Napoleon's Mathematician: The Life and Contradictions of Gaspard Monge!

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In the whirlwind of gunpowder and blood

that defined the end of the 18th

century, a nation's survival depended

not only on the brute force of its

soldiers, but on the absolute precision

of its mathematicians.

While the French Revolution guillotined

the past, one man rewrote the rules of

three-dimensional space, Gaspard [music]

M didn't just see numbers. He saw

reality as a geometric spectacle in

motion to hide French fortifications

from enemy eyes and cannons. He invented

a method so revolutionary that it was

kept as a state secret, descriptive

geometry.

But the brilliant mind that founded the

AOL [music] poly technique and gave rise

to differential geometry harbored a

fatal contradiction. Seduced by power

and glory, he followed Napoleon Bonapart

to the sands of Egypt and to the ashes

of exile. Today we unveil the life of

Gaspard M, [music]

the unparalleled mathematician whose

spatial lucidity walked handinhand with

the blindest political passion.

The Greatest [music] Mathematicians of

All Time. Episode 68. Gaspard Mong.

Gaspard M was born on May 9th, 1746

in Bone, Burgundy, France.

Gaspar M became the count of Paloo later

in life and is sometimes known by this

title. His father was Jacqu Mge, a

merchant originally from upper Seavoi

[music] in southeastern France.

Gasbard's mother, whose maiden name was

Jean Rouso, was a native of Burgundy,

and it was in the town of Bone, also in

Burgundy, that Gasbard was raised.

Around the time of Gasbart's birth, Bone

following a period of decline was

thriving once again due to the success

of the wine trade. Mge attended the

Ortorian College in Bone. This school

catered to young noblemen and was run by

priests. The institution offered a more

liberal education than other religious

schools, providing instruction not only

in the humanities but also in history,

mathematics and natural sciences. It was

at this school that M first demonstrated

his brilliance. In 1762 at the age of

16, Mer went to Leon where he continued

his studies at the college deinit.

Despite being only 17 at the time, he

was put in charge of teaching a physics

course. Upon completing his studies in

1764, Mon returned to Bone where he

created a map of the town.

The bond plan that M constructed would

have a great influence on the direction

his career would take as it was seen by

a member of the faculty at the Echole

Royale de Janei in Mesier.

He was very impressed with [music] Ma's

work and in 1765

M was [music] appointed draftsman of the

institution. Of course, in this

position, he performed tasks that did

not entirely please him as he aspired to

a position in life that made much more

use of his mathematical talents.

However, the AOL royale dujenei put Moj

in contact with Charles Bosu who was the

mathematics professor there. Initially,

Malia's position did not require the use

of his mathematical talents, but he

worked in his free time developing his

own ideas about geometry.

About a year after becoming a draftsman,

M received an assignment that allowed

him to use his mathematical skills.

Tasked with devising a fortification

plan that would prevent the enemy from

seeing or firing at a military position,

regardless of its location, he created

his own graphical method for

constructing such a fortification

instead of using the complex methods

available at the time. This method made

full use of the geometric techniques

that M had been developing. His

mathematical skills were then recognized

at the Akol Royale dujenei and it was

realized that he possessed exceptional

abilities in both theoretical and

practical disciplines. When Bassut was

elected to the academy deants in 1768,

Mge left the AKL de Masier to become a

professor of hydrodnamics at the Louvre.

On January 22nd, 1769,

M wrote to Bassut explaining that he was

writing a paper on the evolutes of

double curvature curves. He asked Bosu

for his opinion on the originality and

usefulness of the work. Bosu must have

responded very positively for in June

the first publication by Munchch was

[music] published in the journal

Encyclopedic presenting a summary of the

results he had obtained. This article in

which m generalized the results obtained

by Huygens [music] on spatial curves as

part of Huygens's investigation of the

pendulum and added many important new

discoveries is described in detail in

Renee Taton's article published in the

review dtoire deceor application volume

19 number two pages 143 to 149.

The complete work was submitted to the

academi dece in Paris in October 1770

and read before the academi in August

1771, although it was not published by

them [music] until 1785.

