Jean-Victor Poncelet was one of the founders of projective geometry. He was born on July 1, 1788, in Metz, France, and grew up to become an officer in Napoleon's army. As a lieutenant of engineers in 1812, he was badly wounded during the Russian campaign and left behind at Krasnoy, where he was thought to be dead. Instead, he was taken prisoner and remained at a camp in Saratov until 1814, when he returned to France. During his two years in prison, Poncelet busied himself with an intensive study of projective geometry—a facet of mathematics dealing with relationships between geometric figures and the projected images (or mappings).
Poncelet went on to study military engineering at Metz (1815-25) and soon became a professor of mechanics at the Ecole d'Application there (1825-35). In 1826, by applying mathematics to working functions of turbines and water wheels, he proposed a design for the first inward-flow turbine, which was not actually built until 1838. In that year, Poncelet became a professor to the faculty of sciences in Paris and held this post for the next 10 years, when he was appointed commandant of the Ecole Polytechnique with the rank of General.
Prior to Poncelet's remarkable theories, there had been only two momentous geometrical developments. They had taken place during the Greek period and at the end of the eighteenth century. Both concerned the eventual subject of projective geometry. One was a theorem discovered and proved by Gerard Desargues (a French mathematician) in 1639; the second was a significant broadening of an earlier theorem (credited to Pappus of Alexandria in the fourth century) by Desargues's countryman, Blaise Pascal, in 1640.
Poncelet's years of study led to his personal belief that geometry could be founded on a series of fundamental principles as general as those on which algebra was based. He carried this belief forward by suggesting that since every straight line and plane extend to a point of infinity, then any new points on a line would be the same for specific parallel lines (or planes). At this time in mathematical history, it was accepted that all infinite elements of space were supposed to lie on the infinite plane of space, known as the projective plane.
Early on, Poncelet's colleagues were extremely reluctant to accept his ideas and resulting theories. However, as time went on, several prominent German mathematicians not only accepted them but contributed to the emerging new science. Among those who recognized Poncelet's breakthrough in the field were Karl Georg Christian von Staudt, Felix Klein, Georg Cantor, Richard Dedekind, and Moritz Pasch. They were later joined by Otto Stolz of Austria who made his own contributions to the field.
In spite of these isolated encouragements, Poncelet finally decided that he could be more effective in his chosen field by returning to his original work and applying mathematics to the design of machines and other technology.
He died on December 22, 1867, in Paris without the recognition he deserved for his brilliant contributions to the world of numbers. His Treatise on the Projective Properties of Figures (1822) is still regarded as the pioneer work in the field.