity to Hydrodynamics).
      

26. Airy on Thales' eclipse
    
    • The great step made in theory, in reference to these inquiries, was the discovery made by Laplace near the end of the last century, of the secular change in the moon's mean motion in longitude (accompanied by similar changes in the motion of the perigee and the node).
      

27. Leonard J Savage: 'Foundations of Statistics
    
    • It was pushed forward in the nineteenth century by Laplace, Gauss, and others, and it has been subject to a fervour of activity since the early twenties of this century, when it received great impetus from the work of R A Fisher.
      

28. James Clerk Maxwell on the nature of Saturn's rings
    
    • We know, since it has been demonstrated by Laplace, that a uniform solid ring cannot revolve permanently about a planet.
      

29. Centenary of John Leslie
    
    • He met Humboldt, Laplace, and other famous men.
      

30. Ernest Hobson addresses the British Association in 1910
    
    • In the classical period of the eighteenth century, the time of Lagrange and Laplace, the nature of the physical investigations, consisting largely of the detailed working out of problems of gravitational Astronomy in accordance with Newton's law, was such that the passage was easy from the concrete problems to the corresponding abstract mathematical ones.
      

31. Charles Tweedie on James Stirling
    
    • Witness, for example, the tribute of praise rendered by Laplace in his papers on Probability and on the Laws of Functions of very large numbers.
      

32. H M Macdonald addresses the British Association in 1934, Part 1
    
    • The modification necessary in this result to make it applicable to the case of crystalline media was effected by Laplace, who made use of the corpuscular theory of light in his investigation and assumed that the velocity of the light particles in a crystalline medium depended on the direction.
      

33. Library of Mathematics
    
    • Solutions of Laplace's equationD R Bland .
      

34. Harriot and binary numbers
    
    • Laplace wrote:- .
      

35. Percy MacMahon addresses the British Association in 1901
    
    • Whereas in 1801 on the Continent there were the leaders Lagrange, Laplace and Legendre, and of rising men, Fourier, Ampere, Poisson and Gauss, we could only claim Thomas Young and Ivory as men who were doing notable work in research.
      

36. H M Macdonald addresses the British Association in 1934
    
    • The modification necessary in this result to make it applicable to the case of crystalline media was effected by Laplace, who made use of the corpuscular theory of light in his investigation and assumed that the velocity of the light particles in a crystalline medium depended on the direction.
      

37. Keynes: 'Probability' Introduction Ch II
    
    • [This view has often been taken, e.g., by Bernoulli and, incidentally, by Laplace; also by Fries (see Czuber, Entwicklung, p.
      

38. Publications of Albert Wangerin
    
    • Laplace, Ivory, Gauss, Chasles und Dirichlet: Uber die Anziehung homogener Ellipsoide (W Engelmann, Leipzig, 1890).
      

39. Dubreil-Jacotin on Mary Somerville
    
    • Mary Somerville's principal work consisted of translating and thus making known to her contemporaries the celestial mechanics of Laplace and of adding to it personal notes of real value.
      

40. Bertrand's work on probability' Introduction
    
    • Bertrand mentioned some of his predecessors (De Moivre, Laplace, Bienayme), but did not refer to other scholars, notably to Chebyshev.
      

Quotations

1. Quotations by Laplace
   
   • Quotations by Pierre-Simon Laplace .
     
   • Laplace: Sire, I had no need of that hypothesis.
     
   • http://www-history.mcs.st-andrews.ac.uk/Quotations/Laplace.html .
     

2. A quotation by Mises
   
   • The unlimited extension of the validity of the exact sciences was a characteristic feature of the exaggerated rationalism of the eighteenth century" (in reference to Laplace).
     

3. Quotations by Lagrange
   
   • One day after [Laplace] had invited Lagrange to dinner, Lagrange asked: "Will it be necessary to wear the costume of a senator?" in a mocking tone, of which everyone sensed the malice, except the amphityron [=host] senator.
     

4. Quotations by Gauss
   
   • Sin2 φ is odious to me, even though Laplace made use of it; should it be feared that sin2 φ might become ambiguous, which would perhaps never occur, or at most very rarely when speaking of sin(φ2), well then, let us write (sin φ)2, but not sin2 φ, which by analogy should signify sin (sin φ) .
     

5. A quotation by Bowditch
   
   • I never came across one of Laplace's Thus it plainly appears without feeling sure that I have hours of hard work before me to fill up the chasm and find out and show how in plainly appears.
     

6. Quotations by Arago
   
   • Eulogy on Laplace .
     

Chronology

1. Mathematical Chronology
   
   • Euler, Lagrange and Laplace also work on the three-body problem.
     
   • Laplace presents his famous nebular hypothesis in Exposition du systeme du monde which views the solar system as originating from the contracting and cooling of a large, flattened, and slowly rotating cloud of incandescent gas.
     
   • Laplace publishes the first volume of five-volume Traite de mecanique celeste (Celestial Mechanics).
     
   • Laplace publishes the two volumes of Theorie Analytique des probabilites (Analytical Theory of Probabilities).
     
   • The second book contains Laplace's definition of probability, Bayes's rule, and mathematical expectation.
     
   • Inspired by the work of Laplace, Adrain publishes Investigation of the figure of the Earth and of the gravity in different latitudes.
     
   • This puts in doubt the stability proofs of the solar system given by Lagrange and Laplace.
     
   • Bateman applies Laplace transforms to integral equations.
     

2. Chronology for 1810 to 1820
   
   • Laplace publishes the two volumes of Theorie Analytique des probabilites (Analytical Theory of Probabilities).
     
   • The second book contains Laplace's definition of probability, Bayes's rule, and mathematical expectation.
     
   • Inspired by the work of Laplace, Adrain publishes Investigation of the figure of the Earth and of the gravity in different latitudes.
     

3. Chronology for 1780 to 1800
   
   • Laplace presents his famous nebular hypothesis in Exposition du systeme du monde which views the solar system as originating from the contracting and cooling of a large, flattened, and slowly rotating cloud of incandescent gas.
     
   • Laplace publishes the first volume of five-volume Traite de mecanique celeste (Celestial Mechanics).
     

4. Chronology for 1890 to 1900
   
   • This puts in doubt the stability proofs of the solar system given by Lagrange and Laplace.
     

5. Chronology for 1900 to 1910
   
   • Bateman applies Laplace transforms to integral equations.
     

6. Chronology for 1740 to 1760
   
   • Euler, Lagrange and Laplace also work on the three-body problem.