Gaspard Monge

{{Short description|French mathematician (1746–1818)}} {{redirect|Monge}} {{Use dmy dates|date=May 2021}} {{Infobox scientist | name = Gaspard Monge | image = Gaspard monge litho delpech.jpg | image_size = 220px | caption = | birth_date = {{birth_date|1746|5|9|df=y}} | birth_place = Beaune, Côte-d'Or, Kingdom of France | death_date = {{death date and age|1818|7|28|1746|5|9|df=y}} | death_place = Paris, Kingdom of France | resting_place = Père Lachaise Cemetery | residence = | citizenship = | nationality = | ethnicity = | field = {{hlist|Mathematics|engineering|education}} | work_institutions = | alma_mater = | doctoral_advisor =  | notable_students = Jean-Baptiste Biot<ref name="Chang">Sooyoung Chang, ''Academic Genealogy of Mathematicians'', World Scientific, 2010, p. 93.</ref><br/>Charles Dupin<br/>Sylvestre François Lacroix<br/>Jean-Victor Poncelet<ref name="Chang"/> | known_for = Descriptive geometry<br>Transportation theory | influences = | influenced = | prizes = | footnotes = | signature = Signature de Gaspard Monge.svg }}

'''Gaspard Monge, Comte de Péluse''' ({{IPA|fr|ɡaspaʁ mɔ̃ʒ kɔ̃t də pelyz|lang}}; 9 May 1746<ref>{{cite web |url=http://www.archinoe.net/console/ir_ead_visu.php?eadid=FRAD021_000000912V2&ir=23251 |title=Registres paroissiaux et/ou d'état civil : 16 janvier 1745 – 1746 |trans-title=Parish and/or civil registers: January 16, 1745 – 1746 |publisher=Archives of the Department of Côte-d'Or |id=FRAD021EC 57/044 |page=174/281 |language=fr |access-date=8 May 2018 }}</ref> – 28 July 1818)<ref>{{citation |chapter-url=http://archives.paris.fr/s/5/etat-civil-reconstitue/?&action=1&todo=modif_recherche |title=Fichiers de l'état civil reconstitué |trans-title=Reconstituted files of civil status |chapter=Monfredy (1845) to Mongé (1831) |publisher=Paris Archives |page=44/51 |id=V3E/D 1076 |language=fr |access-date=8 May 2018 }}</ref> was a French mathematician, commonly presented as the inventor of descriptive geometry,<ref>Albrecht Dürer and Guarino Guarini published works establishing the field before Monge.</ref><ref name=EB1911>{{cite EB1911|wstitle=Monge, Gaspard|author=Arthur Cayley|author-link=Arthur Cayley|volume=18|pages=709–710}}</ref> (the mathematical basis of) technical drawing, and the father of differential geometry.<ref name= "MongeStA">{{MacTutor Biography|id=Monge}}</ref>

He contributed alongside chemist Berthollet, chemist and physician Chaptal, and polymath Laplace to the establishment of Arts et Métiers ParisTech.

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, with Lamblardie and Lazare Carnot, the École Polytechnique, France's most prestigious engineering school.

== 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.<ref name="EB1911" /> 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<ref name=EB1911/> at the age of seventeen.<ref name= "StA">{{cite web|url= http://www-history.mcs.st-andrews.ac.uk/Biographies/Monge.html|publisher= School of Mathematics and Statistics, University of St Andrews, Scotland |first1= O'Connor and |last1=J.J. |last2=Robertson |first2=E.F. |title=Gaspard Monge |access-date=26 March 2012 }}</ref>

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.<ref name=EB1911/> 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.<ref name=EB1911/> L. T. C. Rolt, an engineer and historian of technology, credited Monge with the birth of engineering drawing.<ref name="Rolt1957">{{Citation |last=Rolt |first=L.T.C. |author-link=L. T. C. Rolt |year=1957 |title=Isambard Kingdom Brunel: A Biography |publisher=Longmans Green |lccn=57003475 |postscript=.|title-link=Isambard Kingdom Brunel }}</ref> When in the Royal School, he became a member of a Freemasonry, initiated into ″L’Union parfaite″ lodge.<ref>Alain Queruel, Les franc-maçons de l'Expédition d'Egypte (Editions du Cosmogone, 2012). Snezana Lawrence et Mark McCartney, Mathematicians and their Gods : Interactions between mathematics and religious beliefs (OUP Oxford, 2015). Emmanuel Pierrat et Laurent Kupferman, Le Paris des Francs-Maçons (Le Cherche Midi, 2013)</ref>

