II. 



THE FUTURE OF MATHEMATICS. 



If we wish to foresee the future of mathematics, our 

 proper course is to study the history and present 

 condition of the science. 



For us mathematicians, is not this procedure to 

 some extent professional ? We are accustomed to 

 extrapolation, which is a method of deducing the 

 future from the past and the present ; and since we 

 are well aware of its limitations, we run no risk of 

 deluding ourselves as to the scope of the results it 

 gives us. 



In the past there have been prophets of ill. They 

 took pleasure in repeating that all problems suscep- 

 tible of being solved had already been solved, and that 

 after them there would be nothing left but gleanings. 

 Happily wc are reassured by the example of the 

 past. Many times already men have thought that 

 they had solved all the problems, or at least tiiat 

 they had made an inventory of all that admit of 

 solution. And then the meaning of the word solution 

 has been extended ; the insoluble problems have 

 become the most interesting of all, and other problems 

 hitherto undreamed of have presented themselves. 

 For the Greeks a good solution was one that em- 



