492 



SCIENCE 



[N. S. Vol. L. No. 1300 



largest and most modern general history of 

 mathematics in our language and all English- 

 speaking people who seek reliable information 

 in regard to the development of this subject 

 will naturally turn to it. The general reader 

 ■will find here not only a history of the older 

 mathematical developments but also a large 

 amoimt of information about modern develop- 

 ments with due references to the contribu- 

 tions made by Americans. 



Until recently America's share in the his- 

 tory of the advancement of mathematics was 

 practically confined to the last fifty years, but 

 recent study of the hieroglyphic writings of 

 the Maya Indians of Central America and 

 southern Mexico has established the fact that 

 America has also a place in the history of 

 ancient mathematics. In fact, the Maya used 

 a kind of zero very early, possibly as early as 

 the beginning of the Christian era. Their 

 contributions are, however, very insignificant 

 in comparison with those of the ancient 

 Greeks, so that America has had only a small 

 share in the advancement of mathematics 

 except during the last half century. 



Perhaps the most important feature of the 

 history of science for teachers is the fact that 

 in a broad way the history of the world por- 

 trays the history of the individual. Concepts 

 which the world learned slowly are usually 

 grasped slowly by the individual and the dilS- 

 culties which the world experienced in the 

 assimilation of these concepts are reflected 

 in the individual student. Since the history 

 of mathematics is so very old it is especially 

 rich in suggestions as regards the learning 

 process. 



Another important feature of this history 

 is that it tends to a clearer grasp of the most 

 fimdamental and fruitful facts of science. 

 For instance, a great part of the development 

 of mathematics during the nineteenth cen- 

 tury centers in the ordinary complex numbers 

 and in Taylor's expansion. It is interesting 

 to note that for over fifty years from the time 

 of the discovery of this expansion (1712) its 

 importance was not generally recognized, and 

 this fact furnishes another illustration of the 

 difficulty involved in estimating the value of 

 contemporary work in pure mathematics. 



The history of science is interesting on ac- 

 count of its inexhaustible riches. Substantial 

 progress in this field depends on the use of 

 the intellectual telescope. ISTothwithstanding 

 the great importance of the use of the in- 

 tellectual microscope which characterizes and 

 ought to characterize most of our scientific 

 work there is a charm for the student at times 

 in using also an intellectual telescope in his 

 scientific outlook. Like the distant sun warms 

 and fructifies our earth so distant scientific 

 facts stream into our present life and consti- 

 tute the som-ce of our present scientific 

 activity. Just as we are interested in the 

 sources of the rays of physical light that 

 cheer us by day and by night so we should 

 be interested in the soirrces of the rays of 

 intellectual light shining through the scien- 

 tific literature and illuminating our intellec- 

 tual pathway. 



Few may be interested in a proof of the 

 fact that the point of inflexion of every curve 

 whose equation is of the form 



y = x' -\- av? -\-'bx -\- c 



is a point of symmetry and hence the graph 

 of a quadratic in one unknown has always 

 line symmetry while that of a cubic has 

 always point symmetry, but every one is 

 likely to take an interest in the discussions 

 of the ancient Greeks relating to whether a 

 straight line can be equal to a curved one, as 

 well as in the contention that Achilles could 

 not overtake the tortoise since he must first 

 reach the place from which the tortoise 

 started, but by the time he reaches this place 

 the tortoise has moved ahead. Such scientific 

 ideas from the springtime of intellectual 

 world life have a perennial interest, especially 

 for those in the springtime of their own in- 

 tellectual life. 



The history of science best suited for the 

 young student is that which relates to funda- 

 mental questions which are apt to perplex 

 him and not that relating to the preservation 

 of the obsolete from oblivion. The historic 

 setting should constitute the sugar coating of 

 the otherwise bitter scientific pills. The body 

 of the pill should, however, be selected for its 

 curative properties. It must be remembered 