== Career ==

=== 1764-1818 === Those studying at the officer school were exclusively 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 du Génie. "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."<ref name=EB1911/>

After a year at the École Royale, Monge was asked to produce a ''défilement'' plan for a fortification in such a way as to optimise its defensive arrangement. In military terminology, ''défilement'' is "the science of aligning the summits of fortifications in a vertical plane, so as to evade gunfire from a height outside the fortress".<ref>{{cite book |last=Duffy |first=Christopher |title=Fire and Stone: The Science of Fortress Warfare 1660–1860 |date=2006-01-01 |publisher=Castle |isbn=978-0785821090 |location=London |pages=222 |language=en}}</ref><ref>{{cite book |last=Sakarovitch |first=Joël |title=Épures d’architecture: De la coupe des pierres à la géométrie descriptive XVI – XIX siècles |date=1998-06-16 |publisher=Birkhäuser Basel |isbn=978-3-7643-5701-6 |series=Science Networks. Historical Studies |language=fr |chapter=Chapitre III – La géométrie descriptive : une discipline révolutionnaire Les leçons de l’École normale de l’an III |eissn=2296-6080 |issn=1421-6329}}</ref>

A fort should protect the defenders. That is, from any point on the terrain outside, there cannot be direct line of sight into defending positions inside. This safe space is called the ''defilade'', and could be pictured as follows: Place a lamp at each location where the attacker may fire, then the shadow space cast by the walls is the ''defilade''. The ''défilement'' is a kind of ''defilade'', where the attackers may be raised above the ground. This would protect the defenders against artillery placed on raised platforms built during a siege. ''Defilade'' and ''défilement'' would avoid ''enfilade''.

A particularly dangerous kind of artillery fire is ''enfilade'' fire. The top edge of a fort wall is a polygonal line. On each segment, defenders can move. If an attacker can place an artillery on a point along that straight segment, then the attacker can shoot directly along the line, and hit all the defenders on that line segment.

Computing the ''défilement'' is a complex problem, since to counter the development of artillery, European forts was becoming increasingly complicated in their geometry, as represented by the star fort. The famous military engineer Vauban proposed a slow and manual process to measure the ''défilement''. Soldiers would be sent to strategically critical positions outside the fort. At each position, they would measure the shape of the polygonal line created by the upper edge of the curtain wall. This creates a sequence of triangles that together create a polygonal dome in space. The space under the polygonal dome would then be the ''défilement'' of the walls, within which the defenders are safe from direct lines of sight.<ref>{{Cite journal |last=Carlevaris |first=Laura |date=2014-12-01 |title=Nicolas-François-Antoine de Chastillon: The Défilement of Fortifications at the Roots of Descriptive Geometry |url=https://doi.org/10.1007/s00004-014-0217-5 |journal=Nexus Network Journal |language=en |volume=16 |issue=3 |pages=631–652 |doi=10.1007/s00004-014-0217-5 |issn=1522-4600|hdl=11573/555621 |hdl-access=free }}</ref>

Other than the observational method, there was also an established method for doing this, which involved lengthy calculations that would take a week, but Monge devised a way of solving the problems by using drawings. At first his solution was not accepted, since it had only taken two days, but upon examination the value of the work was recognised, and Monge's exceptional abilities were recognised. The essence of Monge's method was to graphically construct visibility cones. For example, consider a hemisphere ''H'', with a raised point ''p'' above ''H'', representing a point on the fortification wall. The visibility cone at ''p'' is a cone that is tangent to ''H'' and apexed at ''p''. Continuing his researches, Monge began the subject descriptive geometry, which was kept as a French military secret for years.<ref name="EB1911" /><ref>{{Cite journal |last=Lawrence |first=Snežana |date=2011-10-01 |title=Developable Surfaces: Their History and Application |url=https://doi.org/10.1007/s00004-011-0087-z |journal=Nexus Network Journal |language=en |volume=13 |issue=3 |pages=701–714 |doi=10.1007/s00004-011-0087-z |issn=1522-4600}}</ref>

