554 



SCIENCE 



[N. S. Vol. XLV. No. 1170 



much greater freedom in regard to the 

 stage to which they may pursue a problem 

 before announcing results. Hence these 

 may hope for success in dealing with much 

 more difficult questions than the mathema- 

 tician could reasonably hope to solve at the 

 present time. The limitations thus imposed 

 upon the mathematician are compensated, 

 a.t least in part, by the finality of his re- 

 sults as regards questions of rigor. Mathe- 

 matical results call never be disproved, 

 other accepted results have never been dis- 

 proved. With respect to simplicity and 

 style, the mathematical developments are 

 seldom final, and in many cases, they ap- 

 pear to admit endless variations. 



As instances of final mathematical results 

 may be cited the useful tables which when 

 once computed serve all succeeding genera- 

 tions. Such finality may be said to be a 

 ;goal of all scientific endeavor, since the re- 

 sults enrich countless ages by increasing 

 their capacity for accomplishments. In 

 fa(it, such tables may be regarded as typ- 

 ical illustrations of the mathematical con- 

 tributions to the advancement of knowledge 

 even if they constitute a very minor por- 

 tion of these contributions. The fact that 

 mathematical results have increased the 

 capacitj'' of the world for doing things may 

 be emphasized by noting, in particular, that 

 in recent years prime numbers have been 

 found which could not have been proved to 

 be prime by the method employed by 

 Eratosthenes, if the entire human race had 

 been working in an organized manner on 

 this single problem since the days of the 

 ancient Greeks. 



The present seems to be an especially ap- 

 propriate time to consider the interrela- 

 tions of scientific research in view of the 

 rapidly growing public appreciation of the 

 value of such research. Several decades of 

 comparative peace immediately preceding 

 the present great and deplorable conflict 

 were unusually rich in great scientific tri- 



umphs. As well-known instances we may 

 cite wireless telegraphy and the construc- 

 tion of the great Panama Canal, which be- 

 came possible by our advanced knowledge 

 in regard to sanitation. The world-wide 

 health activities under the auspices of the 

 Rockefeller Foundation and the activities 

 of our agricultural colleges in directing at- 

 tention to advantages resulting from scien- 

 tific methods of farming are strong forces 

 working towards a popular appreciation of 

 science. Since the great European war be- 

 gan it has become evident through the new 

 elements introduced by the submarines 

 and other scientific devices that the very 

 existence of a great nation may depend 

 upon the scientific attainment of its peo- 

 ple, and hence the question of scientific 

 research has taken a prominent place among 

 those of national policy. It is perhaps sig- 

 nificant that our National Academy was 

 founded in the midst of the Civil "War. 



Scientific research is as old as civilization 

 and has often been protected by kings in a 

 patronizing manner, but it is a new experi- 

 ence in the history of the world to see kings 

 turn to scientific research for protection. 

 For centuries governments have recognized 

 the value of science and have provided with 

 growing liberality for her development, but 

 now they are calling to her to save them 

 from destruction. They have noticed that 

 in spite of many excellencies in other di- 

 rections the ignorance of causes may entail 

 their destruction as separate nations. This 

 new attitude towards our field of work may 

 at first tend to gratify us, but a second 

 thought reveals the fact that it is fraught 

 with grave dangers. Kings in government 

 and finance are interested in the dead re- 

 sults of science instead of in the great liv- 

 ing and growing organism itself, whose 

 growth seems to have just begun and whose 

 development has always been more keenly 

 inspired by love of truth than by hope of 

 gain. 



