REPORT OF ADVISORY COMMITTEE ON MATHEMATICS 



To the Board of Trustees of the Carnegie Institution. 



Gentlemen : Your Advisor>^ Committee on Mathematics begs 

 leave to submit the following report : 



General Statemeyit. — Mathematics, though abstract and bearing 

 the closest relations to pure logic, is most intimately connected with 

 all the physical sciences, and through the rise of the statistical 

 method is becoming of increasing utility in the other sciences. In 

 this country mathematical research is thoroughly alive and full of 

 promise, especially along various lines of pure mathematics and 

 celestial mechanics. As to the future, it is certainly desirable that 

 more men, with full appreciation of modern mathematical principles 

 and processes, should devote themselves to investigation in the vari- 

 ous natural sciences. 



In the applications of mathematics, statistical methods stand at 

 present in the foreground. They would seem to have a future in 

 the problems of meteorology, biology, and other branches of science. 

 Their natural use arises in connection with attempts to put theories 

 such as Darwin's to a direct test, and in investigating possible inter- 

 relations between one set of physical data and another set. Such 

 inquiries, to have value, require the cooperation of mathematicians 

 who know exactly the true relation of the mathematical machinery 

 and of experts in the particular science ; for the mathematician by 

 himself lacks the quasi-instinctive recognition of absurdit}^ in erro- 

 neous results, and can not estimate the value of the data ; and, on 

 the other hand, the expert by himself is apt to regard conclusions 

 as generally true which are based to some extent on assumptions 

 introduced to simplify the mathematics. 



Thus, for instance, in meteorology and terrestrial magnetism there 

 are enormous accumulations of data, and the investigation as to the 

 existence of certain cycles and the sequence of weather types is of 

 obvious importance. Thus there is a wide field for statistical inves- 

 tigation of a kind that calls for skilled mathematical power, as well 

 as special insight in the subject matter ; and the same is true, no 

 doubt, in biology and anthropology and economics. 



These considerations point to a Bureau of Statistics. 



The American Mathematical Society. — The mathematical interests 

 of this country are already fortunate in that they have secured or- 



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