DEVELOPMENT OF MATHEMATICAL ANALYSIS 517 



The reciprocal influence of analysis and physical theories has been 

 in this regard particularly instructive. 



What does the future hold? 



Problems more difficult, corresponding to an approximation of 

 higher order, will introduce complications which we can only vaguely 

 forecast, in speaking, as I have just done, of functional equations 

 replacing systematically our actual differential equations, or further 

 of integrations of equations infinite in number with an infinity of 

 unknown functions. But even though that happens, mathematical 

 analysis will alw r ays remain that language which, according to the 

 mot of Fourier, has no symbols to express confused notions, a lan- 

 guage endowed with an admirable power of transformation and 

 capable of condensing in its formulas an immense number of results. 



