Gaspard Monge

Gaspard Monge, Comte de Péluse (; 9 May 1746[2] – 28 July 1818[3]) was a French mathematician, the inventor of descriptive geometry[4] (the mathematical basis of technical drawing), and the father of differential geometry.[5] During the French Revolution he served as the Minister of the Marine, and was involved in the reform of the French educational system, helping to found the École Polytechnique.

Gaspard Monge
Gaspard monge litho delpech
Born9 May 1746
Died28 July 1818 (aged 72)
Known forDescriptive geometry
Scientific career
Fieldsmathematics, engineering, education
Notable studentsJean-Baptiste Biot[1]
Sylvestre François Lacroix
Jean-Victor Poncelet[1]


Early life

Monge was born at Beaune, Côte-d'Or, the son of a merchant. He was educated at the college of the Oratorians at Beaune.[4] In 1762 he went to the Collège de la Trinité at Lyon, where, one year after he had begun studying, he was made a teacher of physics[4] at the age of just seventeen.[6]

After finishing his education in 1764 he returned to Beaune, where he made a large-scale plan of the town, inventing the methods of observation and constructing the necessary instruments; the plan was presented to the town, and is still preserved in their library.[4] An officer of engineers who saw it wrote to the commandant of the École Royale du Génie at Mézières, recommending Monge to him and he was given a job as a draftsman.[4] L. T. C. Rolt, an engineer and historian of technology, credited Monge with the birth of engineering drawing.[7]


Those studying at the school were drawn from the aristocracy, so he was not allowed admission to the institution itself. His manual skill was highly regarded, but his mathematical skills were not made use of. Nevertheless, he worked on the development of his ideas in his spare time. At this time he came to contact with Charles Bossut, the professor of mathematics at the École Royale. "I was a thousand times tempted," he said long afterwards, "to tear up my drawings in disgust at the esteem in which they were held, as if I had been good for nothing better."[4]

After a year at the École Royale, Monge was asked to produce a plan for a fortification in such a way as to optimise its defensive arrangement. There was an established method for doing this which involved lengthy calculations but Monge devised a way of solving the problems by using drawings. At first his solution was not accepted, since it had not taken the time judged to be necessary, but upon examination the value of the work was recognized,[4] and Monge's exceptional abilities were recognized.

After Bossut left the École Royale du Génie, Monge took his place in January 1769, and in 1770 he was also appointed instructor in experimental physics.[6]

In 1777, Monge married Cathérine Huart, who owned a forge. This led Monge to develop an interest in metallurgy. In 1780 he became a member of the French Academy of Sciences; his friendship with C. L. Berthollet began at this time.[4] In 1783, after leaving Mézières, he was, on the death of É. Bézout, appointed examiner of naval candidates.[4] Although pressed by the minister to prepare a complete course of mathematics, he declined to do so on the grounds that this would deprive Mme Bézout of her only income, that from the sale of the textbooks written by her late husband.[4] In 1786 he wrote and published his Traité élémentaire de la statique.[4]

1789 and after

Monge's bust in Le Père Lachaise Cemetery in Paris

The French Revolution completely changed the course of Monge's career. He was a strong supporter of the Revolution, and in 1792, on the creation by the Legislative Assembly of an executive council, Monge accepted the office of Minister of the Marine,[4] and held this office from 10 August 1792 to 10 April 1793, when he resigned.[6] When the Committee of Public Safety made an appeal to the academics to assist in the defence of the republic, he applied himself wholly to these operations, and distinguished himself by his energy, writing the Description Le l'art de Fabriquer Les canons and Avis aux ouvriers en fer sur la fabrication de l'acier.[4]

He took a very active part in the measures for the establishment of the Ecole Normale (which existed only during the first four months of the year 1795), and of the school for public works, afterwards the École Polytechnique, and was at each of them professor for descriptive geometry.[4] Géométrie descriptive. Leçons données aux écoles normales was published in 1799 from transcriptions of his lectures given in 1795. He later published Application de l'analyse à la géométrie,[4] which enlarged on the Lectures.