When Basu left the Akol Royale Du Janei

in Masier, M was appointed to succeed

him in January 1769.

In 1770, he received an additional

position at the school being appointed

instructor of experimental physics.

Although this represented a major

[music] step in his career, Mong was

more interested in consolidating his

name as a mathematician in higher

circles.

Realizing he needed the guidance of

leading mathematicians, he sought out

Dalbear and Condors in early 1771.

Condors must have been impressed by the

depth of mathematics demonstrated by m

as he recommended that he submit papers

to the academy desiance in each of the

four areas in which he was researching.

The four papers m submitted to the

academy were on a generalization of the

calculus of variations infinite decimal

geometry the theory of partial

differential equations and

combinotaurics.

In the following years, he submitted a

series of important papers to the

academy on partial differential

equations which he studied from a

geometric point of view. His interest in

subjects beyond mathematics began to

grow and he became interested in

problems in both physics and chemistry.

In 1777,

Mge married Katherine Huart and as his

wife owned a forge, he became interested

in metallurgy in addition to his broad

mathematical and scientific interests.

Still deeply involved in teaching at the

Akol Royale Du Janei in Masier, he

organized the installation of a

chemistry laboratory there. From 1780

onwards, however, he devoted less time

to his work in Mesier as in that year he

was elected associate geometer of the

academia deions in Paris. From then on

he spent long periods in Paris teaching

a course in hydrodnamics as a substitute

for bassu as well as participating in

projects carried out by the academia in

the areas of mathematics, physics and

chemistry. It was not possible to

reconcile all of this and teach all his

courses in Mier. But he kept his

positions there and received his full

salary with which he paid other

professors to teach some courses in his

place. After 3 years dividing his time

between Paris and Mezier, M received

another job offer to replace Beasoot as

an examiner of naval cadets.

M would have liked to keep all these

positions, but after trying to organize

an impossible schedule for about a year,

he decided that he would have to resign

from his positions in Mesier, which he

did in December 1784.

In the following 5 years, despite the

heavy obligations as an examiner, M

carried out research in a wide range of

scientific subjects, presenting papers

to the academy on the composition of

nitrous acid, the generation of curved

surfaces, finite difference equations,

partial differential equations, 1785,

double refraction, and the structure of

Iceland spar, the composition of iron,

steel, and cast iron.

and the action of electric sparks on

carbon dioxide gas, 1786.

Capillary phenomena, 1787, and the

causes of certain meteorological

phenomena, 1788.

And a study in physiological optics,

1789.

It is clear that 1789 was a landmark

year in French history with the storming

of the Bastile on July 14th, 1789

marking the beginning of the French

Revolution.

This event would completely change the

course of Ma's life. At the start of the

revolution, he was one of the leading

scientists in Paris with an exceptional

research record in a wide variety of

sciences, experience as an examiner and

in school reforms which he had

implemented in 1786 as part of his

duties as an examiner.

Politically, M was a strong supporter of

the revolution and his first actions

were to demonstrate his support by

joining various societies that supported

it. But he continued with his normal

duties as an examiner of naval cadets

and as an important figure in the work

of the academy. At this time he was

already part of the important weights

and measures commission of the academy.

Louis V 16th attempted to flee the

country on June 20th, 1791,

but was apprehended in Ven and brought

back to Paris, ending attempts to share

power between the king and an assembly.

Relations with Europe deteriorated when

the National Assembly declared that a

people had the right to

self-determination.

France declared war on Austria and

Prussia on April 20th, 1792.

French defeats led to unrest in France.

And on August 10th, 1792,

further popular revolutions occurred

with assassinations of nobles and clergy

during the month of September.

On September 21st, the monarchy was

abolished in France and a republic was

proclaimed.

The national convention offered Mj the

post of minister of the navy in the

government. Without disrespecting ME, it

was impossible to satisfy the rather

extremist views of many people and his

time as minister of the Navy cannot be

considered a success.

Although he persevered under difficult

circumstances, he remained in office for

only 8 months before giving up the

relentless struggle with his allies and

submitting his resignation on April

10th, 1793.

