SECTION A - ALGEBRA AND ANALYSIS 



(Hall 9, September 22, 10 a. m.) 



CHAIRMAN: PROFESSOR E. H. MOORE, University of Chicago. 



SPEAKERS: PROFESSOR CHARLES EMILE PICARD, The Sorbonne; Member of the 



Institute of France. 



PROFESSOR HEINRICH MASCHKE, University of Chicago. 

 SECRETARY: PROFESSOR A. G. BLISS, University of Chicago. 



ON THE DEVELOPMENT OF MATHEMATICAL ANALYSIS 

 AND ITS RELATIONS TO SOME OTHER SCIENCES 



BY CHARLES EMILE PICARD 

 (Translated from the French by Professor George Bruce Hoisted, Kenyan College} 



[Charles Emile Picard, Professor of Higher Algebra and Higher Analysis, Uni- 

 versity of Paris; also Professor of General Mechanics, 1'Ecole Centrale des 

 Arts et Manufactures, Paris, b. Paris, France, July 24, 1856. LL.D. Clark 

 University, Glasgow University, University of Christiania. Member of In- 

 stitute of France; Academy of Science, Berlin, St. Petersburg, Bologna, 

 Boston, Turin, Copenhagen, Washington, and many others; Mathematical 

 Society of London. Former President of Mathematical Society of France, 

 Mathematical Societies of London and Kharkow, and many other math- 

 ematical societies. Author and editor of Memoirs, Traits and Discussions 

 of Mathematics; Theory of Algebraic Functions of Two Variables.] 



IT is one of the objects of a congress such as this which now 

 brings us together, to show the bonds between the diverse parts of 

 science taken in its most extended acceptation. So the organizers 

 of this meeting have insisted that the relations between different 

 sections should be put in evidence. 



To undertake a study of this sort, somewhat indeterminate in 

 character, it is necessary to forget that all is in all; in what con- 

 cerns algebra and analysis, a Pythagorean would be dismayed at the 

 extent of his task, remembering the celebrated formula of the school: 

 " Things are numbers." From this point of view my subject would 

 be inexhaustible. 



But I, for the best of reasons, will make no such pretensions. 



In casting merely a glance over the development of our science 

 through the ages, and particularly in the last century, I hope to be 

 able to characterize sufficiently the role of mathematical analysis in 

 its relations to certain other sciences. 



It would appear natural to commence by speaking of the concept 

 itself of whole number; but this subject is not alone of logical order, 



