38 UNIVERSITY OF MISSOURI BULLETIN 



to combine in one lecture a statement of the purpose and the 

 meaning of the science which I represent, phrased in terms 

 which can be understood by all; and at the same time to say 

 something of the present activity in the science for the sake 

 of those who are already familiar with mathematics in general. 



PURPOSE AND MEANING 

 Mathematics as a Popular Conception 



The popular conception of mathematics is derived, to a 

 very considerable extent from the courses common in elemen- 

 tary instruction. I suppose that mathematics, according to this 

 conception, consists largely of reckoning, that is, the familiar 

 processes of arithmetic and algebra, and of reasoning, as ap- 

 plied in elementary geometry. That such a conception of 

 mathematics is too narrow I shall point out. It is, indeed, 

 fundamentally misleading. 



The usual elementary courses in mathematics are injurious, 

 not only in creating the misconception of mathematics which 

 I have just mentioned, but also in making the whole subject 

 an offense to those who are compelled against their will, OF 

 rather, before they know their will, to follow ill-advised 

 courses of instruction not suited to their years. Indeed, just 

 such compulsory mathematics was highly favored by those 

 who wished to gain from it discipline and discipline alone : 

 I mean work for work's sake and not for any benefits to be 

 derived from it. No wonder that the child abhors a subject 

 which has been viewed by his teacher as a "discipline" to him 

 in the sense I have mentioned, and we may well infer that 

 the child is father to the man in the establishment of adult 

 prejudice of the same kind. 



Indeed, the popular prejudice against mathematics, and 

 the popular ignorance of that subject is well-nigh proverbial. 

 I was particularly interested in a statement by Sir Oliver 

 Lodge: "Perhaps in no subject is popular ignorance more 