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.<ref name="StA"/>

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 chemist C. L. Berthollet began at this time.<ref name=EB1911/> In 1783, after leaving Mézières, he was, on the death of É. Bézout, appointed examiner of naval candidates.<ref name=EB1911/> 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.<ref name=EB1911/> In 1786 he wrote and published his ''Traité élémentaire de la statique''.<ref name=EB1911/>

===1789-1818=== [[File:Perelachaise-Monge-p1000360.jpg|thumb|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 Navy,<ref name=EB1911/> and held this office from 10 August 1792 to 10 April 1793, when he resigned.<ref name="StA"/> 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''.<ref name=EB1911/>

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.<ref name=EB1911/> ''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'',<ref name=EB1911/> 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.<ref name=EB1911/> While there he became friendly with Napoleon. 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.<ref name=EB1911/>

From there Monge joined Napoleon's expedition to Egypt, taking part with Berthollet<ref name=EB1911/> in the scientific work of the Institut d'Égypte and the Egyptian Institute of Sciences and Arts. They accompanied Napoleon to Egypt, and returned with him in 1799 to France.<ref name=EB1911/> Monge was appointed president of the Egyptian commission, and he resumed his connection with the École Polytechnique.<ref name=EB1911/> 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<ref name=EB1911/> (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.<ref name=EB1911/>

Napoleon Bonaparte stated Monge was an atheist.<ref>"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.</ref><ref>{{cite book|title=The view from planet Earth: man looks at the cosmos|year=1983|publisher=Quill|isbn=9780688014797|page=164|author=Vincent Cronin|quote=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.}}</ref> His remains were first interred in a mausoleum in Le Père Lachaise Cemetery in Paris and later transferred to the Panthéon in Paris.

A [//upload.wikimedia.org/wikipedia/commons/3/35/GaspardMongeStatueBeaune.jpg 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 ''Monge'', named after him.

== Work== 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''" ["On the theory of cut and fill"] (''Mém. de l’acad. de Paris'', 1781),<ref name=EB1911/> 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.<ref name=EB1911/> 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.<ref name=EB1911/> 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.<ref name=EB1911/>

Monge's 1781 memoir is also the earliest known anticipation of linear optimization problems, in particular of the earth-mover's problem, a special case of the optimal 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, Paul Lévy, Leonid Vaseršteĭn, 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.<ref name=EB1911/> It was also in this time, from 1783 - 1784, that Monge worked with (Jean-François, Jean-Baptiste-Paul-Antoine, or Abbé Pierre-Romain) Clouet to liquefy sulfur dioxide by passing a stream of the gas through a U-tube sunken in a refrigerant mixture of ice and salt.<ref>Taton, Rene. “Some Details About The Chemist Clouet and Two of His Namesakes.” Review of the History of Sciences and Their Applications, vol. 5, no. 4, 1952, p. 359–67. {{JSTOR|23905084}}.</ref> This made them the first to liquefy a pure gas.<ref>{{cite web |last=Wisniak |first=Jaime |title=Louis Paul Cailletet—The liquefaction of the permanent gases |date=2003 |url=https://nopr.niscpr.res.in/bitstream/123456789/22723/1/IJCT%2010%282%29%20223-236.pdf }}</ref>

<!-- this section has no references == Students ==

* Charles Julien Brianchon * Jean-Victor Poncelet *Antoine-François Lomet *Barnabé Brisson *Théodore Olivier *Sylvestre François Lacroix *Charles de Tinseau d'Amondans *Théodore Olivier *Charles Dupin *Edme-François Jomard *François Arago *Joseph Fourier *Michel Ange Lancret *Guy de Vernon *Coulomb *Carnot -->

