Pierre-Simon de Laplace: The French Newton and Father of Celestial Mechanics

A Norman Childhood and Early Talent

Born on March 23, 1749 in Beaumont-en-Auge in Normandy, Pierre-Simon Laplace (1749-1827) grew up in a modest peasant family. His exceptional talent for mathematics was noticed early by local teachers who facilitated his access to education.

Educational journey:

• 1765-1766: Studies at the Jesuit college in Caen
• 1766: Recommended for the Military School of Beaumont
• 1768: Arrival in Paris with a letter of recommendation for d'Alembert
• 1770: Became mathematics professor at the Paris Military School

Celestial Mechanics and The System of the World

1. Major Work: Traité de mécanique céleste (1799-1825)

Laplace published his monumental work in 5 volumes:

• Application of Newton's laws to the solar system
• Demonstration of the stability of the solar system over long periods
• Explanation of planetary perturbations by gravitational interactions
• Development of differential equations to describe celestial motions

Fundamental equation of celestial mechanics: $$ \frac{d^2x}{dt^2} + \frac{d^2y}{dt^2} + \frac{d^2z}{dt^2} = \frac{dU}{dx} + \frac{dU}{dy} + \frac{dU}{dz} $$ where \( U \) is the force function.

2. The Nebular Hypothesis (1796)

In Exposition du système du monde, Laplace proposed:

• A theory on the formation of the solar system from a primitive nebula
• Explanation of the rotation of planets in the same direction
• Prediction of Saturn's rings as a result of this rotation
• Major influence on subsequent cosmogonic theories

3. Contributions to Astronomy

Other astronomical discoveries:

• Precise calculation of the masses of Jupiter and Saturn
• Demonstration of the flattening of the Earth at the poles
• Study of tides and their relation to the Moon
• Prediction of the existence of black holes (dark bodies)

Major Contributions to Mathematics

1. Probability Theory

Laplace developed modern probability theory:

• 1812: Published Théorie analytique des probabilités
• Introduced the method of least squares
• Developed the central limit theorem
• Applied probabilities to social sciences and statistics

Laplace's formula for conditional probabilities: $$ P(A|B) = \frac{P(A \cap B)}{P(B)} $$

2. Differential Equations

His work on differential equations includes:

• Solution of partial differential equations
• Development of the Laplace transform
• Applications to mathematical physics
• Study of singular solutions

3. Applied Mathematics

Laplace applied mathematics to various fields:

• Theory of errors and analysis of observations
• Calculation of comet orbits
• Study of capillarity and surface tension
• Contributions to potential theory

Political and Administrative Career

Political career:

• 1795: Member of the Bureau des Longitudes
• 1799: Minister of the Interior under Napoleon (for 6 weeks)
• 1803: Chancellor of the Senate
• 1816: Member of the Académie des sciences (of which he became president)
• 1817: Peer of France

Scientific engagements:

• Member of the Institut de France
• President of the Philomathic Society of Paris
• Foreign member of the Royal Society of London
• Creation of the École normale supérieure

Personal Life and Scientific Relationships

Family life and relationships:

• 1788: Marriage with Marie-Charlotte de Courty de Romanges
• 2 children: a son (died young) and a daughter
• Scientific relationships with:
  • Joseph-Louis Lagrange (collaboration in celestial mechanics)
  • Adrien-Marie Legendre (joint work in mathematics)
  • Napoleon Bonaparte (political and scientific support)
  • Siméon Denis Poisson (successor in mathematics)

Scientific Legacy

Laplace died on March 5, 1827 in Paris, leaving an immense scientific legacy:

• Considered as the "French Newton" for his contributions to:
  • Celestial mechanics
  • Probability theory
  • Differential equations
  • Mathematical physics
• Posthumous honors:
  • His name is inscribed on the Eiffel Tower (with 71 other scientists)
  • Asteroid (4628) Laplace
  • Lunar crater Laplace
  • ESA's Laplace-P mission (study of Jupiter's icy moons)
  • Numerous prizes and medals in mathematics bear his name

Napoleon said of him: "Laplace was a man of genius who brought celestial mechanics to a degree of perfection it had never reached before."