SKETCH OF GEORGE BOOLE. 841 



tained his seventeenth year that he attacked the higher mathematics, 

 and his progress was much retarded by the want of efficient help. 



When about sixteen years of age he became assistant master in a 

 private school in Doncaster, and he maintained himself to the end of 

 his life in one grade or other of the scholastic profession. Few dis- 

 tinguished men, indeed, have had a less eventful career. Almost the 

 only changes which can be called events are his successful establish- 

 ment of a school at Lincoln ; its removal to Waddington ; his appoint- 

 ment, in 1849, as Professor of Mathematics in Queen's College, Cork ; 

 and his marriage, in 1855, to Miss Mary Everest. 



His works are comprised in about fifty scattered articles and a few- 

 separate and individual publications. Only two systematic treatises 

 on mathematical subjects were completed by Boole. These were a 

 " Treatise on Differential Equations," which appeared in 1859, and 

 was followed, next year, by a " Treatise on the Calculus of Finite Dif- 

 ferences," designed to serve as a sequel to its predecessor. In the six- 

 teenth and seventeenth chapters of the former work he lays down a 

 lucid exposition of the symbolic method, the bold and skillful employ- 

 ment of which led to his chief discoveries. 



Boole was one of the most eminent of those who perceived that the 

 symbols of operation could be separated from those of quantity and 

 treated as distinct objects of calculation. His principal characteristic 

 was perfect confidence in any result obtained by the treatment of sym- 

 bols in accordance with their primary laws and conditions, and an 

 almost unrivaled skill and power in tracing out these results. 



During the last few years of his life, Boole was constantly engaged 

 in extending his researches, with the object of producing a second edi- 

 tion of his "Differential Equations," much more complete than the 

 first edition ; and part of his last vacation was spent in arduous study 

 in the libraries of the Royal Society and the British Museum, for the 

 purpose of acquiring a complete knowledge of the less accessible origi- 

 nal memoirs on the subject. It must be always a matter of regret 

 that this new edition was never completed. Even the manuscripts 

 left at his death were so incomplete that Mr. Todhunter, into whose 

 hands they w T ere put, as literary executor, found it impossible to use 

 them in the publication of a second edition of the original treatise, 

 and printed them, as a supplementary volume, in 1865. 



Profound and important as were Boole's discoveries in pure mathe- 

 matics, his writings on logic may be considered as still more original. 

 With the exception of De Morgan, he was probably'the first English 

 mathematician since the time of Wallis (1616-1703) who had also 

 written upon logic ; and his wholly novel views of logical method 

 were due to the same profound confidence in symbolic reasoning 

 to which he had successfully trusted in mathematical investigation. 

 From the preface to his " Mathematical Analysis of Logic," printed as 

 a separate tract in 1847, we learn that speculations concerning a cal- 



