Vll 



Two of his latest mathematical essays were written, one in German, and 

 the other in French. As he had at this time a great wish to take orders 

 in the church, he applied himself for two years to the study of patristic 

 literature by v/ay of preparation for the regular theological course. But 

 the circumstances of his parents and some other difficulties hindered the 

 accomphshment of this design. In his twentieth year he decided on open- 

 ing a school on his own account in his native city. Henceforward mathe- 

 matics becam.e his special study. 



His earliest papers, written, as he himself incidentally mentions, toward 

 the close of the year 1838, were prepared during his perusal of the 

 ' ]\Iecanique Analytique,' in the form of " Notes on Lagrange." From these 

 notes in the following year he made selections, and wrote out w^hat 

 appears to have been his first paper (though not the first published), 

 entitled On certain Theorems in the Calculus of Variation's," wherein he 

 proposed various improvements on methods of investigation employed by 

 the illustrious French analyst. About the same time his attention was 

 attracted to the transformation of homogeneous functions by linear sub- 

 stitutions, a problem which occupies a very conspicuous place in the 

 writings of Lagrange, and which had also employed the powers of Laplace, 

 Lebesque, Jacobi, and other distinguished continental mathematicians. 

 The manner in which Boole dealt with this important problem showed him 

 at once to be a man of most original and independent thought, and in the 

 course of his investigations he was led to discoveries which may be regarded 

 as the foundation of what has been called the Modern Higher Algebra. 

 His first published paper relates to this subject ; and although he after- 

 wards greatly improved and extended his method of analysis, yet his 

 original memoir, entitled " Researches on the Theory of Analytical Trans- 

 formations, with a Special x\pplication to the Reduction of the General 

 Equation of the Second Order," is interesting as showing how the subject 

 first struck his mind. This memoir he communicated in 1839 to the 

 Cambridge Mathem.atical Journal. Other papers in rapid succession 

 followed. The generous assistance of the editor, the late Mr. Duncan F. 

 Gregory, in correcting the imperfections of style which naturally resulted 

 from his want of proper early training, Boole remembered with pleasure 

 and thankfulness to the end of his life. His rising reputation led his friends 

 to wish that he should enter himself at Cambridge. This project also 

 he abandoned, and he continued to work amidst the interruptions and 

 anxieties incident to the occupation of a schoolmaster. While applying 

 the doctrine of the separation of symbols to the solution of differential 

 equations with variable coefficients, Mr. Boole was led to devise a general 

 method in analysis. The work was too elaborate and weighty for the 

 mathematical journal ; and he therefore, by the advice of Mr. Gregory, 

 communicated a paper on the subject to this Society. For this paper, 

 which was printed in the Transactions for 1844, he received the Royal Medal. 



