34 PRESIDENTIAL ADDRESS — -SECTION A. 



never written anything of any use to anyone," is well known 

 to many here ; on the other hand, it is generally accepted that 

 mathematics coined for a special physical purpose are as a rule 

 incomplete, and only find their full development in the hands 

 of the detached pure mathematician untrammelled by the phy- 

 sical ideas which originated the symbolism. 



Mathematics as the language of Science is also exempt 

 from the limitations attaching to its himible origin from counting 

 and elementary arithmetic. It is not limited to quantitatwc sen- 

 tences ; its symbols need not always represent numeral adjectives 

 or ratios. In fact, arithmetic with its practical processes (that 

 will not parse) is only a 'branch of the subject — a specialized 

 interpretation of the symbols. The symbols may be used 

 mathematically to connect any two ideas which can be said to be 

 " equal " or " equivalent," to make any statement connecting 

 cause and effect. From this point of view the main line c^f 

 mathematics begins with the use of the unknown (|uantity, the 

 solution of our friends the problems " think of a number," etc. 

 I think it is arguable that the solution of any mathe- 

 matical equation, whether algebraic or differential, depends on 

 the reversion of simple processes — e.g., subtraction, division, 

 square root, integration. This general process may be well 

 illustrated by the card trick in which the words one, two, three, 

 etc., are spelt, a card being shifted from top to bottom at each 

 letter, and the appropriate card thrown out at the end of each 

 word. I believe this trick is usually done with 13 cards, which 

 are previously arranged by the use of a mnemonic. To bring oft" 

 the trick with the whole 52 cards of a pack seems difficult ; but 

 there is an easy way of arranging the pack by sinijjl}- reversing 

 the spelling- operation and burying a card at the end of each 

 word. 



The first Science to com})lete the stages of evolution sketched 

 at the beginning of this address was Mechanics, including 

 Astronomy. Aristotle (384 B.C.), the accepted founder of 

 " Science " in our civilization, stiff ered the inevitable fate of the 

 pioneer : for want of accumulated facts and from a wish to pro- 

 duce results, he generalized too rapidly, so bequeathing to 

 thinkers, in addition to his grand fundamental rules of experi- 

 ment and classification of facts, a body of unscientific axioms 

 which (as is the way with the dicta of a conspicuous genius in 

 the hands of less capable posterity) became dogmas, and thereby 

 clogged the wheels of Science, and concealed facts which we, 

 with the glorious superiority of the inheritors of an accumu- 

 lated estate, consider almost obvious. Such axioms were : " A 

 heavy body falls faster than a light one," " Perfect motion is 

 circular," " Nature is symmetrical." In a like manner, even 

 Newton tmconsciously kept English thinkers back for a century 

 while continental mathematicians made great advances : and 

 to-day, after two centuries, we are seeing new theories (which 

 have already produced promising first-fruits) suggested by 

 doubts of some of the foundations of the Newtonian philosophy: 



