198 ANNUAL KEPORT SMITHSONIAN INSTITUTION. 19J2. 



mathematicians who are supposed to be well prepared to pass judg- 

 ment on the particular books and articles which they undertake to 

 review. Wliile these re\dews are of very unequal merit, they are 

 rendering a service of the greatest value. 



The main object of such reviews is to enable the true student to 

 learn easily what ])rogress others are making, especially in his own 

 field and in those closely related thereto. They serve, however, 

 another very laudable purpose in the case that they are rehable. We 

 have the pretender and the unscrupulous always with us, and it is 

 almost as important to limit their field of o})eration as to encourage 

 the true investigator. "Companions in zealous research" should be 

 fearless in the pursuit of truth and in the disclosure of falsehood, since 

 these qualities are essential to the atmosphere which is favorable to 

 research. 



While the mathematical investigator is generally so engrossed by 

 the immediate objects in view that he seldom finds time to think of 

 his services to humanity as a whole, yet such thoughts naturally come 

 to him more or less frequently, especially since his direct objects of 

 research seldom are well suited for subjects of general conversation. 

 If these thoughts do come to him they should bring with them great 

 inspiration. Who can estimate the amount of good mathematics has 

 done and is doing now? If all knov/ledge of mathematics could 

 suddenly be taken away from us there would be a state of chaos, and 

 if all those things whose development depended upon mathematical 

 principles could be removed, our lives and thoughts would be pauper- 

 ized immeasurably. This removal would sweep away not only our 

 modern houses and bridges, our commerce and landmarks, but also 

 most of our concepts of the physical universe. 



Some may be tempted to say that the useful parts of mathematics 

 are very elementary and have little contact with modern research. 

 In answer, we may observe that it is very questionable whether the 

 ratio of the developed mathematics to that which is finding direct 

 a])plication to things which relate to material advantages is greater 

 now than it was at the time of the ancient Greeks. The last two 

 centuries ha^'e mtnessed a wonderful advance in the ])ure mathe- 

 matics which is commonl}'- used.* While the advance in the extent 

 of the develojied Helds has also been rapid, it has i)robably not been 

 relatively more rapid. Hence, the mathematical investigator of 

 to-day can pursue his work with the greatest confidence as regards his 

 services to the general uplift both in thought and in material better- 

 ment of the human race. All of his real advances may reasonably be 

 expected to be enduring elements of a structure whose permanence is 

 even more assured than that of granite pillars. 



> In 1726, arithmetic and geometry were studied during the senior year in Harvard College. Natural 

 I'hilosophy and physics were still taught before arithmetic and geometry. Cajori, "The Teaching and 

 History of Mathematics in the United States," 1S90, p. 22. * 



