TENDENCIES IN MATHEMATICAL SCIENCE 341 



If for instance, + 1, 1, V 1 had been called direct, inverse, and 

 lateral units, instead of positive, negative, and imaginary (or even 

 impossible) such an obscurity would have been out of the question. 



Gauss. 



Concluding an address on the history of mathematics in the 

 nineteenth century, a recent writer says : - 



What strikes us at once in our survey of mathematics in the last 

 century is its colossal proportions and rapid growth in nearly all 

 directions, the great variety of its branches, the generality and com- 

 plexity of its methods, an inexhaustible creative imagination, the fear- 

 less introduction and employment of ideal elements, and an apprecia- 

 tion for a refined and logical development of all its parts. Pierpont. 



Probably no other department of knowledge plays a larger part 

 outside its own narrower domain than mathematics. Some of its 

 more elementary conceptions and methods have become part of the 

 common heritage of our civilization, interwoven in the every-day 

 life of the people. Perhaps the greatest labor-saving invention that 

 the world has seen belongs to the formal side of mathematics; I 

 allude to our system of numerical notation. . . . Without taking 

 too literally the celebrated dictum of the great philosopher Kant 

 that the amount of real science to be found in any special subject is 

 the amount of mathematics contained therein, it must be admitted 

 that each branch of science which is concerned with natural phe- 

 nomena, when it has reached a certain stage of development, becomes 

 accessible to, and has need of, mathematical methods and language ; 

 this stage has, for example, been reached in our time by parts of the 

 science of chemistry. Hobson. 



I often say that when you can measure what you are speaking 

 about and express it in numbers, you know something about it ; but 

 when you cannot measure it, when you cannot express it in numbers, 

 your knowledge is of a meager and unsatisfactory kind ; it may be the 

 beginning of knowledge, but you have scarcely in your thoughts 

 advanced to the stage of science. Kelvin. 



THE DISCOVERY OF NEPTUNE. In a century filled with re- 

 markable scientific achievement, no single triumph has been more 

 conspicuous, or in some respects more dramatic, than the discovery 

 of the planet Neptune by Adams and Leverrier. From the time 