From May 1796 to October 1797 Monge was in Italy with C.L. Berthollet and some artists to select the paintings and sculptures being levied from the Italians.[4] While there he became friendly with Napoleon Bonaparte. Upon his return to France, he was appointed as the Director of the École Polytechnique, but early in 1798 he was sent to Italy on a mission that ended in the establishment, of the short-lived Roman Republic.[4]

From there Monge joined Napoleon's expedition to Egypt, taking part with Berthollet[4] in the scientific work of the Institut d'Égypte and the Egyptian Institute of Sciences and Arts. They accompanied Bonaparte to Syria, and returned with him in 1798 to France.[4] Monge was appointed president of the Egyptian commission, and he resumed his connection with the École Polytechnique.[4] His later mathematical papers are published (1794 — 1816) in the Journal and the Correspondence of the École Polytechnique. On the formation of the Sénat conservateur he was appointed a member of that body, with an ample provision and the title of count of Pelusium[4] (Comte de Péluse), and he became the Senate conservateur's president during 1806–7. Then on the fall of Napoleon he had all of his honours taken away, and he was even excluded from the list of members of the reconstituted Institute.[4]

Monge was an atheist.[8][9]

Monge died in Paris on 28 July 1818. His funeral was held 30 July 1818 at St. Thomas Aquinas Church in Paris.[10] His remains were first interred in a mausoleum in Le Père Lachaise Cemetery in Paris and later transferred to the Panthéon in Paris.

A statue portraying him was erected in Beaune in 1849. Monge's name is one of the 72 names inscribed on the base of the Eiffel Tower.

Since 4 November 1992 the Marine Nationale operate the MRIS FS Monge, named after him.


Between 1770 and 1790 Monge contributed various papers on mathematics and physics to the Memoirs of the Academy of Turin, the Mémoires des savantes étrangers of the Academy of Paris, the Mémoires of the same Academy, and the Annales de chimie, including Sur la théorie des déblais et des remblais" (Mém. de l’acad. de Paris, 1781),[4] which is an elegant investigation of the problem with earthworks referred to in the title and establishes in connection with it his capital discovery of the curves of curvature of a surface.[4] It is also noteworthy to mention that in his Mémoire sur quelques phénomènes de la vision Monge proposed an early implicit explanation of the color constancy phenomenon based on several known observations.

Leonhard Euler, in his 1760 paper on curvature in the Berlin Memoirs, had considered, not the normals of the surface, but the normals of the plane sections through a particular normal, so that the question of the intersection of successive normals of the surface had never presented itself to him.[4] Monge's paper gives the ordinary differential equation of the curves of curvature, and establishes the general theory in a very satisfactory manner; the application to the interesting particular case of the ellipsoid was first made by him in a later paper in 1795.[4]

Monge's 1781 memoir is also the earliest known anticipation of Linear Programming type of problems, in particular of the transportation problem. Related to that, the Monge soil-transport problem leads to a weak-topology definition of a distance between distributions rediscovered many times since by such as L. V. Kantorovich, P. Levy, L. N. Wasserstein, and others; and bearing their names in various combinations in various contexts.

Another of his papers in the volume for 1783 relates to the production of water by the combustion of hydrogen. Monge's results had been anticipated by Henry Cavendish.[4]

