196 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1941 



That the latter is the attitude with which the scientist should ap- 

 proach his task we are assured in the retiring address of President 

 George D. Birkhoff, of the American Association for the Advancement 

 of Science, delivered this past year at the Christmas meeting in Rich- 

 mond. There one of America's foremost mathematicians spoke to 

 America's scientists of the faith that is his. It is fitting that we here 

 try to catch an overtone of that meeting. 



Mr. Birkhoff claimed that whether it is the mathematician dealing 

 with number, or the physicist with matter, the biologist with organism, 

 the psychologist with mind, or the sociologist with social values, there 

 is behind one and all an inherent faith guiding the reasoned super- 

 structure which they create upon intuitional concepts. Whether it is 

 the mathematician's belief in the existence of infinite classes, the phys- 

 icist's belief in the presence of a discontinuous process at work in 

 the theory of radiation, the biologist's belief in a vitalistic theory of 

 life, the psychologist's belief in a physiological accompaniment to 

 every psychical fact, or the sociologist's belief in societal progress, 

 Birkhoff emphasizes faith as an ''heuristically valuable, more general 

 point of view, beyond reason, often in apparent contradiction, 

 which the thinker regards as of supreme importance as he endeavors 

 to give his conclusions the greatest possible scope." 



Some think that there is an opprobrium attached to any belief, that 

 belief and science are mutually exclusive. Do these same people believe 

 in the processes of logic ? Do they have faith in the rationality of the 

 human mind, in the similarity of the perceptive and reasoning fac- 

 ulties of normal, civilized beings ? Is it not in their code that nature 

 is orderly, and that there are spiritual values underlying material 

 facts? 



CONCLUSION 



In the foregoing we have traced in broad outline the advance in 

 scientific thought from the earliest time down to the present. We 

 have pictured the scientist journeying down this path with his guide, 

 the mathematician. We have noted some of the scenes from certain 

 plateaus and valleys in the path. Continuity, causation, deter- 

 minism, law, the postulational method, symbolism, prediction, inven- 

 tion, cosmology, social implication, faith, have passed in review. We 

 have endeavored to point out how the guiding hand of the mathema- 

 tician has aided the traveler along the way. The physical aspects 

 of science, particularly those relative to the structure of matter, have 

 been stressed because they are better known and because of the major 

 importance of matter as "the building blocks" of the universe. There 

 has been no disposition to indulge in propaganda for mathematics. 

 Mathematics needs no "sales talk" to the scientist. It has been rather 



