president's address — SECTION A. 13 



menta Nova, . . . ), and lean be well satisfied with what he says. 

 But M. Poisson should not have repeated in his report a foolish phrase 

 of the late M. Fourier, where he reproaches us (Abel and me) for not 

 having turned our attention to the flow of heat. It is true that M. 

 Fourier believed that the principal aim of Mathematics was practical 

 utility, and the explanation it could give of natural phenomena. But 

 a philosopher of his standing should have known that the sole end of 

 science is the honour of the human intelligence. And, from this point 

 of view, a problem in the Theory of Numbers is as important as a 

 question arising in Celestial Mechanics." 



Some of the greatest triumphs of Mathematics have no doubt 

 been won in the conquest of nature and the elucidation of her laws. 

 In the discoveries which marked the nineteenth century, and changed 

 the face of the civilized world, the mathematicians were often found 

 among the pioneers. By many people it is from this stand-point that 

 Mathematics is regarded. She is the Servant of the Sciences. A 

 place of honour may be hers ; but it is for service rendered and with 

 the lively expectation of greater benefits in the future. 



" I am not making before you a defence of Mathematics," said 

 Cayley, in his presidential address to the British Association in 1883, 

 "but, if Iwere, Ishould desire to do it in such manner as in the Republic 

 Socrates was required to defend justice — quite irrespective of the 

 worldly advantages which may accompany a life of virtue and justice, 

 and to show that, independently of all these, justice was a thing 

 desirable in itself, and for its own sake ; not by speaking to you of the 

 utility of Mathematics in any of the questions of common life or of 

 physical science. ... I would, on the contrary, rather consider 

 the obligations of Mathematics to these different subjects, as the 

 sources of mathematical theories now as remote from them, and in 

 as different regions of thought — for, instance, Geometry from the 

 measurement of land, or the Theory of Numbers from Arithmetic — as 

 a river at its mouth is from its mountain source." 



And, again, to quote another great Pure Mathematician, Weier- 

 strass : " I am not afraid that I shall be blamed for detracting from 

 the value to which Mathematics as a pure science lays claim, with such 

 perfect right, when I attach special importance to the fact that it is 

 only through Mathematics that a true and satisfactory understanding 

 of natural phenomena can be obtained. Indeed, no one can be readier 

 than I to admit that we must not seek for the end of a science outside 

 itself. Such action not only does not add to its dignity ; it is an ofience 

 against it. Instead of devoting ourselves to it with our whole heart, we 

 desire from it only some service, and use it only for some other discipline, 

 or for the needs of ordinary life. ... In this way we would 

 neglect -every path which did not seem immediately to promise results 

 of practical value. It is my opinion that we must obtain a truer 



