MATHEMATICS 41 



scientific method, namely, that phase in which the results 

 derived experimentally are classified, examined and reduced 

 to simple laws. This phase of the scientific method is not 

 always performed by processes recognized as mathematical, 

 but all processes of mathematics are typical of this phase, 

 which must exist in every scientific investigation. I shall 

 later point out some exceedingly definite connections with 

 particular sciences. Just now I would emphasize the depen- 

 dence of mathematics on science for its very source, and, 

 conversely, its usefulness to science through its conclusions. 

 This fact is borne out particularly in physics, in mechanics, 

 in engineering, as is known to all of you. In other fields, 

 such as life insurance, the dependence is not less intimate, 

 and to a less degree every science, and indeed, all reasoned 

 life, depends on the methods which mathematics typifies. The 

 grand reason for this is brought out more clearly by the 

 definition quoted above, that ''Mathematics is the science 

 which draws necessary conclusions." 



Content 



But I must pass to some more definite explanation of 

 the content of mathematics than could be drawn from the 

 preceding general remarks. The first and most obvious por- 

 tion of mathematics is that which I shall group under the 

 term of "reckoning." This includes the whole question of 

 elementary arithmetic, the formal rules of operation, and 

 algebra. Perhaps I should insist again that the shorthand 

 which characterizes algebra to most minds is not logically 

 a part of mathematics at all. It is a scheme, a device for 

 putting down what might otherwise be quite impossible 

 through lack of time. Logically it is altogether unnecessary 

 it is merely a human necessity, if we are to express in a 

 reasonable length of time the facts which we now know. 

 Perhaps a more suitable definition of mathematics than that 

 I gave above would be that it consists in intelligent laziness, — 