Selected publications

See also


  1. ^ a b Sooyoung Chang, Academic Genealogy of Mathematicians, World Scientific, 2010, p. 93.
  2. ^ "Registres paroissiaux et/ou d'état civil : 16 janvier 1745 - 1746" [Parish and/or civil registers: January 16, 1745 - 1746] (in French). Archives of the Department of Côte-d'Or. p. 174/281. FRAD021EC 57/044. Retrieved 8 May 2018.
  3. ^ "Monfredy (1845) to Mongé (1831)", Fichiers de l'état civil reconstitué [Reconstituted files of civil status] (in French), Paris Archives, p. 44/51, V3E/D 1076, retrieved 8 May 2018
  4. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa Wikisource Arthur Cayley (1911). "Monge, Gaspard" . In Chisholm, Hugh. Encyclopædia Britannica. 18 (11th ed.). Cambridge University Press. pp. 709–710.
  5. ^ O'Connor, John J.; Robertson, Edmund F., "Gaspard Monge", MacTutor History of Mathematics archive, University of St Andrews.
  6. ^ a b c J.J., O'Connor and; Robertson, E.F. "Gaspard Monge". School of Mathematics and Statistics, University of St Andrews, Scotland. Retrieved 26 March 2012.
  7. ^ Rolt, L.T.C. (1957), Isambard Kingdom Brunel: A Biography, Longmans Green, LCCN 57003475.
  8. ^ "Napoleon replies: "How comes it, then, that Laplace was an atheist? At the Institute neither he nor Monge, nor Berthollet, nor Lagrange believed in God. But they did not like to say so." Baron Gaspard Gourgaud, Talks of Napoleon at St. Helena with General Baron Gourgaud (1904), page 274.
  9. ^ Vincent Cronin (1983). The view from planet Earth: man looks at the cosmos. Quill. p. 164. ISBN 9780688014797. Yet, sailing to Egypt, he had lain on deck, asking his scientists whether the planets were inhabited, how old the Earth was, and whether it would perish by fire or by flood. Many, like his friend Gaspard Monge, the first man to liquefy a gas, were atheists.
  10. ^'Aquin%22%20monge&f=false

External links

Media related to Gaspard Monge at Wikimedia Commons

Political offices
Preceded by
François Joseph de Gratet, vicomte Dubouchage
Minister of the Navy and the Colonies
10 August 1792 – 10 April 1793
Succeeded by
Jean Dalbarade
1818 in France

Events from the year 1818 in France.

Antonio Onofri

Antonio Onofri (born 1759, died February 26, 1825 ) was a politician and diplomat of San Marino, a key figure in the country's political scene in the first half of the nineteenth century, and his "prudence and patriotism" during this challenging period in the Republic's history earned him a statue in the Public Council Hall and the description "the Father of his country".He came from an old family that had a great influence on the fate of the Republic for centuries. He received a thorough education in philosophy and law. In 1787 he was appointed as secretary of state, and in 1789 he was elected a member of the Grand and General Council. During his long career, he also served as Captain Regent seven times.

Onofri's accomplishments are linked in particular to foreign policy, whose skillful creation led to the recognition of San Marino by other European countries. In 1797, when Napoleon Bonaparte was camped at nearby Pesaro, the proposal to increase the territory of the Republic offered by the general's envoy Gaspard Monge was graciously rejected by Onofri on behalf of the Republic. However, he accepted 15,000 quintals of wheat and the promise of four pieces of artillery, the latter of which seems never to have been delivered. Onofri insisted that it was San Marino's experience that their greatest safeguard was not coveting their neighbours' territory. This prudent move (justified by Onofri thus: "wars end, but neighbours remain") is speculated to have saved the Republic from repercussions upon the later defeat of Napoleon.In 1798 he signed a treaty on trade and friendly relations with the Republic of Rome, and several months later also with the Cisalpine Republic. A similar agreement was also reached with the Italian Republic, which took the place of the two previously mentioned, in June 1802.

On May 26, 1805, again as Captain Regent, he attended the coronation of Napoleon Bonaparte as the King of Italy in Milan, where he received an "amiable audience" with the now-Emperor.After the Congress of Vienna, Onofri helped establish good relations with Louis XVIII, Charles X and Louis Philippe, as well as negotiating the country's way into the favour of Pope Leo XII, who after an audience with Onofri wrote a

letter to the Captains Regent, "assuring them of his friendship and renewing the ancient conventions with them".In 2005, the 180th anniversary of Onofri's death was marked by a special commemorative silver €5 coin.