== Selected publications == * 1781: ''[http://gallica.bnf.fr/ark:/12148/bpt6k35800/f796 Mémoire sur la théorie des déblais et des remblais]'' De l'Imprimerie Royale. * 1793: (with Alexandre-Théophile Vandermonde and Claude-Louis Berthollet) ''[https://gallica.bnf.fr/services/engine/search/sru?operation=searchRetrieve&version=1.2&collapsing=disabled&query=dc.relation%20all%20%22cb33253679t%22# Avis aux ouvriers en fer, sur la fabrication de l'acier. Tome 8]'' (Advice to ironworkers, on the manufacture of steel) * 1794: ''[https://gallica.bnf.fr/ark:/12148/bpt6k56990q/f276.image Description de l'art de fabriquer des canons]'' (Description of the art of making cannon) * 1795: ''[https://www.e-rara.ch/zut/doi/10.3931/e-rara-57893 Application d'analyse à la géométrie]'' * 1799: ''[http://gallica.bnf.fr/ark:/12148/bpt6k5783452x Géométrie descriptive. Leçons données aux écoles normales]'' (Descriptive Geometry) * 1807: ''[https://books.google.com/books?id=aSEOAAAAQAAJ Application de l'analyse à la géométrie, à l'usage de l'Ecole impériale polytechnique]''. * 1810: (with Jean Nicolas Pierre Hachette) ''Traité élémentaire de statique, a l'usage des écoles de la Marine'', chez Courcier, Imprimeur-libraire, pour les mathematiques, quai des Augustins, 1852 translation: ''[https://archive.org/details/anelementarytre02monggoog An elementary treatise on statics]''.

==References== {{Reflist|2}}

==External links== *{{commons category-inline}} * {{MacTutor Biography|id=Monge}} * [https://archive.org/details/anelementarytre02monggoog/page/n20  ''An Elementary Treatise on Statics with a Biographical Notice of the Author''] (Biddle, Philadelphia, 1851). * [https://books.google.com/books?id=UjEDAAAAQAAJ ''An elementary treatise on descriptive geometry, with a theory of shadows and of perspective''] (Weale, London, 1851). * [http://gallica.bnf.fr/ark:/12148/bpt6k5783452x.r=%22gaspard+monge%22.langFR ''Géométrie descriptive. Leçons données aux Écoles normales, l'an 3 de la République; Par Gaspard Monge, de l'Institut national''] (Baudouin, Paris, 1798) * [http://digitalcollections.ucsc.edu/cdm/search/collection/p265101coll10/searchterm/Gaspard%20Monge/order/title Portrait of Gaspard Monge from the Lick Observatory Records Digital Archive, UC Santa Cruz Library's Digital Collections] {{Webarchive|url=https://web.archive.org/web/20181106183317/http://digitalcollections.ucsc.edu/cdm/search/collection/p265101coll10/searchterm/Gaspard%20Monge/order/title |date=6 November 2018 }} * Gaspard Monge (1789) [http://lhldigital.lindahall.org/cdm/ref/collection/color/id/17 "Mémoire sur quelques phenomenes de la vision."] {{Webarchive|url=https://web.archive.org/web/20181106180127/http://lhldigital.lindahall.org/cdm/ref/collection/color/id/17 |date=6 November 2018 }} ''Annales de Chimie. Ser. 1, bk. 3'' p. 131–147 – digital facsimile from the Linda Hall Library * {{Cite NIE|wstitle=Monge, Gaspard|short=x}}

{{s-start}} {{s-off}} {{succession box |title=Minister of the Navy and the Colonies |before=François Joseph de Gratet, vicomte Dubouchage |after=Jean Dalbarade |years=10 August 1792 – 10 April 1793 }} {{s-end}}

{{DEFAULTSORT:Monge, Gaspard}} Category:1746 births Category:1818 deaths Category:18th-century French mathematicians Category:19th-century French mathematicians Category:French atheists Category:French Freemasons Category:People from Beaune Category:Commission des Sciences et des Arts members Category:Differential geometers Category:Burials at the Panthéon, Paris Category:Burials at Père Lachaise Cemetery Category:Members of the Sénat conservateur Category:Members of the French Academy of Sciences Category:Ministers of marine and the colonies Category:Academic staff of the École normale supérieure (Paris) Category:18th-century French inventors