Henri Poincaré and the Disc Model of non-Euclidean Geometry

Abstract

Jules Henri Poincaré was born at Nancy, a town in Lorraine in the East of France, on 29 April 1854. His father was professor of medicine at the university there, his mother, a very active and intelligent women, consistently encouraged him intellectually, and his childhood seems to have been very happy, at least until the war intervened. The town was surrendered to the Germans as part of the settlement of the Franco-Prussian war 1870—1871, and Poincaré remembered seeing German troops occupying it. This may have been one reason for his choosing the military school, the École Polytechnique, over the increasingly popular civilian École Normale, when the time came. As a child he did not at first show an exceptional aptitude for mathematics, but towards the end of his school career his brilliance became apparent, and he entered the École Polytechnique at the top of his class. Even then he displayed what were to be life-long characteristics: a capacity to immerse himself completely in abstract thought, seldom bothering to resort to pen and paper, a great clarity of ideas, a dislike for taking notes so that he gave the impression of taking ideas in directly, and a perfect memory for details of all kinds. When asked to solved a problem he could reply, it was said, with the swiftness of an arrow. He had a slight stoop, he could not draw at all, which was a problem more for his examiners than for him, and he was totally incompetent in physical exercises.