Clebsch representation

In physics and mathematics, the Clebsch representation of an arbitrary three-dimensional vector field is:

where the scalar fields and are known as Clebsch potentials or Monge potentials, named after Alfred Clebsch (1833–1872) and Gaspard Monge (1746–1818), and is the gradient operator.

Descriptive geometry

Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art. The theoretical basis for descriptive geometry is provided by planar geometric projections. The earliest known publication on the technique was "Underweysung der Messung mit dem Zirckel und Richtscheyt", published in Linien, Nuremberg: 1525, by Albrecht Dürer. Gaspard Monge is usually considered the "father of descriptive geometry" due to his developments in geometric problem solving. His first discoveries were in 1765 while he was working as a draftsman for military fortifications, although his findings were published later on.Monge's protocols allow an imaginary object to be drawn in such a way that it may be modeled in three dimensions. All geometric aspects of the imaginary object are accounted for in true size/to-scale and shape, and can be imaged as seen from any position in space. All images are represented on a two-dimensional surface.

Descriptive geometry uses the image-creating technique of imaginary, parallel projectors emanating from an imaginary object and intersecting an imaginary plane of projection at right angles. The cumulative points of intersections create the desired image.

François Jouffroy

François Jouffroy (1 February 1806 – 25 June 1882) was a French sculptor.

French ship Monge

Monge (A601), named after the 18th century mathematician Gaspard Monge, is a Missile Range Instrumentation Ship of the French Navy dedicated to tracking and measuring rocket trajectories. She was built for the trials of the Submarine-launched ballistic missiles of the Navy, and is also used to monitor the launch of Ariane rockets. Monge is one of the few ships in the world to have this capacity.

Gaspard Monge's mausoleum

Gaspard Monge, whose remains are deposited in the burying ground in Père Lachaise Cemetery, at Paris, in a magnificent mausoleum, was professor of geometry in the École polytechnique at Paris, and with Denon accompanied Napoleon Bonaparte on his memorable expedition to Egypt; one to make drawings of the architectural antiquities and sculpture, and the other the geographical delineations of that ancient country. He returned to Paris, where he assisted Denon in the publication of his antiquities. At his decease the pupils of the Polytechnique School erected this mausoleum to his memory, as a testimony of their esteem, after a design made by his friend, Monsieur Denon. The mausoleum is of Egyptian architecture, with which Denon had become familiarly acquainted.

History of European research universities

European research universities date from the founding of the University of Bologna in 1088 or the University of Paris (c. 1150–70). In the 19th and 20th centuries, European universities concentrated upon science and research, their structures and philosophies having shaped the contemporary university. The original medieval universities arose from the Roman Catholic Church schools that became “the university." Their purposes included training professionals, scientific investigation, improving society, and teaching critical thinking and research. External influences, such as Renaissance humanism (c. mid-14th century), the Age of Enlightenment (18th century), the Protestant Reformation (1517), political revolution, and the discovery of the New World (1492) added human rights and international law to the university curricula.

By the 18th century, universities published academic journals; by the 19th century, the German and the French university models were established. The French established the Ecole Polytechnique in 1794 by the mathematician Gaspard Monge during the French Revolution, and it became a military academy under Napoleon I in 1804. The German university — the Humboldtian model — established by Wilhelm von Humboldt was based upon Friedrich Schleiermacher’s liberal ideas about the importance of freedom, seminars, and laboratories, which, like the French university model, involved strict discipline and control of every aspect of the university. In the 19th and 20th centuries, the universities concentrated upon science, but were not open to the general populace until after 1914. Moreover, until the 19th century’s end, religion exerted a significant, limiting influence upon academic curricula and research, by when the German university model had become the world standard. Elsewhere, the British also had established universities world-wide, thus making higher education available to the world’s populaces.