For a few months, M returned to his work

at the Academy of Sciences. But this did

not last long as on August 8th, 1793,

the institution was abolished by the

National Convention. Still a staunch

Republican and supporter [music] of the

revolution, M worked on several military

projects related to weapons and

explosives. He wrote articles on the

subjects and also taught courses on

these military matters. He continued to

serve on the commission of weights and

measures which survived despite the end

of the academy desiance. He also

proposed educational reforms to the

national convention. However, although

his proposal was accepted on September

15th, 1793,

it was rejected the following day. Such

was the volatile nature of decisions in

that unstable period.

M was appointed by the national

convention on March 11th, 1794

to the body created to establish the

Akolle central devo public which would

soon become the AOL poly technique. He

not only had a great influence on the

creation of the institution using his

experience in messier very effectively

but was also appointed instructor of

descriptive geometry on November 9th

1794.

His first task as instructor was to

train the future teachers of the school

which began operating in June 1795.

Ma's lectures on infinite decimal

geometry would form the basis of his

book application de la Analise allege

geometry. Another educational

institution the aol normal was created

to train secondary school teachers and m

taught a course in descriptive geometry

there. He was also a great supporter of

the academia deos and worked hard to

have it reinstated as the institute

national.

The national convention approved the new

institution on October 26th 1795.

However, from May 1796

to October 1797,

M was in Italy on a mission to select

the finest artistic treasures for the

conquerors and bring them to France. Of

particular importance was the fact that

he befriended Napoleon Bonapart during

his stay in Italy.

Napoleon had defeated Austria and signed

the treaty of Campo Formio on October

17th, 1797,

an exceptionally advantageous agreement

for France, which preserved most of the

French conquests.

Mge returned to Paris, bringing with him

the text of the treaty of Campo Formio.

Back in Paris, M resumed his previous

duties and was appointed to the

prestigious position of director of the

AOL poly technique. In February 1798,

M was back in Rome involved in the

founding of the Roman Republic. In

particular, he proposed a project for

advanced schools in the Roman Republic.

Napoleon Bonapart then asked M to join

him on his expedition to Egypt and

somewhat reluctantly M agreed. Mge left

Italy on May 26th 1798 and joined

Napoleon's expeditionary force. The

expedition which included the

mathematicians Forier and Mollis as well

as Moj was initially a great success.

Malta was occupied on June 10th, 1798.

Alexandria was stormed on July 1st, and

the Nile Delta was quickly conquered.

However, on August 1st, [music] 1798,

the French fleet was completely

destroyed by Nelson's [music] fleet at

the Battle of the Nile. So, Napoleon

found himself confined to the lands he

occupied. M was appointed president of

the Egyptian institute in Cairo on

August 21st.

The institute had 12 members in the

mathematics division including Forier

Mollis

and Napoleon Bonapart himself.

During the [music] difficult times with

Napoleon in Egypt and Syria, Mj

continued to work on perfecting his

treatis [music] application donles

algeometry.

Napoleon abandoned his army and returned

to Paris in 1799.

Soon seizing absolute power in France, M

returned to Paris on October 16th, 1799

and resumed his post as director of the

AOL poly technique. He discovered that

his academic memoir geometry descriptive

had been published earlier in 1799.

This had happened at the request of his

wife and was compiled by Hashet from

Mong's lectures at the Akol normal.

On November 9th, 1799,

Napoleon and two other leaders seized

power in a military coup and a new

government, the consulate, was

established.

Napoleon appointed Maul a senator for

life of the consulate. Maul gladly

accepted, although his Republican views

meant he opposed the military

dictatorship Napoleon imposed on France.

The truth must be that M was dazzled by

Napoleon and accepted all the honors and

gifts the emperor bestowed upon him.

Grand officer of the Legion of Honor in

1804, president of the Senate in 1806,

Count of Paloo in 1808 among others. In

the following years, M continued to

pursue a range of activities, fulfilling

his role as a senator and maintaining an

interest in mathematical research.

Although his mathematical work primarily

involved teaching and writing books for

students at the Akal Poly technique.

