 In 1871 Poincaré passed the exams in letters with the grade “good” and that in science with the grade “fair.” He received a zero in mathematics for answering a different question from the one that was asked, apparently having misunderstood the question. He then took the preparatory classes in mathematics and was first in his class, also first in the academic competition and first in the national competition (concours général) in elementary mathematics. In Paris, he entered the École Polytechnique in 1873 and after graduating in 1875 (second in his class having apparently lost points for his inability to draw), entered the École des Mines. An extensive correspondence with his mother has been preserved from this period of study in Paris (Rollet 2017). After brief service as a mine inspector, he submitted a dissertation on partial differential equations and was then hired to teach the course on differential and integral calculus at the University of Caen. In 1880 he submitted a paper solving a problem in the theory of differential equations to the competition for the grand prize in mathematics of the Academy of Sciences in Paris. For the first time he made use of non-Euclidean geometry, which was seen by most of his contemporaries as purely speculative.