One of the enduring legacies of Napoleon was the French system of grandes écoles, the elite schools that train the country's top technocratic and managerial students even today. ... Biographies of French mathematicians often begin with awed accounts of how well they did on the entrance tests, and how they fared on various national exams and competitions. Poincaré was no exception. He obtained the first prize in several national competitions, and was among the highest-ranking applicants to the École Polytechnique and the École Normale Supérieure in Paris, schools especially famous for the quality of their mathematics.