Gradually [music] he became less

involved in mathematical research and

from 1809 onwards [music]

abandoned teaching due to his failing

health. In June 1812, Napoleon assembled

his grand army numbering approximately

453,000

men, including Prussian and Austrian

soldiers who were forced to serve and

marched on Russia. The campaign was a

disaster, but in September, Napoleon's

army entered a deserted Moscow. Napoleon

retreated. The Prussians and Austrians

deserted the Grand Arma and there were

coup attempts against the emperor in

Paris. Mge was dismayed by the situation

and his health suddenly deteriorated.

He recovered slowly after Napoleon

abandoned what remained of his army and

returned to Paris to reaffirm his

authority. After Napoleon achieved some

military success in 1813, the Allied

armies against him grew stronger, Mong

was sent to Leazge to organize the

city's defense against an attack. The

Allied armies began to advance on France

and Mj fled. When Napoleon abdicated on

April 6th, 1814, Mge was not in Paris,

but he soon returned and tried to

rebuild his life. Napoleon escaped from

Elba where he had been [music] exiled

and by March 20th 1815 he was back in

Paris. Mge immediately joined him and

gave him his unconditional support.

After Napoleon's defeat in Waterloo, Mge

continued to see him until the emperor

was put aboard a ship on July 15th. In

October, Mge feared for his life and

fled France, returning to Paris only in

March 1816.

2 days after his return, he was expelled

[music] from the institute to France and

from then on his life became extremely

difficult as he [music] was politically

persecuted and constantly threatened.

Manga's political career is treated with

benevolence, but Gorland adopts a more

critical view.

Manga's management of the Ministry of

the Navy was a complete failure and he

presided over the cultural plunder of

Italy and Egypt. If Napoleon really said

that M loved him like a mistress, this

proves that the most absolute

mathematical clarity can go hand in hand

with political blindness.

We have frequently discussed M's [music]

scientific work. He is considered the

father of differential geometry due to

his work application danala geometry in

which he introduced the concept of lines

of curvature on a surface in

three-dimensional space. He developed a

general method for applying geometry to

construction problems in

three-dimensional space. He also

introduced two mutually perpendicular

planes of projection for the graphical

description of solid objects. These

techniques were generalized into a

system called geometry descriptive known

today as orthographic projection. The

graphical method used in modern

mechanical drafting. The basic

philosophy behind Monga's mathematical

approach is discussed by Edward Glass in

on the dynamics of mathematical change

in the case of M and the French

Revolution.

Studies in history and philosophy of

science volume 17 1986 pp 249 to 268

where the author states that ma's

objectives were

the geometrization of mathematics based

on first the analogy or correspondence

between operations in analysis and

geometric transformations.

Second, the genetic classification and

parameterization of surfaces through the

analysis of the motion of generating

lines. Mange viewed analysis not as a

self-sufficient language, but merely as

the script for the geometric spectacle

in motion that constitutes reality. His

new approach focused on the deeper, more

intimate and universal relationships

within space and its transformations,

placing him in a position to

interconnect geometry and analysis in a

fertile and unprecedented way. Practical

concerns led Maj to perceive the object

and function of mathematics in a new

light in defiance of the formalist

linguistic standards established by the

revered patrons of mathematics. The fall

of the Napoleonic Empire also brought

about the tragic end for its most

devoted scientist. With Napoleon's final

defeat at Waterlue and the restoration

of the monarchy in 1815,

Gasbard M went from national hero to a

hunted man. Expelled from the Institute

to France, stripped of his [music]

honors and living under constant

political threat, his once unshakable

health collapsed. Mge passed away on

July 28th, 1818 in Paris. The royal

government, fearing the influence of his

legacy, strictly forbade any public

tribute. Yet, in an act of quiet

defiance and profound respect, students

from the Ale [music]

technique defied state orders and

marched to the cemetery to pay their

final respects to their [music] master.

Ma's life leaves us with a troubling

question. Does even the most brilliant

mathematical [music]

clarity justify such blind political

loyalty? Leave your opinion in [music]

the comments below. And if you want to

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