PREFACE. xxi 



for the greater part of the past nine years to write this history? Because 

 it fitted in with his conviction that every person should aim to perform at 

 some time in his life some serious, useful work for which it is highly im- 

 probable that there will be any reward whatever other than his satisfaction 

 therefrom. Certainly, the eight mathematicians mentioned below, who co- 

 operated with the author, are justly entitled to enjoy the same satisfaction 

 from their work. 



Concerning the various sources of references consulted and the various 

 libraries in America and Europe in which the material was collected, the 

 remarks made on page XI of the Preface to Volume I apply also to the 

 present volume. In particular, those references in the Subject Index of the 

 Royal Society Catalogue of Scientific Papers, Volume I, 1908, which relate 

 to Diophantine analysis were used not only in the preparation of the manu- 

 script, but were checked on the proof-sheets. The references to Diophantus 

 follow the usual numbering and hence not that in the second edition by 

 Heath. 



The reports in Chapters XI-XXVI have been checked by the original 

 papers in case they are to be found in Chicago. The computations occurring 

 in the reports in Chapters XXI-XXIV were checked by the author and 

 various errors in the original papers were detected. Moreover the reports 

 in four chapters were read carefully and critically by an authority on the 

 subject of the chapter as follows: Chapter III on partitions by Major 

 P. A. Mac Mahon, Chapter XXIV on sets of integers with equal sums of 

 like powers by E. B. Escott, Chapter XXV on Waring's problem by A. J. 

 Kempner, and Chapter XXVI on Fermat's last theorem by H. S. Vandiver. 

 A high degree of accuracy and clearness for these Chapters III, XXI-XXVI 

 was especially desired since they are the ones which will be most frequently 

 consulted. Also Chapters I-XII were read minutely by Kempner, thanks 

 to whom various imperfections and errors have been removed. Further- 

 more, the proof-sheets of the entire volume were read by R. D. Carmichael, 

 A. Cunningham, E. B. Escott, A. Gerardin, and E. Maillet, each of whom 

 has written extensively on Diophantine equations and made very valuable 

 suggestions on the present work. To these eight experts, who gave so 

 generously of their time to perfect this volume, is due the gratitude not 

 merely of the author but also of every devotee of Diophantine analysis who 

 may derive benefit or pleasure from this history. 



Miss Minna J. Schick read the proof-sheets of the first eleven chapters 

 and compared them with the original manuscript, for which purpose the 

 authorities at the University of Chicago considerately relieved her of the 

 duties connected with her fellowship in mathematics. Mrs. Louise M. 

 Swain, who had just completed a year of postgraduate studies in mathe- 

 matics at the University of Chicago, read the proof-sheets of the last 

 fifteen chapters, checked the many cross-references throughout the volume, 

 constructed and checked the author indexes, helped to check the references 

 with the Royal Society Catalogue, and checked the page-proofs with the 

 galleys and separately for various types of faults. The author is under 



