An American mathematician, celebrated for a love of epigram tempered by some regard for truth, has asserted that George Boole has the sour distinction of being the most severely under-rated mathematician of the 19th century There is some substance in this judgement. During Boole’s lifetime, his work was recognised and admired in this country, but British mathematics was then very insular, paying small attention to the great progress being made in Europe, and, reciprocally, being little regarded by Continental mathematicians. Boole’s reputation was localised, and, moreover, it rested very much on what we should now consider to be the less valuable of his contributions to mathematics. The title of his greatest work, The Laws of Thought, does not suggest a strictly professional study of pure mathematics but rather a digression into philosophy and metaphysics. Yet Bertrand Russell has declared that Boole, in this work, was the first person to discern clearly the essential characteristics of pure mathematics, and today, when Boolean algebra is a topic for school texts as well as for research journals, we can see that Boole’s work, under-valued at the time of its appearance, was an essential step in the development of pure mathematics as an abstract and axiomatic structure.