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Rh 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 distinguished men, indeed, have had a less eventful career. Almost the only changes which can be called events are his successful establishment of a school at Lincoln; its removal to Waddington; his appointment, 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 Differences," designed to serve as a sequel to its predecessor. In the sixteenth and seventeenth chapters of the former work he lays down a lucid exposition of the symbolic method, the bold and skillful employment 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 symbols 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 edition 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 original 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 were 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 mathematics, 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