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I it is safe to trace back to any single man the origin of those conceptions with which pure mathematical analysis has been chiefly occupied during the nineteenth century and up to the present time, we must, I think, trace it back to Jean Baptiste Joseph Fourier (1768- 1830). Fourier was first and foremost a physicist, and he expressed very definitely his view that mathematics only justifies itself by the help it gives towards the solution of physical problems, and yet the light that was thrown on the general conception of a function and its "continuity," of the "convergence" of infinite series, and of an integral, first began to shine as a result of Fourier's original and bold treatment of the problems of the conduction of heat. This it was that gave the impetus to the formation and development of the theories of functions. The broadminded physicist will approve of this refining Rh