Napoleon asked him, where is God in your system? Laplace answered, I had no need of that hypothesis.
This was the man who completed Newton's work, founded probability theory, and imagined an
intelligence that could predict the entire future of the universe. Pierre-Simon Laplace,
the Newton of France. Last time we met Joseph Louis Lagrange, who transformed mechanics into
pure algebra with his Lagrangian method. His work contained not a single figure,
the triumph of analysis over geometry. Welcome back to Men of Mathematics.
Today we meet the man who took mathematics further into the cosmos than anyone before,
Pierre-Simon Laplace. He proved the solar system is stable, founded modern probability,
and articulated the deterministic vision that defined classical physics.
Pierre-Simon Laplace was born on March 23, 1749, to a farming family in Normandy.
His mathematical abilities attracted patronage that sent him to Paris,
where by age 24 he was presenting papers to the Academy of Sciences.
D'Alembert recognized his genius and helped launch his career.
Within a few years, Laplace was tackling the most difficult problems in celestial mechanics.
Laplace navigated the French Revolution, Napoleon's Empire, and the Bourbon Restoration
with remarkable political dexterity. He served Napoleon briefly as Minister of the Interior.
Napoleon later said he brought the spirit of infinitesimals into government. Not a compliment.
He was made a count under Napoleon, then a Marquis under the restored monarchy.
Laplace's books are notorious for the phrase, il est-ezé avoir, it is easy to see, followed
by pages of difficult derivations.
When a student asked him to explain one such passage Laplace reportedly spent an hour working it out then confirmed yes it is easy to see Newton Principia explained planetary motion
but left a crucial question open. Is the solar system stable? Small perturbations from planet
to planet gravitational attraction might accumulate until planets collide or escape.
Laplace proved the system is stable, irregularities are periodic, and bounded.
His five-volume Mechanique Celeste, published between 1799 and 1825,
systematized everything known about planetary motion.
How did the solar system form?
Laplace proposed that it condensed from a rotating cloud of gas,
as a success on the next trial.
Laplace-derived, the probability equals s plus 1 divided by n plus 2.
This Bayesian approach smooths estimates.
With zero successes and zero trials, it gives one-half, complete uncertainty.
With many observations, it approaches the observed rate.
Consider the sunrise problem.
If the sun has risen every day for a million days, what's the probability it rises tomorrow?
Naive answer, 100%.
Laplace, 1000
Million days, what's the probability it rises tomorrow?
Naive answer, 100%.
Laplace, 1,000, and 1, over 1,012, approximately 99.99999%.
The plus 1 accounts for our residual uncertainty.
In regions without sources, gravitational and electric potentials satisfy Laplace's equation.
the second partial derivatives with respect to x, y, and z, summed together, equal zero.
Solutions are harmonic functions with beautiful smoothness properties.
This equation appears throughout physics, electrostatics, fluid flow, heat conduction.
Laplace developed a powerful technique for solving differential equations.
The Laplace transform converts differential equations into algebraic equations,
making them much easier to solve. It's essential in engineering and physics.
Laplace articulated the ultimate deterministic vision, an intelligence that knew the position
and momentum of every particle could predict the entire future and reconstruct the entire past.
In his famous passage, an intellect which at a certain moment would know all forces,
and all positions of all items of which nature is composed.
For such an intellect, nothing would be uncertain,
and the future, just like the past, would be present before its eyes.
This Laplace's demon represents classical determinism.
Randomness is just ignorance.
Twentieth century physics challenged this vision.
Quantum mechanics, Heisenberg's uncertainty principle, limits what can be known simultaneously.
Chaos theory, tiny uncertainties in initial conditions grow exponentially.
Computational limits some systems are inherently unpredictable Laplace demon is dead but understanding why took two centuries Laplace calculated that a star 250 times the sun diameter but same density would trap its own
light. These dark stars anticipated black holes, though the mechanism, general relativity, was
unknown. Laplace developed the mathematics of functions on spheres, essential for geophysics,
quantum mechanics, and modern computer graphics.
Pierre-Simon Laplace completed Newton's program for celestial mechanics,
founded modern probability theory,
and articulated classical determinism in its purest form.
His mathematics described the cosmos from nebulae to planetary orbits.
His probability described everything from coin flips to scientific inference.
I had no need of that hypothesis wasn't arrogance.
It was a statement of method.
Laplace's universe ran on mathematics alone. Bell notes Laplace often failed to credit others'
work. He absorbed results and presented them as his own. Yet his achievement is undeniable,
taking all mathematics and astronomy for his province and cultivating it royally.
His final words, what we know is not much. What we do not know is immense.
As E.T. Bell wrote, Laplace was the complete mathematical physicist.
He took all mathematics and theoretical astronomy for his province and cultivated it royally.
Next time on Men of Mathematics, we enter the revolutionary era with Gaspar Mange,
the man who invented descriptive geometry and organized science for Napoleon's armies.
From the siege of Mezières to the expedition to Egypt,
Mange combined mathematical brilliance with practical engineering.
Thank you for joining us on this journey through mathematical history.
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I'll see you next time.