622 



SCIENCE 



[N. S. Vol. XXXVI. No. 932 



permanent agriculture could easily be 

 cited. 



All long-continued investigations and, 

 likewise, all practical agricultural experi- 

 ence show that great reduction in crop 

 yields ultimately occurs unless plant food 

 is restored to the soil; and, as a rule, the 

 chemical composition of normal soil is an 

 exceedingly valuable guide in determining 

 the kinds of material which should be sup- 

 plied in practical systems of soil enrich- 

 ment and preservation. 



Cykil G. Hopkins 



University op Illinois 



THE FIFTH INTERNATIONAL CONGRESS 

 OF MATHEMATICIANS 



Once every four years the mathematicians 

 of the world meet together to discuss the new 

 discoveries made in the various branches of 

 their science, to review the work accomplished 

 during the past quadrennial period, to listen 

 to mathematical papers and to become ac- 

 quainted with one another. The fifth Inter- 

 national Congress of Mathematicians was 

 held at Cambridge University, August 21 to 

 28, 1912, at the invitation of the Cambridge 

 Philosophical Society. The four former con- 

 gresses were Zurich, 1897 ; Paris, 1900 ; Heidel- 

 berg, 1904 ; Rome, 1908. During the World's 

 Pair at Chicago in 1893, a similar interna- 

 tional gathering of mathematicians was held, 

 but this meeting is not usually included in 

 the list of meetings of the International Con- 

 gress. 



The opening meeting was devoted to wel- 

 coming addresses by the president of the 

 Cambridge Philosophical Society, Sir George 

 Darwin, and the vice-chancellor of the univer- 

 sity, Mr. E. F. Scott. Sir George Darwin 

 emphasized the great trend towards speciali- 

 zation among modern mathematicians and re- 

 ferred to the great loss sustained by mathe- 

 matics in the recent death of Henri Poincare, 

 who was probably the one man competent to 

 appreciate mathematical research in all its 

 diverse branches. Darwin referred to the 

 Cambridge School of Applied Mathematicians 



in the last century, mentioning Airy, Adams, 

 Maxwell, Stokes, Kelvin and Eayleigh, and 

 analyzed the characteristic differences in the 

 mental attitudes of the pure and applied 

 mathematician. 



The officers of the congress were elected as 

 follows: President, Sir George Darwin; Vice- 

 presidents, W. von Dyck, L. Fejer, E. Puji- 

 sawa, J. Hadamard, J. L. W. V. Jensen, P. A. 

 MacMahon, G. Mitlag-Lefiler, E. H. Moore, P. 

 Eudio, P. H. Schoute, M. S. Smoluchowski, 

 V. A. Steklov, V. Volterra; General Secre- 

 taries, E. W. Hobson and A. E. H. Lore. 



The congress was organized in four sections 

 devoted, respectively, to arithmetic-algebra- 

 analysis, geometry, applied mathematics and 

 philosophical, historical and didactical ques- 

 tions. The section of applied mathematics 

 was divided into two, one for mathematical 

 physics and astronomy, the other for econom- 

 ics and statistics. This was done also in the 

 case of the fourth section, one section taking 

 up philosophy and history, the other didactics. 

 The international committee having charge of 

 the program appointed the first chairmen of 

 the sections, each of whom gave a short in- 

 troductory address. The other chairmen were 

 appointed by the sections from day to day. 



Section I. Arithmetic, Algebra, Analysis. — 

 The first meeting was presided over by Pro- 

 fessor E. B. Elliott, who in his opening ad- 

 dress defended the British mathematician 

 from the attacks of those who have said he is 

 too self-centered and cared little for the 

 furtherance of mathematical thought. In the 

 five meetings of this section 28 papers were 

 offered and open for discussion. Many of the 

 papers dealt with that part of the field of 

 analysis which centers about the integral 

 equation. The chairmen for the meetings 

 after the first were Professors E. Landau, E. 

 Borel, E. H. Moore, H. von Koch. 



Section II. Geometry. — The chairman of 

 the first meeting, Dr. H. P. Baker, gare a 

 brief survey of the present state of the theory 

 of surfaces and extensions to space of more 

 than three dimensions, and gave reasons for 

 his belief that geometers were now on the 

 threshold of many new discoveries through the 



