June 1, 1917] 



SCIENCE 



555 



Is there not a danger that the sudden 

 recognition of the great political importance 

 of certain types of research will have some- 

 what the same effect on science as the dis- 

 covery of gold in California and in Aus- 

 tralia about the middle of the preceding 

 century had on the development of the re- 

 gions concerned? People flocked from one 

 mining camp to the other and often neg- 

 lected duties which are essential for the 

 harmonious development of the resources 

 of a country. Hence there seems to be a 

 special need at present to urge our col- 

 leagues to remain at their posts of duty, 

 notwithstanding glowing reports of chances 

 to amass scientific fortunes quickly in cer- 

 tain newly discovered gold fields. The get- 

 rich-quickly schemes in science should be 

 scrutinized as carefully as similar schemes 

 relating to the accumulation of money. 



The remaining at one's post of duty in 

 scientific research does not imply a lack of 

 support in the solution of pressing prob- 

 ' lems or a lack of vacation trips and ac- 

 quaintance with other fields of work. In 

 fact, such support and acquaintance are 

 highly desirable. It is, however, a question 

 whether the nomadic scientific life, which 

 seems to have become fashionable during 

 the last few decades, at least in mathemat- 

 ics, is the one which will in the long run 

 bring the best results. Science is not pri- 

 marily a grazing country. Large tracts are 

 suited for agriculture and mining. What 

 is new is not necessarily good and what is 

 good is not necessarily new, and prophesies 

 in regard to the great importance of certain 

 new developments have not always been ful- 

 filled. On the other hand, it should be re- 

 membered that reasonable hope and opti- 

 mism are essential for progress, and that we 

 need prospectors as well as miners in the 

 scientific world. 



It should be noted that the miner needs 

 some of the qualifications of the prospector 

 since he is apt to meet with new situations 



and needs to take advantage of the avail- 

 able by-products. In fact, while he is min- 

 ing for gold he may strike deposits of cop- 

 per which are richer than the gold deposits 

 which he was primarily seeking. Some of 

 the richest mathematical discoveries were 

 made while the investigator was looking pri- 

 marily for other results, and even problems 

 which have not been solved at all up to the 

 present have been the source of very useful 

 developments. I understand that similar 

 conditions hold in other fields of scientific 

 effort and these facts point to the great im- 

 portance of freedom on the part of the in- 

 vestigator, and, incidentally to the danger 

 of too much organization in scientific re- 

 search. 



As a very recent instance of an unex- 

 pected mathematical by-product, I may be 

 pardoned for referring to a somewhat 

 trivial case which has, however, the impor- 

 tant property that it can be understood by 

 all. It is well known that the theory of 

 substitution groups was developed for the 

 purpose of clarifying the theory of alge- 

 braic equations and not for the purpose of 

 adding to the enjoyment of parties engaged 

 in playing games of cards. In fact, the 

 study of such an advanced mathematical 

 theory as that of substitution groups might 

 appear to involve concepts, which are at 

 the opposite pole from those entering the 

 minds of people seeking recreation at card 

 tournaments. 



Notwithstanding this apparent wide sep- 

 aration, I was pleased to be able to say re- 

 cently to a friend, who desired to have each 

 one of a large party play once and only 

 once with each of the others during a series 

 of successive games, that an arrangement of 

 the players meeting this condition could be 

 determined directly by means of substitu- 

 tions of certain transitive groups. This 

 should perhaps have been expected, since a 

 transitive substitution group is an ideal re- 

 public treating all its letters in exactly the 



