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131 Chapter 7 } Hadamard, Hardy, Noether, and Ramanujan Jacques Hadamard Jacques Hadamard was born in Versailles, southwest of Paris, on 8 December 1865. Most of his forebears on both sides were intellectuals of Jewish extraction, and had been based in Paris since 1808. Hadamard’s father taught Latin at the Lycée Charlemagne, and his mother was a noted music teacher who taught her son to play the violin at an early age. In 1871, returning from exile at the end of the Paris Commune, they found that their house had been burned down and they had lost all their possessions. After recovering from this setback, they sent their son to the lycée where his father taught; he shone in every subject except mathematics, which he did not care for. Although he won prizes in other subjects in the national Concours Généraux, at first he showed no mathematical ability whatsoever. In 1875, when his father was transferred to the more prestigious Lycée Louisle -Grand, the young Jacques followed him there and experienced mathematics teaching of high quality. When he took the Concours Général in mathematics again, he placed second in the whole of France: throughout his life he felt ashamed of his failure to take first place. He then sat the entrance examinations for the École Polytechnique and the École Normale Supérieure. In 1884, at the age of 18, Hadamard came first, in the whole of France, in both examinations. He chose the Normale. After graduating in 1888, Hadamard spent a further year studying in Paris, supported by a sinecure teaching post at Caen. He then taught for three years at the Lycée Bu√on, where he was not a success. ‘‘M. Hadamard believes himself exempted from everything because of his remarkable 132 Twenty Mathematical Personalities mathematical abilities,’’ reported the headmaster to the minister of education . After five years on the faculty of the University of Bordeaux, he returned to Paris as lecturer at the Sorbonne and deputy professor at the Collège de France, and from then on Hadamard’s career was one of unbroken success. By 1912 he was also professor of analysis at the École Polytechnique . When the Academy announced a prize competition, it was often Hadamard that won it. The death of Poincaré left a vacancy at the Paris Academy to which Hadamard, who had been candidate several times previously, was finally elected at the age of 47. He was one of Poincaré’s greatest admirers; when Poincaré died Hadamard put everything else aside to write on the life and work of the friend and colleague he described as the supreme genius. Hadamard married a childhood sweetheart with a similar background to his own. She was a vivacious young woman named Louise who shared his love of music. They had five children: Pierre in 1894, Etienne in 1897, Mathieu in 1899, Cecile in 1901, and Jacqueline in 1902. Jacques and Louise made sure all of the children learned to play at least one musical instrument. Hadamard mainly worked at home. His daughter Jacqueline gave a picture of her father at work: He practically never wrote a word. He always told me that he thought without words, and that for him the greatest di≈culty was to translate his thoughts into words. He only scribbled down equations, not at a table but at a high wooden plinth of the kind that were normally used at that time to put a bust on (at my grandmother’s it was a bust of Beethoven, of course). In the hall he would write down his mathematical formulas while walking up and down and for many years I used to hear my mother taking down dictated sentences of the kind ‘‘we integrate-poum we see that the equation-poum-poum-poum’’ (the number of poums indicated the length of the space to be left for the formulas). The Hadamards kept open house for guests. The years before the First World War were an exceptionally happy time for Jacques: new theorems, lectures, a loving wife and children, friends, and a comfortable house filled with the sound of music. At one stage the Hadamards, in collaboration with some other like-minded academics, educated their children at home. Later the sons attended their father’s old school, the Lycée Louis-le-Grand. Pierre, the eldest, had just been accepted for the École Polytechnique when the war came, while Etienne, the second eldest, was accepted for...

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