IGM may refer to:

Initiative on Global Markets, at the University of Chicago Booth School of Business

IG Metall, German metalworkers' union

IGM Financial, Canada

Institut Gaspard Monge, at the University of Marne la Vallée

International Grandmaster, a chess title

Intergalactic medium

Intragroup medium

Kingman Airport (Arizona) (IATA Code: IGM)

Istituto Geografico Militare, Italian national mapping agency

Institut Gaspard Monge

The Gaspard Monge Institute of electronics and computer science is the research and teaching body of the University of Marne la Vallée in the fields of computer science, electronics, telecommunications and networks. It is named for Gaspard Monge.

The Institute is composed of four branches:

The Computing research laboratoryThe fields in which the Institute carries out its research are: text algorithms, combinatorial mathematics, computer science applied to linguistics, image synthesis, networks, signal and communications.

The postgraduate degree for Fundamental Computer Science can also be prepared within the framework of the laboratory.

The laboratory of communication systemsThis laboratory carries out research in the following fields: electromagnetism, applications and measures, numericals, radio communications, microsystems and microtechnologies, photonics and microwaves.

The postgraduate degree in Electronics and Telecommunications can be prepared within the framework of the laboratory.

The computer science training unitThe teachings of this University department lead to the bachelor's degree in mathematics and computer science and the postgraduate degree in computer science

The electronics training unitThe degrees that are prepared within this unit are the bachelor's degree in material science and the postgraduate degree in electronics and telecommunications

List of École Polytechnique faculty

This list of École Polytechnique faculty includes current and former professors of École Polytechnique, a French scientific higher education institution established during the French Revolution in 1794 in Paris and moved to Palaiseau in 1976. In 2007, École Polytechnique became a founding member of the ParisTech group of leading Paris-area engineering schools.

Monge's theorem

In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is completely inside one of the others, the intersection points of each of the three pairs of external tangent lines are collinear.

For any two circles in a plane, an external tangent is a line that is tangent to both circles but does not pass between them. There are two such external tangent lines for any two circles. Each such pair has a unique intersection point in the extended Euclidean plane. Monge's theorem states that the three such points given by the three pairs of circles always lie in a straight line. In the case of two of the circles being of equal size, the two external tangent lines are parallel. In this case Monge's theorem asserts that the other two intersection points must lie on a line parallel to those two external tangents. In other words, if the two external tangents are considered to intersect at the point at infinity, then the other two intersection points must be on a line passing through the same point at infinity, so the line between them takes the same angle as the external tangent.

Monge (crater)

Monge is a lunar impact crater that lies along the southwestern edge of the Mare Fecunditatis. It was named after French mathematician Gaspard Monge. The outer rim is somewhat irregular in shape, with an outward bulge to the east and smaller bulges to the north and northwest. The interior floor is somewhat irregular in the eastern half, and there are accumulations along the bases of the sloping interior walls. The nearest named crater is Cook to the northeast, while the larger Santbech is located to the west-southwest.

Monge Island

Monge Island is a small rocky island off the coast of Antarctica, lying immediately south of La Conchée and 0.9 kilometres (0.5 nmi) northeast of Cape Mousse. It was charted in 1951 by the French Antarctic Expedition and named after French mathematician Gaspard Monge.

Monge array

In mathematics applied to computer science, Monge arrays, or Monge matrices, are mathematical objects named for their discoverer, the French mathematician Gaspard Monge.

An m-by-n matrix is said to be a Monge array if, for all such that

one obtains

So for any two rows and two columns of a Monge array (a 2 × 2 sub-matrix) the four elements at the intersection points have the property that the sum of the upper-left and lower right elements (across the main diagonal) is less than or equal to the sum of the lower-left and upper-right elements (across the antidiagonal).

This matrix is a Monge array:

For example, take the intersection of rows 2 and 4 with columns 1 and 5. The four elements are:

17 + 7 = 24
23 + 11 = 34

The sum of the upper-left and lower right elements is less than or equal to the sum of the lower-left and upper-right elements.

