552 



SCIENCE 



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



processes, mathematicians are perhaps not 

 to be blamed for their reluctance in leaving 

 extensive developments, which seem to ad- 

 mit of growth in every direction, for new 

 fields where mathematical insight appears 

 more or less uncertain. 



The mathematicians, therefore, may be re- 

 garded as the old conservative party among 

 scientists. They are the standpatters 

 among the scientists of to-day. This does 

 not say that they are making no progress. 

 On the contrarj^ they have made and are 

 making rapid progress, and are entering 

 new fields, but fortunately the world is 

 moving ahead so rapidly scientifically that 

 no scientific party is able to embody in its 

 platform all the desirable new features. In 

 times of revolution conservatism is not apt 

 to be popular, and in the midst of the scien- 

 tific revolution in which we are finding our- 

 selves the mathematical party is naturally 

 receiving blows which the calmer days 

 of the future will doubtless declare to have 

 been too severe. These blows tend at the 

 present time to work downward into our 

 elementary and secondary education and 

 they ought to be matters of great concern 

 for all scientists; for, without the clarify- 

 ing influence of mathematics, the whole 

 structure of science would suffer seriously. 



In recent decades the churches of our 

 land have tended towards unity in action 

 and towards a higher appreciation of the 

 merits of the great common principles. Is 

 it not likely that what is common to all the 

 sciences, viz., the formation of ideas and 

 the investigation of relationships existing 

 between these ideas, will receive more em- 

 phasis as we understand better the value of 

 scientific work ? Monopoly in science is the 

 worst type of monopoly. Mathematical 

 ideas have an unusually wide range, but are 

 comparatively barren in local content, for 

 the richer an idea is, as regards local con- 

 tent, the poorer it usually is as regards 

 range. 



The present movement to organize re- 

 search work is strongly represented in Eng- 

 land by the Imperial Trust for the Encour- 

 agement of Scientific and Industrial Re- 

 search and the Advisory Council. In Amer- 

 ica this same movement is represented by 

 the Committee of One Hundred on Scien- 

 tific Research of the American Association 

 for the Advancement of Science, appointed 

 in 1914,^ and its various subcommittees ap- 

 pointed in 1916, and by the National Re- 

 search Council, organized on September 20, 

 1916, by the National Academy of Sciences 

 at the request of the President of the United 

 States, and its plexus of committees repre- 

 senting the various domains of science.^ 

 This movement should tend to emphasize 

 the common ground of scientific research 

 as well as to clarify the atmosphere by di- 

 recting attention to the fact that there are 

 many grades of scientific research. It 

 should be emphasized that the greatest 

 danger of research to-day is that its pop- 

 ularity tends to research hypocrisy. 



While the common ground of scientific 

 research can not be said to be mathematics 

 at the present time, it will doubtless be ad- 

 mitted that its ideal is mathematics. In 

 fact, this common ground consists largely 

 in so coordinating facts of observation or 

 deduction as to lead to certain conclusions. 

 These conclusions are not always necessary, 

 but with the advance of knowledge they 

 naturally tend towards becoming necessary. 

 As soon as the conclusions become neces- 

 sary, if certain explicit assumptions are 

 made, and are not merely very probable, the 

 reasoning becomes mathematical. Mathe- 

 matical reasoning thus appears to be the 

 goal towards which scientific reasoning is 

 striving, and lack of sufficient knowledge 

 furnishes the main reason why mathemat- 



2 Science, N. S., Vol. 39 (1914), p. 680; Vol. 

 45 (1917), p. 57. 



3 Proceedings of the National Academy of Sci- 

 ences, Vol. 2 (1916), p. 607. 



