1749 – 1827
The French Newton — who proved the solar system's stability, founded mathematical probability, and gave us the Laplace equation governing everything from gravity to heat
"You see that I pay little heed to recommendations. You have no need of them; you have made yourself known to me in a much better way." — d'Alembert's response after reading Laplace's paper on the principles of mechanics.
Five volumes systematically applying Newtonian gravity to the entire solar system. Proved the long-term stability of planetary orbits, computed tidal theory, and derived the shape of the Earth.
The first comprehensive mathematical treatment of probability. Introduced the central limit theorem, generating functions, Bayesian reasoning, and least-squares estimation.
Served under Louis XVI, the Revolution, Napoleon (briefly as Minister of the Interior), the Restoration, and the Bourbon monarchy. Adapted his politics to each regime.
∇²φ = 0. Derived in the context of gravitational potential theory, this equation became central to electrostatics, fluid dynamics, and all of mathematical physics.
Newton himself worried that planetary perturbations might accumulate and destabilize the solar system. Laplace proved otherwise.
∇²φ = ∂²φ/∂x² + ∂²φ/∂y² + ∂²φ/∂z² = 0
F(s) = ∫0∞ f(t) e−st dt
Transforms differential equations into algebraic equations. The inverse transform recovers the solution.
Laplace created the first comprehensive mathematical theory of probability, going far beyond the gambling problems of Pascal and Fermat.
Laplace systematized and generalized Bayes' theorem, applying it widely:
P(H|D) = P(D|H) · P(H) / P(D)
posterior = likelihood × prior / evidence
"An intellect which at a certain moment would know all forces and all positions... could embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain." This famous thought experiment articulated determinism — and paradoxically showed why probability is needed in practice.
Alongside Gauss and Legendre, Laplace provided probabilistic justification for the method of least squares in data fitting, showing it minimises the expected error under reasonable assumptions.
Proposed that the solar system formed from a rotating cloud of gas that contracted and spun off rings, which condensed into planets. This idea, independently proposed by Kant, remains the basis of modern planetary formation theory.
Calculated that a body with the density of the Earth but 250 times the Sun's radius would have an escape velocity exceeding the speed of light. These "dark stars" anticipated black holes by over a century.
Corrected Newton's formula for the speed of sound by recognizing that sound propagation is adiabatic (no heat exchange), not isothermal. His correction gave a value matching experiment.
Developed the mathematical theory of capillary forces and surface tension, explaining how liquids rise in narrow tubes against gravity.
Express physical systems as differential equations
Use integral transforms to simplify equations
Expand solutions in power series for small parameters
Extract numerical predictions and uncertainties
Laplace notoriously wrote "il est aisé à voir" ("it is easy to see") when skipping lengthy calculations. Legend has it he sometimes spent hours reconstructing what he had called "easy." This made his books famously difficult to read.
When Napoleon asked why the Mécanique Céleste never mentioned God, Laplace reportedly replied: "Sire, I had no need of that hypothesis." His deterministic universe ran on mathematics alone.
"He sought subtleties everywhere, had only problematic ideas, and finally carried the spirit of the infinitely small into administration."
— Napoleon Bonaparte, on Laplace as ministerDespite his reputation, Laplace mentored many young scientists including Poisson, Biot, and Gay-Lussac. He could be generous when there was no threat to his own priority.
The Laplace equation and its inhomogeneous cousin (Poisson's equation) are central to electrostatics, gravitation, heat conduction, and fluid dynamics. Every physics student solves them.
The Central Limit Theorem, Bayesian inference, and generating functions are foundations of modern statistics, data science, and machine learning.
The Laplace transform is indispensable in engineering, systems theory, and signal processing. Its discrete analogue, the Z-transform, underpins digital signal processing.
Laplace's methods for solar system stability evolved into modern perturbation theory, used in quantum mechanics, plasma physics, and orbital mechanics.
The Laplace transform converts circuit differential equations into algebraic equations in the s-domain.
Spherical harmonics decompose atmospheric and oceanic fields for global climate simulations.
Bayesian methods underpin MRI reconstruction, CT filtering, and machine-learning diagnostic systems.
Earth's gravitational field is modeled as a spherical harmonic expansion — directly from Laplace's equation.
Transfer functions, stability analysis, and feedback control all use the Laplace transform framework.
Bayesian spam filtering, pioneered by Paul Graham, uses Laplace's probabilistic framework to classify emails.
Charles Coulston Gillispie (1997). The standard scholarly biography.
Pierre-Simon Laplace, trans. Truscott & Emory (1902). Laplace's popular exposition of his probability theory.
Primary sources available in various translations. Essential for understanding the scope of Laplace's mathematical physics.
Sharon Bertsch McGrayne (2011). The story of Bayes' theorem from Laplace to modern applications.
"What we know is not much. What we do not know is immense."
— Pierre-Simon Laplace, reportedly his last words (1827)Pierre-Simon Laplace · 1749–1827 · The Newton of France