Monge cone

In the mathematical theory of partial differential equations (PDE), the Monge cone is a geometrical object associated with a first-order equation. It is named for Gaspard Monge. In two dimensions, let

be a PDE for an unknown real-valued function u in two variables x and y. Assume that this PDE is non-degenerate in the sense that and are not both zero in the domain of definition. Fix a point (x0, y0, z0) and consider solution functions u which have

Each solution to (1) satisfying (2) determines the tangent plane to the graph

through the point (x0,y0,z0). As the pair (ux, uy) solving (1) varies, the tangent planes envelope a cone in R3 with vertex at (x0,y0,z0), called the Monge cone. When F is quasilinear, the Monge cone degenerates to a single line called the Monge axis. Otherwise, the Monge cone is a proper cone since a nontrivial and non-coaxial one-parameter family of planes through a fixed point envelopes a cone. Explicitly, the original partial differential equation gives rise to a scalar-valued function on the cotangent bundle of R3, defined at a point (x,y,z) by

Vanishing of F determines a curve in the projective plane with homogeneous coordinates (a:b:c). The dual curve is a curve in the projective tangent space at the point, and the affine cone over this curve is the Monge cone. The cone may have multiple branches, each one an affine cone over a simple closed curve in the projective tangent space.

As the base point (x0,y0,z0) varies, the cone also varies. Thus the Monge cone is a cone field on R3. Finding solutions of (1) can thus be interpreted as finding a surface which is everywhere tangent to the Monge cone at the point. This is the method of characteristics.

The technique generalizes to scalar first-order partial differential equations in n spatial variables; namely,

Through each point , the Monge cone (or axis in the quasilinear case) is the envelope of solutions of the PDE with .

Monge–Ampère equation

In mathematics, a (real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function u of two variables x,y is of Monge–Ampère type if it is linear in the determinant of the Hessian matrix of u and in the second-order partial derivatives of u. The independent variables (x,y) vary over a given domain D of R2. The term also applies to analogous equations with n independent variables. The most complete results so far have been obtained when the equation is elliptic.

Monge–Ampère equations frequently arise in differential geometry, for example, in the Weyl and Minkowski problems in differential geometry of surfaces. They were first studied by Gaspard Monge in 1784 and later by André-Marie Ampère in 1820. Important results in the theory of Monge–Ampère equations have been obtained by Sergei Bernstein, Aleksei Pogorelov, Charles Fefferman, and Louis Nirenberg.

Place Monge (Paris Métro)

Place Monge is a station of the Paris Métro, opened on 15 February 1930 as part of a planned section of line Line 7, which was temporarily operated as part of Line 10 until the completion of the under-Seine crossing of line 7 from Pont de Sully to Place Monge. The station was integrated into line 7 on 26 April 1931. It is named after the street of Place Monge, named after Gaspard Monge (1746–1818), a French mathematician and inventor of descriptive geometry.

The station is located under Place Monge, in the 5th arrondissement, in the eastern part of the Latin Quarter. Nearby are the Jardin des Plantes (botanical garden), the Roman remains of the Arènes de Lutèce and the Rue Mouffetard, a street with restaurants and a lively street market.

Transportation theory (mathematics)

In mathematics and economics, transportation theory or transport theory is a name given to the study of optimal transportation and allocation of resources. The problem was formalized by the French mathematician Gaspard Monge in 1781.In the 1920s A.N. Tolstoi was one of the first to study the transportation problem mathematically. In 1930, in the collection Transportation Planning Volume I for the National Commissariat of Transportation of the Soviet Union, he published a paper "Methods of Finding the Minimal Kilometrage in Cargo-transportation in space".Major advances were made in the field during World War II by the Soviet mathematician and economist Leonid Kantorovich. Consequently, the problem as it is stated is sometimes known as the Monge–Kantorovich transportation problem. The linear programming formulation of the transportation problem is also known as the Hitchcock–Koopmans transportation problem.

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