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SCIENCE 



[N. S. Vol. XXX. No. 765 



the sun and stars. No better illustration 

 of this could be given than Professor 

 Hale's recent discovery of the Zeeman ef- 

 fect in the light from sunspots; in chem- 

 istry, too, the physicist finds in the be- 

 havior of whole series of reactions illustra- 

 tions of the great laws of thermodynamics, 

 while if he turns to the biological sciences 

 he is confronted by problems, mostly un- 

 solved, of unsurpassed interest. Consider 

 for a moment the problem presented by 

 almost any plant — the characteristic and 

 often exquisite detail of flower, leaf and 

 habit— and remember that the mechanism 

 which controls this almost infinite com- 

 plexity was once contained in a seed per- 

 iaps hardly large enough to be visible. 

 We have here one of the most entrancing 

 problems in chemistry and physics it is 

 possible to conceive. 



Again the specialization prevalent in 

 schools often prevents students of science 

 from acquiring sufficient knowledge of 

 mathematics; it is true that most of those 

 who study physics do some mathematics, 

 but I hold that, in general, they do not do 

 enough, and that they are not as efficient 

 physicists as they would be if they had a 

 wider knowledge of that subject. There 

 seems at present a tendency in some quar- 

 ters to discourage the use of mathematics 

 in physics; indeed, one might infer, from 

 the statements of some writers in quasi- 

 scientific journals, that ignorance of mathe- 

 matics is almost a virtue. If this is so, 

 then surely of all the virtues this is the 

 easiest and most prevalent. 



I do not for a moment urge that the 

 physicist should confine himself to looking 

 at his problems from the mathematical 

 point of view; on the contrary, I think a 

 famous French mathematician and physi- 

 cist was guilty of only slight exaggera- 

 tion when he said that no discovery was 

 really important or properly understood by 



its author unless and until he could explain 

 it to the first man he met in the street. 



But two points of view are better than 

 one, and the physicist who is also a mathe- 

 matician possesses a most powerful instru- 

 ment for scientific research with which 

 many of the greatest discoveries have been 

 made ; for example, electric waves were dis- 

 covered by mathematics long before they 

 were detected in the laboratory. He has 

 also at his command a language clear, con- 

 cise and universal, and there is no better 

 way of detecting ambiguities and discrep- 

 ancies in his ideas than by trying to express 

 them in this language. Again, it often 

 happens that we are not able to appreciate 

 the full significance of some physical dis- 

 covery until we have subjected it to mathe- 

 matical treatment, when we find that the 

 effect we have discovered involves other 

 effects which have not been detected, and 

 we are able by this means to duplicate the 

 discovery. Thus James Thomson, starting 

 from the fact that ice floats on water, 

 showed that it follows by mathematics that 

 ice can be melted and water prevented 

 from freezing by pressure. This effect, 

 which was at that time unknown, was after- 

 wards verified by his brother, Lord Kelvin. 

 Multitudes of similar duplication of phys- 

 ical discoveries by mathematics could be 

 quoted. 



I have been pleading in the interests of 

 physics for a greater study of mathematics 

 by physicists. I would also plead for a 

 greater study of physics by mathematicians 

 in the interest of pure mathematics. 



The history of pure mathematics shows 

 that many of the most important branches 

 of the subject have arisen from the at- 

 tempts made to get a mathematical solution 

 of a problem suggested by physics. Thus 

 the differential calculus arose from at- 

 tempts to deal with the problem of moving 

 bodies. Fourier's theorem resulted from 



