The Life and Work of George Boole (Review)
George Boole (1815-1864) was a mathematician best known as the progenitor of the Boolean algebra, the system of logic that acts as a fundamental layer within digital systems. Although he never gained a college degree, he spent many productive years as the chair of mathematics at Queen’s College, Cork. Desmond MacHale’s The Life and Work of George Boole is a well-written exploration of Boole’s life, personality, and impact.
The Life and Work of George Boole: A Prelude to the Digital Age by Desmond MacHale. 2014. First published in 1985 by Boole Press Limited. Cork University Press. Publisher Link
Organized largely chronologically, the book covers the entirety of Boole’s life, details on his parents, and features a chapter detailing his wife’s life after his death and the lives of his children, many of which led adventurous lives. Boole’s mathematics and contributions are covered at a general reader level; MacHale explicitly does not try to convey Boole’s innovations at a professional level. That said, the book does not shy from equations (e.g. the key \(x^2=x\)) and Boole’s contributions are described with precision. Boole is covered as a “full” human being and MacHale covers Boole’s social attitudes, marriage and family relationships, academic relations and politics, and attitudes towards religion.
MacHale’s biography is not a hagiography and he includes criticism of Boole and places his work into context. For example, George showed an early passion for Greek and Latin texts and was largely self-taught as a translator. When George was 14, his father sent George’s translation of Ode to the Spring by Meleager to the Lincoln Herald. A reader of the Herald objected that this supposed youth must have had help or cribbed the translation from someone else, which led to a series of letters to the editor about this supposed plagarism. While there is no evidence of plagarism and MacHale could have let the anecdote stand as a humorous controversy, he submitted the translation to several experts to ascertain its quality. The expert review helps cast Boole’s “boy genius” exploits into a more grounded account.
While Boole made important contributions to differential equations and difference equations, his work on logic has merited him the most fame. His first publication on logic was his book, Mathematical Analysis of Logic (1847). The book was published hurriedly and features some vague writing and a poor choice of notation, which led to a poor reception and minimal impact. Boole returned to the subject in 1854 with The Laws of Thought, which was far better received. As MacHale notes, however, Boole’s algebra is not the Boolean algebra we know today, but some further development of notation and terminology (e.g. Boole used ‘or’ to mean ‘exclusive-or’, while some readers assumed ‘inclusive-or’; later mathematicians made the choice of ‘or’ explicit) made the concepts clearer. The development of mathematics is often messy.
The book is well-written and MacHale manages to keep the reader interested even when the subject is conflicts about university management. Boole, after all, was an educator who was mostly home-bound and avoided controversy. Chapters on Boole’s religion, social work, and poetry all add insight to his character. The book features about two dozen photographs and illustrations, although half date to after Boole’s death.
Negatively, with the subtitle “a prelude to the digital age,” we would have expected a more explicit connection between Boole’s work and digital systems. We are not disputing the existence of that connection, but rather the author seems to treat it as a given. Victorian mathematics fell behind mathematics on the continent, but Boole was one of the few mathematicians to have name recognition across the Channel. We would have liked to see this explored, but the book focuses far more on relations within the United Kingdom (including an intriguing chapter on why Boole and Sir William Rowan Hamilton, both in Ireland, never collaborated).
We recommend this book, particularly to those with an interest in the history of mathematics.
For additional context on Victorian mathematics, we recommend Mathematics in Victorian Britain by Raymond Flood, Adrian Rice, and Robin Wilson (Oxford University Press). Additionally, New Light on George Boole is a 2018 book from Demond MacHale and Yvonne Cohen that is a supplement to Life and Work. At the time of this review, we have ordered a copy of this book but have not yet read it.