president's address — SECTION A. 15 



" The reconstruction in 1909 of the Mathematical Tripos, and the 

 destruction of many of the distinctive features of the former scheme 

 must profoundly modify the future history of Mathematics at Cam- 

 bridge. . . . The changes in the Tripos regulations have been 

 accompanied by a curious alteration in the popular subjects, and to-day 

 but few of the young graduates who desired the change are interesting 

 themselves in those branches of Applied Mathematics once generally 

 studied, but rather are turning their attention to subjects like the 

 theories of functions or groups." 



To me the tendency to which Ball calls attention in these words is a 

 matter for surprise and regret. The English School of Mathematics 

 certainly had inclined to an excessive degree to the Applied Studies. 

 It was natural that there should be a reaction ; and that the branches 

 of Pure Mathematics which had been cultivated with such success in 

 the schools of Paris, Berlin, and Gottingen would find their adherents- 

 in greater numbers on the banks of the Cam. But the traditions of 

 Cambridge Mathematics are worthy of being maintained, and progress 

 in Applied Mathematics should not now be left to such an extent to 

 the Continental Mathematician. 



Open the Cambridge Calendar and glance down the Mathematical 

 Tripos lists from 1837 to 1887. There were very few English mathe- 

 maticians who flourished in that time whose names we do not find 

 among the first few wranglers, and in far the greatest number they are 

 the names of men who are known wherever Mathematics is cultivated 

 as those who made notable advances in Applied Mathematics. 



In 1837 we have Green, the discoverer of Green's Theorem, who 

 Cc^me up to Caius College at the age of 40, with his greatest discoveries 

 already made. And now in 1913 his name meets us more frequently 

 tlian ever in mathematical journals, for Green's Functions have come 

 to life again in the new branch of Mathematics called Integral 

 Equations. And in the same year as Green, who was fourth Avrangler, 

 we find Sylvester, as second. His name is as remarkable in the history 

 of Pure Mathematics as Green's is in Applied. We read that " Green 

 and Sylvester were the first men of the year, but Green's want of 

 familiarity with ordinary boy's Mathematics prevented him from 

 coming to the top in a time race." 



Passing on, we find in rapid succession Stokes, Adams, Thomson 

 (Lord Kelvin), Tait, Routh, Clerk-Maxwell, Strutt (Lord Rayleigh), 

 Niven, Darwin, Greenhill, Lamb, Hicks, Poynting, Glazebrook, 

 Larmor, J. J. Thomson, Turner, Bragg, Love, Bryan, and Michell of 

 your own University. 



And to turn to the Pure Mathematicians of that period, we pass 

 from Sylvester, in 1837, to Cayley, in 1842 ; then there is a gap till we 

 reach Clifford, in 1867 ; after him come Glaisher, Burnside, Chrystal, 

 Hobson, Forsyth, Heath, Mathews, AVTiitehead, Young, Berry, Richmond, 

 and Dixon, 



