From becoming a Fellow of the Royal Society, to publishing four books, Boole had a wide range of professional achievements..
Having by now earned a formidable reputation in the field of mathematics, along with his deep interest in psychology, Boole was proposed for admission as a Fellow to the highly prestigious Royal Society of London. The list of those who supported his proposal was very impressive, representing some of the greatest minds of the time. Supporting him from ‘General Knowledge’ were Donkin, Walker, Lloyd, Kelland, Pollock, Baden-Powell and Tyndall, and from ‘Personal Knowledge’ the list included John T. Graves, Bartholomew Price, James Joseph Sylvester, James Booth, William Thomson (First Baron Kelvin), Arthur Cayley, and Jukes who proposed him.
On 20 November 1856 the proposal was read to members of the Society and the following year, on 11 June 1857, he was elected a Fellow of the Royal Society. Boole was very proud of this great honour and subsequently he used the designation ‘FRS’ when writing his name.
During 1855 and the following year Boole was working on a very significant work entitled On the Application of the Theory of Probabilities to the Question of the Combination of Testimonies or Judgements. Anticipating the awarding of Scotland’s prestigious biennial Keith Prize by the Royal Society of Edinburgh, Boole submitted this 56-page paper for consideration for the award, which consisted of a gold medal and up to £50.00. His submission met with great acclaim and was published in the Transactions of the Royal Society of Edinburgh, being the subject of the award for the 1855-1857 session. He was presented with the Keith Prize the following year on 1 March.
Towards the end of the 1850s Boole had spread his academic net wide. He was still working on probability, logic and operator theory but his first love, in terms of mathematics, had been differential calculus. In fact this discipline had influenced several of his key discoveries. At this time he felt a need to produce a textbook on differential equations. As his work progressed on this volume he also produced important original research on this and other related topics. The resulting book was entitled A Treatise on Differential Equations and was published in 1859. Boole was very happy when he received the news that the University of Cambridge had adopted this work as a college textbook. Indeed this book is as relevant today as it was over a century-and-a-half ago.
Taking into account the impact of his mathematical work of the previous 20 years, Boole now re-examined his published output and realised that many of his methods and techniques in relation to calculus problems needed to be reassessed, because of their potentially wider range of applications. Difference equations began to occupy his mind and he set to work on his fourth and final book, a textbook called A Treatise on the Calculus of Finite Difference. The purpose of this new work was to shine light on the connections between difference equations and differential equations, while bringing into focus the power of abstract operator methods as applied to a new area of mathematics. Students today widely use this book, which like his Laws of Thought of 1854 was acknowledged as a masterpiece.
Through the publication of this book it could be said that George Boole had anticipated developments during the twentieth century, as computers and calculating machines are based on the discrete difference equation rather than on the continuous differential equation.