Biology and Mathematics 245- 



Knows neither weal nor woe, knows 



Neither praise nor blaming. 



To unknown lands I stride in war, in whirlwind. 



I know no aim, no end and no beginning. 



I beget and I destroy, not prating, never angry, 



The elephant and the worm, the 



Wise man and the foolish. 



So live as all live. Float out on the 



Flood eternal 



One instant brief, and vanish then forever. 



Presume not stupid-bold with me to wage a contest, 



With me eternal mother of all living and all dead." 



So thunders Nature with a million voices 



In hail, in surge, in storm- wind and the lightning. 



So much for the continuity world-scheme in biology. 



But the latest advances in mathematics have rendered, 

 unnecessary for biology the wearing of this mis-fit garment. 



The new mathematics gives now a standpoint for the expla- 

 nation and treatment of natural phenomena from which the 

 individuality of the biologic elements need not be suppressed. 



It has triumphed for its own domain in cases where the con- 

 tinuity methods were wholly inapplicable, where arithmology, 

 discrete mathematics was called-for and victorious. 



Such are the problems which relate to the properties of 

 whole numbers, solved so brilliantly in number-theory. 



Such again are the questions relating to the enumeration of 

 the geometric forms within parameters which satisfy n given 

 conditions. These even in the simplest cases showed themselves 

 insoluble until finally between "ISGO and '70 the French math- 

 ematicians created special discrete methods. Thence sprang a. 

 wholly new branch of mathematics, Enumerative Geometry. 



A third, an epoch-making universe of discrete mathematics 

 is the wonderful Invariant Theory of the great Sylvester and his 

 brother-in-arms Cayley, two men whose loss left the English- 

 speaking world without a single mathematician of first rank, of 

 the rank of Hilbert and Poincare. 



In chemistry this discrete mathematics has shown itself of 

 such use and power that we may assuredly say chemistry owes 

 its present stand-point almost wholly to two lines of advance 

 both discrete, the atomic structure theory of Kekule, and 

 Mendelieev's periodic system of the chemical elements. 



The brilliant and rapid advances in chemistry have come- 

 not from suppressing but from stressing the individuality of the 

 elements. Its mathematics has been essentially discrete. 



The arithmologic scheme of chemical research, the atomic 

 structure theory of Kekule, coincides completely with the scheme 

 of the symbolic invariant theory, though both were worked out 

 independently. 



