# Pierre-Simon Laplace

# Pierre-Simon Laplace

**1749-1827**

**French Mathematician and Astronomer**

Pierre-Simon Laplace, sometimes called "the Newton of France," was a mathematician and astronomer who made many important contributions to the fields of mathematical astronomy and probability. Laplace's *Mécanique Céleste *(*Celestial Mechanics*) was the most important work in mathematical astronomy since Isaac Newton. His *Théorie Analytique des Probabilités *(*Analytical Theory of Probability*) influenced work on statistical probability for most of the nineteenth century. These two works alone guaranteed Laplace's place among the great scientists of the age.

Born to a middle-class family in Normandy, Laplace attended a Benedictine school between the ages of 7 and 16, thanks to wealthy neighbors who noticed Laplace's abilities at an early age. At the age of 16 Laplace entered Caen University to study theology. Laplace soon found that his talents and interests lay in mathematics and began a long and successful career pursuing those interests.

At the age of 19 Laplace was appointed to a chair of mathematics at the Military Academy of Paris. After becoming an associate member of the Paris Academy of Sciences in 1773, Laplace read a paper in which he showed that the planetary motions were stable. The question of the stability of the solar system had been a point of contention between scientists since Isaac Newton (1642-1727) had speculated that God's intervention might be occasionally required to keep the planets in their respective orbits. Laplace became a full member of the Academy of Sciences in 1785.

In 1796 Laplace published his famous nebular hypothesis. This hypothesis states that the solar system evolved from a mass of rotating gases which, as it cooled, had rings break away from its outer edges. These rings cooled further and condensed to form the planets. The sun is the remaining central core of the original gases.

In *Mécanique Céleste,* published in five volumes from 1799 to 1825, Laplace expanded his previous work on the stability of the solar system. In this monumental work, Laplace accounted for the effects of gravitation on all the bodies in the solar system. When presented a copy of *Mécanique Céleste,* Napoleon asked Laplace why God was never mentioned in his book. Laplace replied, "I had no need of that hypothesis."

The second branch of mathematics that occupied much of Laplace's thought was probability. Laplace's 1812 classic, *Théorie Analytique des Probabilités,* became the model of classic probability. Laplace's contributions to mathematical probability included a formal proof of the least squares rule, the method of inverse probability, and the first statement of the central-limit theorem. These and other discoveries in probability by Laplace were made primarily for use in his mathematical astronomy.

In addition to his mathematical contributions, Laplace's philosophy of probability influenced the way scientists thought in the nineteenth century. Laplace made his philosophy known in *Essais philosophique sur les probabilités *(1814), a popularized account of *Théorie Analytique des Probabilités.* Laplace defined probability as the ratio of the number of particular cases in question to the total of all the cases possible. Laplace believed that probability was a measure of the degree of certainty or a rational belief that an event would occur. This philosophy, called classical probability, dominated scientific thought on probability through much of the nineteenth century.

Laplace wrote that probability addresses "the important questions of life" for which complete knowledge was "problematical." One of the questions addressed by probability concerned legal testimony. Laplace wrote that the reliability of testimony depends on the reputation of the witnesses, the number of witnesses, whether there were conflicting testimonies, and whether the testimony was an eyewitness account or passed through other people. For Laplace, probability was a guide for the actions of a rational man.

In addition to his work in mathematics, Laplace was politically active through a very tumultuous time in French history. Laplace was involved in the commission that designed the metric system in 1790. He became a member, then chancellor, of the Senate under Napoleon. Laplace received the Legion of Honor in 1805, became Count of the Empire in 1806, and was named a Marquis in 1817.

**TODD TIMMONS**

## "THUS IT PLAINLY APPEARS"

In *Mécanique Céleste,* Laplace did not generally acknowledge the work of his predecessors, implying that the results were his even when they were not. In addition, Laplace's text was very dense and difficult to follow, even for accomplished mathematicians. He often gave results with little or no details concerning their derivation, prefacing many difficult results with comments such as "It is easy to see...." Nathaniel Bowditch (1773-1838), the American mathematician who translated and commented on the first four volumes of *Mécanique Céleste,* stated that "Whenever I meet in LaPlace with the words 'Thus it plainly appears,' I am sure that hours, and perhaps days, of hard study will alone enable me to discover *how* it plainly appears."

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**Pierre-Simon Laplace**