162 SCIENCE PROGRESS 



intellectual luxury. It may be conjectured that mathematics 

 will never be the favourite intellectual luxury of the educated 

 Britisher ; if the subject is to appeal to him, the appeal must 

 come from another side. And here I do not want to be 

 suspected of maintaining that mathematics can appeal to a 

 Briton only as a means of filling his pocket. It is difficult 

 to turn mathematics into much money ; a distinguished engineer 

 has told us that he can buy all the mathematics he needs at 

 a very moderate number of shillings per week. Mathematics 

 is not a bread-and-butter subject except for those who are 

 satisfied with this simple diet. The argument must be put 

 on a higher plane. 



Modern civilisation stands on a foundation of applied 

 mathematics ; without mathematics the earth could not support 

 its present population. This statement will not be contro- 

 verted by any one familiar with the work of modern scientists 

 and engineers and with the part played by mathematics in 

 their achievements. The average man takes no direct part 

 in these developments but it is not fitting that he should live 

 as a mere parasite on the organisation that keeps him alive. 

 It is the work of the few to develop steam, electricity and 

 machinery ; to render navigation secure by predicting years 

 ahead the motions of the heavenly bodies ; to join the con- 

 tinents together with steamship lines and electric cables ; to 

 cover new corn-bearing lands with railways ; to tunnel the 

 Alps and the Andes ; to prepare for the day when our coal 

 will fail by extracting electric power from water-falls and tides. 

 These are some of the contributions of science to our means 

 of existence ; and mathematics is one of the chief tools that 

 science uses. The modern man should have at least some 

 conception of the means by which these results, so vital to 

 him, are obtained. Geography will teach him what is being 

 done and how, directly or indirectly, his life is affected thereby. 

 Mathematics and science will teach him howthese things are done. 

 Here I am urging the " outlook " value of mathematics, 

 .rather than the utilitarian. I am assuming that the majority 

 of boys will not make any direct use of mathematics in after- 

 life, that they will not even be able to follow in detail the 

 mathematical methods of engineering and applied science. But 

 they can be so taught that a vista is opened through which 

 may be seen the tremendous potentialities of the study of which 



