A teenage son of a knife grinder invents a method so powerful for designing fortresses
that the French government classifies it as a military secret.
For 15 years, he teaches it only to those with security clearance.
Then, the revolution comes.
And suddenly, this secret becomes the foundation of a new kind of education
that will transform the world.
Last time, we met Pierre-Simon Laplace,
the Newton of France who completed celestial mechanics and founded probability theory.
We saw his demon of perfect determinism and his cool response to Napoleon.
I had no need of that hypothesis.
Welcome back to Men of Mathematics.
Today, we enter the revolutionary era with Gaspar Monge,
the man who invented descriptive geometry,
founded the École Polytechnique, and shaped technical education for centuries to come.
Gaspard Monge was born on May 9, 1746, in Beaune, Burgundy. His father was a knife grinder and
peddler, about as far from the aristocracy as one could be in pre-revolutionary France.
Young Monge showed exceptional ability early. A map of his hometown that he drew at 14
so impressed local officials that they arranged for him to attend a military school in Mezieres.
At the school, Mange was assigned to help draft fortification plans,
work considered beneath the aristocratic officer students.
Asked to design a fortress defense system a task that normally required weeks of calculation Manj developed a graphical method that solved it in hours The officers refused to believe his
solution until they checked every calculation. Then they classified his method as a military
secret. For 15 years, Manj taught his descriptive geometry only to those with security clearance.
It was too valuable for fortress design to risk falling into enemy hands.
What was this secret method?
Mange invented a systematic way to represent three-dimensional objects
using two-dimensional drawings,
using multiple views, plan, and elevation that capture all spatial information.
Before Mange, architects and engineers communicated through perspective drawings
that couldn't be measured.
After Manj, they had a precise language for three-dimensional design.
Every CAD system, every engineering drawing, every architectural blueprint
descends from Manj's descriptive geometry.
Manj's method grew from stereotomy, the ancient art of stone cutting.
How do you cut stones to fit together in arches and vaults?
Each stone must be shaped precisely to bear loads and meet its neighbors.
The Romans knew how to do this through trial and error.
Mange made it mathematical.
In 1781, Mange posed a problem that seemed simple.
Given piles of dirt and holes to fill, what's the cheapest way to move the dirt?
This optimal transport problem has become fundamental to modern mathematics and machine learning It appears in economics for matching supply and demand in image processing for comparing shapes
in machine learning with Wasserstein distances, and in meteorology for tracking air masses.
Monge also contributed to the study of curved surfaces. He investigated the lines of curvature
on surfaces, special curves that point in the directions of maximum and minimum bending.
This work influenced Gauss's later development of differential geometry.
The French Revolution swept away the old order, including the old educational system.
In 1794, the revolutionary government needed to train engineers fast.
Mange was called upon to help create a new kind of school.
The Ecole Polytechnique was revolutionary in its approach.
Science taught through rigorous mathematics.
No distinction by birth.
Talent was all that mattered.
Practical applications alongside pure theory.
The blackboard method of teaching.
The Ecole produced an extraordinary concentration of mathematical talent.
Cauchy for rigorous analysis.
Fourier for the heat equation and Fourier series.
Poisson for probability and physics,
Carnot for thermodynamics,
Fresnel for wave optics,
and Coriolis for rotating systems.
French mathematics dominated the early 19th century,
largely because of Mange's institution.
Mange accompanied Napoleon to Egypt
as part of the scientific expedition.
He helped found the Institut d and contributed to the Description de l the massive survey that sparked European fascination with ancient Egypt Napoleon trusted Mange like few others
Gaspard Mange rose from poverty to transform technical education. His descriptive geometry
gave engineers a precise language for three-dimensional design. His optimal transport
problem continues to generate research today. His École Polytechnique became the model for
technical schools worldwide, and he did it all while remaining devoted to Napoleon,
a loyalty that would cost him everything. After Waterloo, the restored monarchy stripped
Mange of his honors and expelled him from the Institut de France. His health broke.
When he died in 1818, the government forbade students from attending his funeral.
they came anyway. As E.T. Bell wrote,
Manj was one of those rare spirits who excel both as creators and as teachers.
His influence on French mathematics was profound.
Next time on Men of Mathematics, we meet Joseph Fourier, the orphan who conquered heat.
From revolutionary politics to Egyptian deserts to the mathematics of heat conduction,
Fourier discovered that any periodic function can be broken into simple waves.
His series changed mathematics, physics, and engineering forever.
Thank you for joining us on this journey through mathematical history.
If you appreciate the mind that gave us modern technical drawing, subscribe and hit the notification
bell. New episodes release every week. I'll see you next time.