SCIENCE 



Friday, December 15, 1916 

 contents 



The Relation of Mathematics to the Natural 

 Sciences : Professor Thos. E. Mason .... 835 



Education after the War: Professors W. S. 

 Franklin and Barry MacNutt 841 



The Value of the Sanitary Survey: Professor 

 W. P. Mason 844 



The Convocation-Week Meetings of Scientific 

 Societies 845 



Scientific Notes and News 848 



University and Educational News 851 



Discussion and Correspondence: — 



Opinions on Some Ciliary Activities: Pro- 

 fessor James L. Kellogg. Chlorosis of Pine- 

 apples: P. L. Gile. Relative Importance of 

 Fungi and Bacteria in Soil: H. Joel Conn. 

 The Sudden Appearance of Great Numbers 

 of Medusa; in a Kentucky Creek: Harrison 

 Garman 852 



Scientific Books: — 



Taylor's With Scott: General A. W. 

 Greely. Blatchley and Leng on Weevils of 

 Northeastern America: H. C. Pall 860 



Scientific Journals and Articles: — 



Bollettino Bibliografia e Storia delle Scienze 

 Matematiche : Professor David Eugene 

 Smith. The American Mineralogist: G. 

 P. K 862 



Nitrate Deposits in the United States 864 



Agriculture of the Hidatsa Indians: Pro- 

 fessor Albert Ernest Jenks 864 



Special Articles: — 



The Chemical Constitution of Chitin: Dr. 

 S. Morgulis. Outliers of the Maxville 

 Limestone in Ohio: Professor G. P. Lamb. 

 A Method for maintaining a Constant Vol- 

 ume of Nutrient Solutions: Dr. Orton L. 

 Clark 866 



Societies and Academies: — 



The Botanical Society of Washington: Dr. 

 W. E. Safford. The South Dakota Acad- 

 emy of Science: P. J. Gilmore 869 



MSS. Intended for publication and books, etc., intended for 

 review should be sent to Professor J. McKeen Cattell, Ga 

 On-Hudson. N. Y. 



THE RELATION OF MATHEMATICS TO 

 THE NATURAL SCIENCES* 



In considering the relationship of mathe- 

 matics to the natural sciences, we shall do 

 well to see what mathematics is and what 

 are its methods. 



Mathematics has not always been looked 

 at through the same glasses. The field of 

 mathematics to the early workers was num- 

 ber and quantity. Euclid put into his 

 axioms what he considered to be the funda- 

 mental facts of the world about him. 

 Diophantus, of Alexandria, a worker in 

 algebra, considered only positive roots of 

 equations. They were dealing with reali- 

 ties and not with abstract matters. Some 

 time later mathematicians tried to prove 

 their axioms — often called self-evident 

 truths — and made a wonderful discovery. 

 That was, that a "self-evident truth" might 

 be replaced by its contrary and the result 

 still be a consistent body of doctrine. And 

 thus the glasses were changed, to be mathe- 

 matical the conclusions must be the result 

 of the assumptions and these must be con- 

 sistent. The assumptions need have no 

 physical interpretation, indeed they might 

 contradict any of our theories, but they 

 must not contradict each other. There 

 might be foreign war, but no internal con- 

 flict. I like the following of Professor 

 Keyser, of Columbia University •? 



He (the mathematician) is not absolutely cer- 

 tain, but he believes profoundly that it is pos- 

 sible to find axioms, sets of a few propositions 

 each, such that the propositions of each set are 

 compatible, that the propositions of such a set 

 imply other propositions, and that the latter can 



i Bead before the Purdue University chapter of 

 Sigma Xi, October 25, 1916. 

 2 Science, Vol. 35 (1912), p. 107. 



