=1922.= It seems to be expected of every pilgrim up the slopes of the mathematical Parnassus, that he will at some point or other of his journey sit down and invent a definite integral or two towards the increase of the common stock.--SYLVESTER, J. J. _Notes to the Meditation on Poncelet’s Theorem; Mathematical Papers, Vol. 2, p. 214._ =1923.= The experimental verification of a theory concerning any natural phenomenon generally rests on the result of an integration.--MELLOR, J. W. _Higher Mathematics for Students of Chemistry and Physics (New York, 1902), p. 150._ =1924.= Among all the mathematical disciplines the theory of differential equations is the most important.... It furnishes the explanation of all those elementary manifestations of nature which involve time....--LIE, SOPHUS. _Leipziger Berichte, 47 (1895); Math.-phys. Classe, p. 262._ =1925.= If the mathematical expression of our ideas leads to equations which cannot be integrated, the working hypothesis will either have to be verified some other way, or else relegated to the great repository of unverified speculations.--MELLOR, J. W. _Higher Mathematics for Students of Chemistry and Physics (New York, 1902), p. 157._ =1926.= It is well known that the central problem of the whole of modern mathematics is the study of the transcendental functions defined by differential equations.--KLEIN, F. _Lectures on Mathematics (New York, 1911), p. 8._ =1927.= Every one knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.... A curve is the totality of points, whose co-ordinates are functions of a parameter which may be differentiated as often as may be required.--KLEIN, F. _Elementar Mathematik vom höheren Standpunkte aus. (Leipzig. 1909) Vol. 2, p. 354._ =1928.= Fourier’s theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics. To mention only sonorous vibrations, the propagation of electric signals along telegraph wires, and the conduction of heat by the earth’s crust, as subjects in their generality intractable without it, is to give but a feeble idea of its importance.--THOMSON AND TAIT. _Elements of Natural Philosophy, chap. 1._