SECTION C APPLIED MATHEMATICS 



(Hall 7, September 24, 3 p. TO.) 



CHAIRMAN: PROFESSOR ARTHUR G. WEBSTER, Clark University, Worcester, 

 Mass. 



SPEAKERS: PROFESSOR LUDWIG BOLTZMANN, University of Vienna. 



PROFESSOR HENRI POINCARE, The Sorbonne; Member of the Insti- 

 tute of France. 



SECRETARY: PROFESSOR HENRY T. EDDY, University of Minnesota. 



THE RELATIONS OF APPLIED MATHEMATICS 



BY LUDWIG BOLTZMANN 

 (Translated from tJie German by Professor S. Epsteen, University of Chicago) 



[Ludwig Boltzmann, Professor of Physics, University of Vienna, since 1902. 

 b. Vienna, Austria, 1840. Studied, Vienna, Heidelberg, and Berlin. Professor 

 of Physico-Mathematics, University of Gratz, 1869-73; Professor of Mathe- 

 matics, University of Vienna, 1873-76; Professor of Experimental Physics, 

 University of Gratz, 1876-90; Professor of Theoretical Physics, University 

 of Munich, 1891-95; ibid. University of Vienna, 1895-1900; Professor of 

 Physics, University of Leipzig, 1900-02. Author of Vorlesungen iiber Max- 

 well's Theorie der Elekt rizitat und des Lichts; Vorlesungen iiber Kinetische 

 Gastheorie; Vorlesungen iiber die Prinzipe der Mechanik.] 



MY present lecture has been put under the heading of applied 

 mathematics, while my activity as a teacher and investigator be- 

 longs to the science of physics. The immense gap which divides 

 the latter science into two distinct camps has almost nowhere been 

 so sharply emphasized as in the division of the lecture material 

 of this scientific congress, which covers such an enormous range of 

 subjects that one may designate it as a flood, or, to preserve local 

 coloring, as a Niagara of scientific lectures. I speak of the division 

 of physics into theoretical and experimental. Although I have 

 been assigned, as representative of theoretical physics, to "A. - 

 Normative Science," experimental physics appears much later under 

 " C. Physical Science." Between them lie history, science of lan- 

 guage, literature, art, and science of religion. Over all this, however, 

 the theoretical physicist must extend his hand to the experimental 

 physicist. We shall therefore not be able to avoid entirely the ques- 

 tion of the justification of dividing physics into two parts and, in 

 particular, into theoretical and experimental. 



Let us listen first of all to an investigator of a time when natural 

 science had not yet grown beyond its first beginnings, to Emmanuel 

 Kant. Kant requires of each science that it should be developed 



