THE SCIENTIFIC 

 MONTHLY 



MAY. 1921 



THE HISTORY OF MATHEMATICS* 



By Professor ERNEST W. BROWN 



YALE UNIVERSITY 



THE earliest dawn of science is without doubt not different from 

 that of intelligence. But the civilized man of to-day, far removed 

 as he is from the lowest of existing human races, is probably as far 

 again from the being whom one would not differentiate from the 

 animals as far as mental powers are concerned. What this difference 

 is, neither ethnologist nor psychologist can yet tell. Perhaps the 

 nearest approach to a definition, at least from the point of view of this 

 article, is contained in the distinction between unconscious and con- 

 scious observation. We are familiar with both sides even in ourselves : 

 records can be impressed on the brain and remain there apparently 

 dormant until some stimulus brings them to fruition, and again, record 

 and stimulus can appear together so that a train of thought is im- 

 mediately started. 



The faculty of conscious observation is a fundamental requirement 

 of a scientific training, and no development can take place until it has 

 been acquired to some extent. Although this is only the first step, it 

 was probably a long one in the history of the race, just as it is relatively 

 long in the lives of the majority of individuals. Reasoning concern- 

 ing the observation follows, but not much success can be attained until 

 a considerable number of observations have been accumulated. We 

 may indeed put two and two together to make four, but experience 

 shows that with phenomena the answer is more often wrong than right: 

 we need much more information in order to get a correct answer. 



We expect, then, that the earlier stage of a science will be one not 

 so much of discovery as of conscious observation of phenomena which 

 are apparent as soon as attention is called to them. The habit once 

 acquired, the search for the less obvious facts of nature begins, and 



*A lecture delivered at Yale University, February 26, 1920, the first of a 

 series on the History of Science under the auspices of the Gamma Alpha 

 Graduate Scientific Fraternity. 



VOL. XII.— 25. 



