Study of Diophantine Analysis in the Uhited States. 47 



all such problems could be solved, and thus elaborated the all- 

 important law of the Probability of Errors, — he did work of 

 immeasurably greater value to science. "When the future histo- 

 rian writes the history of indeterminate analysis, we fear that 

 work in Diophantine Analysis done in this country will count 

 for little or nothing. It is to be regretted that American math- 

 ematicians did not fall in line with leading foreigners and follow 

 the path marked out by the illustrious Gauss in the Theory of 

 Numbers. The modern theory of numbers is a field, wonder- 

 fully beautiful, and adorned by most elegant and powerful 

 general methods. In a few mathematical centres of the United 

 States the theory of numbers is now taught, but original con- 

 tributions are still rare. In the past, Professors Benjamin 

 Peirce and Theodore Strong are the only ones who by their 

 publications in journals exhibited a knowledge of Gaussian 

 methods. A quotation from an article by Dr. J. W. L. Glaisher 

 {Natui'e, September 11, 1890) will apply to the United States 

 much more forcibly than to England: "It is much to be 

 regretted that this great theory, perhaps the greatest and most 

 perfect of all the mathematical theories, should have been 

 so little cultivated in this country. * * * From the mo- 

 ment that Gauss, in his wonderful treatise of 1801, laid down 

 the true lines of the theory, it entered upon a new day, and 

 no one is likely to he able to do useful work in any part of the 

 subject lolio is unacquainted with the principles and conceptions 

 with which he endowed it.''' 



