Considered the founder of descriptive and differential geometry, Gaspard Monge was one of the most famous mathematicians of his day and renowned for his application of geometry to problems of construction. A man of many interests, Monge also worked in chemistry and physics, as well as education, training a generation of mathematicians and paving the way for the extension of his theories to projective geometry. A fervent republican, Monge was a supporter of the French Revolution, and was for a time minister of the navy. He helped to establish the metric systemand was a founder of the École Polytechnique, which he directed in its early years. Made a count in 1808, Monge is sometimes known as Comte de Peluse. His major work, Geometrie descriptive, leads directly to the methods employed in modern mechanical drawing known as orthographic projection.
Monge was born on May 9, 1746, in Beaune, France, to Jacques Monge and Jeanne Rousseaux. The elder Monge was a knife grinder and peddler with a belief in the power of education. Young Monge was considered the genius of the family and excelled at the college of the Orations in Beaune which he attended until 1762. From 1762 to 1764, he attended college in Lyons where, at age 16, he was made a physics instructor. On vacation in Beaune in 1762, Monge spent his free time by completing a map of the town, developing both the means of such large scale projection as well as the surveying equipment necessary for its completion. This work caught the eye of an officer of engineers who recommended Monge for a place at the military school at Mezieres, even though as the son of a commoner, he would never be eligible for an officer's commission.
Monge made an early name for himself by devising a plan for gun emplacements in a proposed fortress. He managed to substitute a geometrical process for such a calculation, avoiding the cumbersome arithmetic techniques then in use, and it was this breakthrough which in part led to his contributions in descriptive geometry. Initially, Monge's plan was ignored, as the officer in charge felt there was some trickery involved, though when finally his plan was examined, it was found to be of such value that he was pledged to secrecy. For the next fifteen years, Monge's method of descriptive geometry--representing three-dimensional objects in two dimensions--was kept under wraps as a military secret. Monge was made a professor at the École Royale du Genie in Mezieres, and from 1768 to 1783 taught both physics and mathematics, developing the field of geometry in service to the solution of construction and mechanical problems: everything from fortifications to scaffolding and general architecture.
Monge married Catherine Huart in 1777, and the couple eventually had three daughters. With his election to the French Académie Royale des Sciences in 1780, he began to spend more time in Paris, dividing his time between the capital city and Mezieres. He participated in research of sponsored by the Académie and presented several papers there. In 1783, Monge was named examiner of naval cadets, a position which made it impossible for him to continue his professorship in Mezieres. For the next nine years he was busy with tours of inspection of the naval schools and his academic duties in Paris. The most fruitful years of research were behind him.
At the outbreak of revolution in 1789, Monge was one of the best known French scientists. His support of the Revolution, however, was kept relatively quiet until 1792 with his membership in several revolutionary clubs. With the fall of the monarchy and the takeover of the Legislative Assembly, Monge was appointed minister of the navy, a position he held for a scant eight months. His politics were considered too moderate for the men in charge, and thereafter Monge's political activity was at a minimum. He did, however, continue to work for the democratic goals of the Revolution, even after the suppression of the Académie in 1793. Working with the Temporary Commission on Weights and Measures, Monge helped to develop the metric system. Lecturing at the École Normale in Paris in 1794, he was first allowed to teach his methods of descriptive geometry in public. Heeding an appeal for scientific men to come to the aid of French industry in support the war effort, Monge even supervised foundries and wrote a factory handbook. Important for the future course of mathematics, Monge was influential in preparing the way for the École Polytechnique, which opened in 1795. His lectures in infinitesimal geometry held there were eventually printed first as Feuilles d'analyse appliquee a la geometrie, and later as Application de l'analyse a la geometrie.This text established the algebraic principles of three-dimensional geometry and helped to revolutionize engineering design.
In 1796, Monge left for what would be a protracted absence from France, first on a mission to Italy, and thereafter in service to Napoleon Bonaparte in Egypt, where he was assigned various technical and scientific tasks, including the establishment of the Institut d'Egypt in Cairo. With the defeat of Napoleon by the British fleet, Monge escaped back to France. During these years, he had continued his analytical researches, adding chapters to his Application de l'analyse a la geometrie, making it in effect a textbook of differential geometry with his introduction of the idea of lines of curvature in space.
Back in Paris, Monge resumed his duties at the École Polytechnique, and with the advent of the new century, honors and awards started coming his way. He was named a grand officer of the Legion of Honor in 1804, president of the Senate in 1806, and made a count in 1808. His duties as a senator accordingly took away from his work at the École Polytechnique, yet he was still able to see his monumental Application de l'analyse a la geometrie published in 1807. With the ultimate defeat of Napoleon and his abdication, Monge fled France for a time. Stripped of his honors and professional position by the restored Bourbon monarchy, Monge returned to Paris in 1816, and lived out the last two years of his life reviled by many for his part in the Bonaparte regime. At his death in 1818, and despite government censure, many in the scientific community, both his students and colleagues, paid Monge respect by defying a government ban and placing a wreath on his grave the day after his funeral.
Monge is remembered primarily for his development of descriptive geometry, which he developed from 1766 to 1775, and its practical applications in the fields of construction and architecture. Though much of this was a codification of what others had done before, Monge made a system of such projective techniques. Such techniques paved the path ultimately for the development of projective geometry. Monge also pioneered techniques in analytic and infinitesimal geometry, a particular favorite of his, researching the properties of surfaces and of space curves. In particular, Monge is known for the application of the calculus to the examination of the curvature of surfaces. Additionally, Monge made important progress in the field of differential equations.
Less well known is Monge's work in mechanics, chemistry, and technology. In addition to books on the theory of machines, Monge also worked in caloric theory, acoustics, and optics. Perhaps his most famous work in chemistry dealt with the composition of water. In all, Monge's accomplishments in mathematical research and technology have won him a lasting position in the canon of mathematical greats. He was, as E. T. Bell described him in Men of Mathematics, "a born geometer and engineer with an unsurpassed gift for visualizing complicated space-relations."
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