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Just after the discovery of infinitesmal calculus, physicists began by needing only very simple methods of integration, the problems in general reducing to elementary differential equations. But when higher partial differential equations were introduced, the corresponding problems almost immediatelly proved to be far above the level of those which contemporary mathematics could treat.

— Jacques Hadamard Four lectures on mathematics, delivered at Columbia University in 1911 (1915)

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In the case of partial differential equations employed in connection with physical problems, their use must be given up in most circumstances, for two reasons: first, it is in general impossible to get the general solution or general integral, and second, it is in general of no use even when it is obtained.

Four lectures on mathematics, delivered at Columbia University in 1911 (1915)

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