Laplace, Pierre Simon de

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Laplace, Pierre Simon de (1749-1827): French. Mathematician and Natural Scientist.

Laplace was born into a peasant family in Normandy and schooled at the military academy in Beaumont where he first showed signs of his remarkable ability. He moved to Paris at eighteen, where Jean d’Alembert recommended him to a professorial post at the École Militaire.

In 1773 Laplace started his major life work: the rigorous application of Newton’s laws of motion to the dynamics of the solar system. Starting with the assumption of a steady-state universe, he proved the invariance of mean planetary motion in a memoir that earned him associate membership in the French Academy of Sciences in the same year. In 1786 he took a further step by proving the conservative and periodic effects of planetary perturbations by tackling the orbits of Saturn and Jupiter. Finally, he worked out the relationship between lunar acceleration and the eccentricity of the earth’s orbit in 1787, thus completing his model of an eternally stable—though very highly idealized—solar system. All of these discoveries were published in his monumental Celestial Mechanics between 1798 and 1827. Ever anxious to expand his readership, he also wrote The System of the World (1796), a verbal exposition of his work aimed at the general reader in which he advanced, among other things, the nebular hypothesis (which has since become known as the Kant(Kant, Immanuel)-Laplace hypothesis) of the origin of the solar system, stating that the solar system originated in a gaseous nebula. Proving the stability of the solar system was Laplace’s crowning achievement, eventually earning him the title, “the Newton of France.”

Laplace’s interest in planetary astronomy went hand in hand with his investigation of the theory of probability. He turned from the theory of chance events in the early 1770s to probability proper, giving in his “Memoir on Probability” (1781) a formula for the error curve allowing a mean value to be determined from a series of observations, though a practical technique for doing so eluded him. His work in probability theory culminated in yet another text aimed at the general reader, his Philosophical Essay on Probability (1814), as well as the more comprehensive Analytic Theory of Probability (1812).

A versatile man, Laplace also collaborated with Lavoisier, Antoine Laurent on the theory of heat. Together they demonstrated that respiration is a form of combustion in the Memoir on Heat (1783). The following year, Laplace turned his attention to the problem of spheroid attraction, proving that the potentials of confocal ellipsoids at any given point are proportional to their volumes in his Treatise on the Movement and Elliptical Shape of the Planets (1784). This was also the period that saw him exploit Lagrange, Joseph Louis’s concept of potentials, giving rise to the equation that now bears Laplace’s name: Image:Laplace1.jpg, often abbreviated Image:Laplace2.jpg, where V is the potential function and the operator Image:Laplace3.jpg called the Laplacian. While it was first published in his paper on the rings of Saturn (1789), the equation has applications in several fields including fluid dynamics, electromagnetism and the theory of heat.

Although he could be generous with younger mathematicians, Laplace often plagiarized the work of older ones, including d’Alembert, Bayes, de Moivre and Legendre, Adrien Marie. Unlike Lagrange, who considered physical problems an excuse for the exercise of an awesome mathematical intellect, Laplace saw mathematics as a tool for solving physical problems, an attitude that may explain his apparent lack of interest in number theory. His ability to curry favor with whoever was in power on any given day in France saw him collect honors and awards aplenty, culminating in his being named count of the Empire in 1806 under Bonaparte, Napoleon and Marquis by Louis XVIII in 1816. Under Napoleon’s auspices, he had helped to found the Society of Arcueil, a scientific organization that he turned, perhaps inevitably, into a platform for his views. These tended towards dogmatism, as witness his staunch opposition to the wave theory of light despite glaring experimental evidence in its favor. Ironically, it was Laplace’s mathematical work that paved the way for the development of wave equations by James Clerk Maxwell and Erwin Schrödinger. Laplace also adhered to his belief in the essentially fluid character of heat and electricity long after such views were experimentally discredited.

Nowadays, Laplace’s name occurs most frequently in reference to the Laplace transform method of solving differential, difference and integral equations. This powerful mathematical tool allows a given function, f, say, to be transformed into another, Image:Laplace4.jpg, via the equation Image:Laplace5.jpg for all real, positive numbers s. Once transformed, the problem can be solved in Image:Laplace4.jpg before being converted back to f by the inverse transform, Image:Laplace6.jpg , where C is a contour in the s plane. Thus finding the solution to a differential equation can frequently be reduced to a simple problem in algebra.

Further Reading:

Charles Coulston Gillispie, Robert Fox, and Ivor Grattan-Guinness, Pierre-Simon Laplace, 1749-1827: A Life in Exact Science, 1997.

Morris Kline, Mathematical Thought from Ancient to Modern Times, 1972.

Ziad Elmarsafy

University of York

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