While investigating the theory of differential equations in 1843, Boole invented what he called ‘a general method in analysis’, applying algebraic methods to the solution of differential equations. He wrote a major paper, but realised it was too lengthy for the Cambridge Mathematical Journal.
He considered publishing at his own expense until it was suggested he might submit the paper to the Royal Society for its Philosophical Transactions, a proposal endorsed by Duncan Gregory.
Boole had established contact in 1842 with Augustus de Morgan, who was the first Professor of Mathematics at the University of London and became a lifelong friend. Boole sent his paper On a General Method of Analysis to de Morgan for final vetting before submitting it for publication.
It is known that the paper had a stormy passage through the Council of the Royal Society, but Thomas Davies of the Mathematics Committee argued that it be given a fair hearing. Philip Kelland, Professor of Mathematics at the University of Edinburgh, strongly recommended Boole’s paper for publication in the Transactions, and recommended it for a special award.
In November 1844, for his paper On a General Method of Analysis, George Boole was awarded the Royal Medal for Mathematics presented by the Royal Society. His paper was judged the most significant on mathematics communicated to the RS between June 1841 and June 1844.
His Transactions paper and the award of the Royal Medal brought Boole’s name to the attention of leading mathematicians and scientists in Britain. His confidence reinforced, he read his research paper On the Equation of Laplace’s Functions to the Annual Meeting of the British Association for the Advancement of Science in Cambridge,1845.
Boole’s interest in the connection between mathematics and logic was stimulated in 1847 by a public controversy between his friend, the mathematician Augustus de Morgan, and the Scottish philosopher and logician Sir William Hamilton. The two men had conflicting theories concerning the principles that govern logical thought.
Observing the dispute from a distance, it occurred to Boole that their rival approaches could be synthesised - each class of objects could be represented by a single symbol, while relations between classes could be represented by algebraic equations linking the symbols.
Boole’s striking insight inspired his first book The Mathematical Analysis of Logic, being an Essay Towards a Calculus of Deductive Reasoning, published in 1847.
This work expanded the horizon of mathematics through ‘symbolic logic’. Classical mathematics was centred on concepts of shape and number - when symbols were employed, they were usually interpreted in terms of number. Boole introduced the notion of interpreting symbols as classes or sets of objects - the study of defined sets of objects could now be tackled through mathematics.
In 1846, George Boole resolved to pursue a full-time professional career as a mathematician. The opportunity presented itself with the founding of the three new Queen’s Colleges in Belfast, Cork and Galway by Sir Robert Peel’s administration.
In September 1846, Boole tendered his application to the Lord Lieutenant of Ireland ‘to offer myself as a candidate for a Professorship of Mathematics or Natural Philosophy in any of her Majesty’s colleges, now in the course of being established in Ireland’.
His application was supported by an outstanding array of professional and personal testimonials, led by those from Professors de Morgan and Kelland and Professor Charles Graves of Trinity College Dublin, and a testimonial from the Mayor and respected citizens of Lincoln.
Through 1847 and for most of 1848, Boole waited anxiously but received no response. Ireland was enduring the aftermath of the disastrous potato famine. Also, the non-denominational character of the Queen’s Colleges had sparked religious controversy.
Yet he persevered and re-submitted his application, encouraged particularly by Professor Graves. Boole’s resolve was reinforced by his father’s death in December 1848, after a long illness.
To Boole’s delight, he was appointed in August 1849 the first Professor of Mathematics at Queen’s College Cork, which planned to open its doors to students in November 1849.