Author: Eoin Gill is a chartered engineer and a lecturer at Waterford Institute of Technology where he is also co-director of Calmast STEM outreach group
On November 2, 1815, when a son was born to a Lincoln cobbler John Boole and his wife, Mary, it would hardly have been expected that this child would create mathematics that would run the world. Although from a relatively humble background, George Boole, despite never having attended college, became the first professor of mathematics on the foundation of Queen’s College Cork, now UCC.
John Boole, despite his modest position, was a man devoted to learning and to science and he engendered a love of knowledge in the young George. He constructed telescopes and microscopes and he was also able to teach his son Latin until George surpassed him and had to be passed on to a tutor. George then taught himself Greek from books displaying auto-didactic powers that would see him as an older teenager reading the great European mathematicians.
While George attended school he was also able to draw on the assistance of learned men in Lincoln who recognised his talents. John Boole was also involved with the Lincoln Mechanics Institute and George had access to that library and to a network of learned men. John Boole perhaps expended too much energy as a frustrated scientist and his business failed.
Enlightened educational outlook
The 16-year-old George on leaving school immediately became a teacher to help support his family. He progressed to owning his own school. Contemporary accounts suggest that in his early teaching career he wasn’t very patient with boys who couldn’t understand material straight away, but Boole’s own writings show that within a few years he had developed a remarkably enlightened educational outlook.
Constrained by economic circumstances, attending university was out of the question, but Boole persevered in his own study of mathematics and entered into a correspondence with Duncan Gregory, editor of the newly established Cambridge Mathematical Journal (shortly afterwards to become ‘The Cambridge and Dublin Mathematical Journal’). Gregory mentored Boole and helped him prepare material for publication in the journal.
Through this, Boole developed links with many of the leading mathematicians of the day including Thomson (Kelvin), Cayley, Graves, Ellis and de Morgan. Boole published on differential equations and a paper establishing invariant theory. His paper
On a General Method of Analysis won the Royal Society’s Gold medal in 1844. Boole, the provincial school master, was now established in the mathematical world.
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George Boole, 1815 - 1864[/caption]
In 1845, the Queen’s College Act made provision for three colleges in Belfast, Galway and Cork. In 1848 Boole applied for the post as professor of mathematics in the soon-to-be-opened Queens College Cork. Despite not having a university education but armed with his Royal Society medal and references from some of the greatest mathematicians of the day, Boole was appointed as first professor of mathematics at Cork in 1849. Boole was a conscientious teacher and as his new position gave him greater social mobility he became involved in wider Cork society.
Unitarian leanings and the study of scripture
Boole had Unitarian leanings and was given to the study of scripture. He believed that arguments in language could be expressed mathematically and that this could help give clear and sound scriptural interpretations. He published a short book called the
Mathematical Analysis of Logic in 1847 and he was to substantially refine these ideas in his early years in Cork and publish the seminal
Laws of Thought in 1854.
In this book, Boole presents his algebra for expressing logical arguments and the rules for manipulating these algebraic statements. Boole finds that some of the laws of arithmetic hold in his world but there are some important differences. Boole likens the “or” statement in language to addition and the “and” statement in language to multiplication. One of the implications of the latter is the peculiar result that x
2 = x.
This can be seen if x is the collection of all engineers. Then the collection that is all engineers AND all engineers (x.x) is simply the collection of all engineers (x).
The consequence of this is that the equation x
2 = x is only true when x = 1, x = 0. So Boole tells us that his algebra has only meaning when output is 1 or 0. Here we can see that this algebra is suited to binary systems where for Boole “1” and “0” represents “True” and “False” and of course in modern digital systems high voltage (1) or low (or no) voltage (0). Boole demonstrates the power of his system in interpreting scriptural passages, proving that God exists and on other examples that seem quite remote from the digital world. The last part of the book deals with probability.
It was in the 1930s that a young master’s student at MIT began investigating relay circuits and spotted a link. Claude Shannon (1916-2001) had studied both mathematics and electrical engineering at the University of Michigan and moved to MIT to work on Vannevar Bush’s famous differential analyser. In his mathematics undergraduate work he had been introduced to Boolean algebra and quickly spotted that it could be applied to relay switches which had two states – “on” or “off”.
Shannon’s 1936 master’s thesis “
A symbolic Analysis of Relay and Switching Circuits” followed by a paper of the same name in 1938 presented Boole’s algebra to the electronic world. The rest as they say is history. Every digital device uses Boolean algebra in design and operation. It is a fundamental part of programming and it is essential for internet searches.
Boole was to never see these applications or indeed never could have dreamt of them. He attended to his lecturing and was to publish two important textbooks: on Differential Equations in 1859 and on Finite Differences in 1860. He also had greater demands in his personal life as he married in 1855 and fathered five daughters.
Walked to work and got thoroughly soaked
Mary Everest Boole was a niece of colleague and college vice-president John Ryall. Mary was an extraordinary woman and had strong ideas which she expressed forcefully. Unfortunately Boole walked to work one November day and got thoroughly soaked. He took to his bed with a chill and died on December 8, 1864, a father of a young family and one of the great original thinkers of the age. Boole’s daughters despite the restrictions of the age and because of a strong-willed mother, and perhaps their father’s genes, went on to make remarkable contributions in maths, science and literature.
The profession of engineering, of course, owes a great debt to George Boole. While he was a mathematician and his Boolean algebra is seen as one of the first developments of “pure mathematics”, his maths now is primarily of importance to engineers and programmers. It is perhaps worthy to make two final comments about the use of the term “pure maths”, which summons an idea of something rarefied and self-indulgent with no practical applications.
First, Boole himself was quite interested in practical application of mathematics and science and indeed saw his algebra as quite useful albeit in an area quite removed from its current use. Second, Boole’s life also teaches us that pure mathematics or science may have applications most useful to society, and it takes a genius like Boole to create it, and another genius like Shannon to see the applications.
A recent lecture by Eoin Gill for the Engineers Ireland heritage society, available to view below, offers a more in-depth treatment of Boole's Life, how he developed his mathematics and how this maths came to be applied in engineering:
www.georgeboole.com