to counter the effects of the absence of Catholic university education in France. These activities did not make Cauchy popular with his colleagues, who, on the whole, supported the Enlightenment ideals of the French Revolution. When a chair of mathematics became vacant at the Collège de France in 1843, Cauchy applied for it, but received just three of 45 votes. The year 1848 was the year of revolution all over Europe; revolutions broke out in numerous countries, beginning in France. King Louis-Philippe, fearful of sharing the fate of Louis XVI, fled to England. The oath of allegiance was abolished, and the road to an academic appointment was finally clear for Cauchy. On March 1, 1849, he was reinstated at the Faculté de Sciences, as a professor of mathematical astronomy. After political turmoil all through 1848, France chose to become a Republic, under the Presidency of Louis Napoleon Bonaparte, nephew of Napoleon Bonaparte and son of Napoleon's brother, who had been installed as the first king of Holland. Soon (early 1852) the President made himself Emperor of France, and took the name Napoleon III. Not unexpectedly, the idea came up in bureaucratic circles that it would be useful to again require a loyalty oath from all state functionaries, including university professors. This time a cabinet minister was able to convince the Emperor to exempt Cauchy from the oath. Cauchy remained a professor at the university until his death at the age of 67. He received the Last Rites and died of a bronchial condition at 4 a.m. on 23 May 1857. His name is one of the 72 names inscribed on the Eiffel Tower. Work Early work The genius of Cauchy was illustrated in his simple solution of the problem of Apollonius—describing a circle touching three given circles—which he discovered in 1805, his generalization of Euler's formula on polyhedra in 1811, and in several other elegant problems. More important is his memoir on wave propagation, which obtained the Grand Prix of the French Academy of Sciences in 1816. Cauchy's writings covered notable topics. In the theory of series he developed the notion of convergence and discovered many of the basic formulas for q-series. In the theory of numbers and complex quantities, he was the first to define complex numbers as pairs of real numbers. He also wrote on the theory of groups and substitutions, the theory of functions, differential equations and