300 



SCIENCE 



[N. S. Vol. LIV. No. 1396 



ture for identification. During recent excava- 

 tions in Davidson County, Tenn., Mr. Meyer 

 came upon a number of stone slab graves con- 

 taining mortuary vessels. Some of these held 

 specimens of charred maize in fairly good con- 

 dition. From the size and shape of the grains 

 it was possible to identify the variety as Many- 

 Eowed Tropical Flint, a form about half way 

 between true flint and popcorn. The same type 

 of Indian corn occurs in the West Indies, and 

 there appears to have been a very early commu- 

 nication between the West Indies and North 

 America. Not only corn but beans, squashes, 

 pumpkins, and tobacco are of tropical and sub- 

 tropical origin. These staples, now so import- 

 ant throughout both hemispheres, found their 

 way into North America and were cultivated 

 beyond the Great Lakes in Canada long before 

 the discovery of America. There is abundant 

 evidence of communication between the West 

 Indies and Florida, and up the Mississippi and 

 its tributaries. 



The Brazil Medico announces that Dr. 

 Cleef, professor of chemistry at Bello Hori- 

 zonte, reports the discovery in Minas Geraes 

 of a mineral substance hitherto unknown 

 which possesses great radioactive properties. 



Mr. Henry E. Henze, who received his 

 Ph.D. degree from Yale in June, 1921, has 

 become adjunct professor of chemistry in the 

 medical school of the University of Texas 

 at Galveston. 



UNIVERSITY AND EDUCATIONAL 

 NEWS 



Yale University has begun the construc- 

 tion of the new Sterling Chemical Labora- 

 tory. It is hoped that this building will be 

 ready for the use of the department of 

 chemistry in October, 1922. 



New members of the faculty at the Uni- 

 versity of North Carolina, at the beginning 

 of the fall term include G. M. Braune, pro- 

 fessor of civil engineering; H. B. Anderson, 

 associate professor of pathology; H. F. 

 Janda, associate professor of highway en- 

 gineering; F. C. Vilbrandt, associate pro- 

 fessor of industrial chemistry; H. W. Crane, 

 associate professor of psychology, and E. 

 L. Mackie, assistant professor of mathematics. 



Miss Edith Nason, Ph.D., Yale, 1921, has 

 been appointed an instructor in organic 

 chemistry at the University of Illinois. 



DISCUSSION AND CORRESPONDENCE 



A NEW DEFINITION OF PURE MATHEMATICS 



During the present year there appeared a 

 volume of the Acta Mathematica, volume 38, 

 which was dedicated to the memory of H. 

 Poincare, the noted French mathematician 

 who died in 1912. This volume opens with 

 an account of his own works by Poincare in 

 which he deals briefly with his own contribu- 

 tions to the advancement of various subjects. 

 This is followed by a report on the theory of 

 groups and the works of E. Cartan, which 

 Poincare read before the council of the faculty 

 of sciences of the University of Paris on the 

 eve of the operation resulting in his death. 

 The rest of the volume is devoted to letters 

 and to various articles written by others but 

 relating to Poincare and his works. 



In the present note we desire to direct at- 

 tention to the second article mentioned above, 

 which seems to be one of the last articles, if 

 not the last article, written by Poincare, and 

 contains some remarkable statements in re- 

 gard to the theory of groups. One of these 

 is as follows : " The theory of groups is, 

 so to say, entire mathematics, divested of its 

 matter and reduced to a pure form." The in- 

 terest in this statement should be increased 

 by the fact that it may be regarded as a new 

 definition of pure mathematics, the skyscraper 

 among scientific structures. One of the best 

 knovm other definitions is due to B. Peirce, 

 who stated that " mathematics is the science 

 which draws necessary conclusions." It 

 should, however, not be inferred that the lat- 

 ter definition has been generally accepted as 

 an entirely satisfactory one, nor do we want 

 to create the impression that the former is 

 likely to be universally adopted. 



It may, however, be a matter of wide in- 

 terest to see what Poincare meant by the 

 statement quoted above. Such an insight can 

 probably be best gained by reading his own 



