In 1831, John Boole’s precarious business foundered and George Boole, aged only 16, found himself the main provider for his family.
Abandoning thoughts of becoming a clergyman, George took work as an assistant teacher, first in Doncaster and then Liverpool, moving in 1833 to Hall’s Academy at Waddington, near Lincoln.
Recognising that an assistant teacher’s salary could not provide adequately for his family, he took the courageous step in 1834 of opening his own school in Free School Lane, Lincoln. This was reasonably successful in financial terms, and his reputation grew as a conscientious teacher.
In 1838, when his former employer Robert Hall died, George Boole was invited to take charge of Waddington Academy. He responded enthusiastically, and he and his family moved to Waddington to run the school, which took both day and boarding pupils.
The Academy flourished under Boole’s direction but he was not the owner. To improve his family’s financial security, he opened his own ‘Boarding School for Young Gentlemen’ in 1840, at Pottergate, Lincoln. His family moved into the school premises to help with administration and teaching.
From 1831, Boole began an ambitious programme of self-education in mathematics. The first advanced text he tackled was the Lacroix Calcul Différentiel, which he read in the original French.
He moved on to the French mathematicians Lagrange and Laplace, painstakingly mastering these books by repeated readings until he understood their use of differential and integrated calculus. He also read and mastered Sir Isaac Newton’s monumental Principia around this time.
George Boole’s initial motivation to study mathematics was to deepen his understanding of practical science, particularly mechanics, optics and astronomy. As his mastery of the subject advanced, he recognised that mathematics is a most exciting and creative subject in its own right.
In the late1830s, his mathematical development benefitted from the support of Sir Edward ffrench Bromhead of Thurlby Hall near Lincoln. A Cambridge graduate in mathematics and a Fellow of the Royal Society, Bromhead had a fine library and introduced Boole to advanced mathematical texts, lending works to Boole and providing comments on his researches.
In 1838, Boole worked in Waddington on his first paper for publication, On Certain Theorems in the Calculus of Variations, prompted by his reading of Lagrange’s Mécanique Analytique.
His next paper was his first to be published, Researches on the Theory of Analytical Transformations. It was inspired by the same Lagrange work and was published in 1841 in the recently-founded Cambridge Mathematical Journal, which published his first paper on Calculus of Variations later that year, together with a third paper On the Integration of Linear Differential Equations with Constant Coefficients.
Boole’s thinking was strongly influenced by the first editor of the Cambridge Mathematical Journal, the brilliant Scottish mathematician Duncan Gregory. They met in Cambridge in 1839, and Boole recognised his need to have contact with leading mathematicians if his research was to flourish.
Boole and Gregory discussed Boole’s aspiration to take a Cambridge degree in mathematics, but regrettably this was incompatible with making a living as a schoolmaster and supporting his family.
When in 1841 the Cambridge Mathematical Journal published Boole’s paper Exposition of a General Theory of Linear Transformations, it initiated a new branch of mathematics - the algebraic theory of variants. Boole published a further paper on this subject in 1845.