Boole’s Legacy
This is something I wrote about celebrated mathematician (and honorary Cork man) George Boole back in 2015 for a publication that ran into financial problems (I was never paid, boo) leading to this piece afaik never seeing the light of day.
I remember thoroughly enjoying researching and writing this, so I thought I’d share it now.
If asked to visualise computer programming most of us invariably conjure up images of binary code: those little ones and zeros that sweep across the screens of hackers in movies like The Matrix.
Well, those little ones and zeros are the bits and bytes of digital computing and, when used in combination with the mathematical work of a certain George Boole, they can perform any computation you can think of. That is to say, without Boole we would most certainly not have the digital landscape of iPhones, tablets and Twitter that we live in today.
George Boole was a 19th century mathematical genius who became University College Cork’s first appointed Professor of Mathematics, a great feat considering he never received a formal university education and was almost entirely self-educated. In 2015 we are celebrating the 200th anniversary of his birth in recognition of a brilliant mind who can be credited not only as the father of the information age but the father of pure mathematics.
Prof. Desmond MacHale is a lecturer in the School of Mathematical Sciences at University College Cork. He penned the first autobiography on Boole in 1985, which has been updated and reissued this year by Cork University Press.
Although now acknowledged as one of the foremost experts on Boole, MacHale says that he wasn’t familiar with his story until he arrived in UCC: “I’d never heard about Boole until I came to Cork in 1971. I realised that he was very important and that nothing had been written about him so I decided to write his biography.”
“A [mathematical] breakthrough will only happen if you are also inspired and enjoy what’s going on.”
“I do the same type of mathematics as Boole did. He invented Boolean algebra and I feel very much a kinship with him in the sense that his attitude towards mathematics was very much like mine,” explains MacHale.
“It’s a pity that more people don’t study algebra; it’s a beautiful area of knowledge. My attitude is that it is the one area of life where you will find absolute certainty and I find that very satisfying. If you prove something now it is proved for all time,” he adds.
Although MacHale points out that a good maths teacher is key to loving the subject he notes that Boole was the exception to the rule in that he was self-taught: “Boole had no teacher at all, which just goes to show how much you can do by yourself if you’re clever enough and you work hard enough.
“A [mathematical] breakthrough will only happen if you are also inspired and enjoy what’s going on,” he adds.
Boole was born on November 2nd, 1815, to English shoemaker John Boole and his wife Mary Ann. Although John Boole was an intelligent man who was curious about the way the world worked, he didn’t have the money to provide an education beyond primary school for his son George. Early on, however, the Boole’s noticed how bright their son was and how quick
he was to learn. They nurtured his intellectual ability as best they could and trusted him to fill in the gaps with his own reading.
Boole was not only a quick learner, he also became a teacher by setting up a boarding school in his hometown of Lincoln at the tender age of 19. Perhaps freed from the shackles of a formal secondary education and formal training, Boole developed his own unique teaching methods aimed at bypassing rote learning and helping the student to understand at a deeper level.
In his Essay on Education, Boole’s philosophy seemed ahead of its time and echoes that of modern pedagogical practice: “The pupil is required to commit nothing to memory before it is understood.”
“In those days nobody was going to ask you what your qualifications were or if you were being trained, so you could set up your own school if you were clever enough and Boole was clever enough,” says MacHale.
Boole truly was one of a kind, both in terms of his intellect and his drive to push the boundaries of knowledge for others as well as for himself. As MacHale notes: “Most people wouldn’t be able to do this and go on to make a living on their own knowledge and their own ingenuity.”
One of the important reasons for MacHale to celebrate Boole’s achievements is to highlight the importance of mathematical reasoning as a skill for everyone. We might live in a technologically advanced world but most of us don’t know what is going on under the bonnet.
“Most people you meet literally cannot think logically because they don’t know the basic rules of logic.”
“Boolean algebra has made its way into the mainstream but only for the elite few. It’s a bit like the situation where you don’t have to know how the engine of a car works in order to drive it and most people won’t be able to fix an engine if something goes wrong.
MacHale says that while young adults use technology all the time they don’t necessarily understand how it is created or how it works. By looking to Boole’s life and work we can perhaps ignite an interest in the world of mathematical thinking.
“When he was a professor at UCC, Boole wanted every student in Cork to take a course in logic. I think I agree with him because most people you meet literally cannot think logically because they don’t know the basic rules of logic.”
But how did the work of a mathematician from County Cork end up as a driving force behind modern computing?
“The modern computer is, in a sense, due to Boole’s work. He envisaged computers as things that carried out calculations, I don’t think he saw them as the medium for communication that they have become,” says MacHale.
Ironically, it was the field of communications that brought Boole’s work to light after many years because although Boolean algebra was interesting to fellow mathematicians it had no practical use in the real world.
This was the case until the 1930s when mathematician, electronic engineer and cryptographer Claude Shannon applied Boole’s logic to telephone switch design. Shannon was a student at the Massachusetts Institute of Technology where he wrote a master’s thesis titled A Symbolic Analysis of Relay and Switching Circuits in which he applied Boolean algebra to the design of logic circuits.
“Electronic devices obviously didn’t exist in Boole’s day. Shannon was an important player because he saw the relevance of Boole’s work to modern circuitry.”
When talking of Boole, MacHale says it is important to note that he wasn’t only a mathematical genius. He was a 19th century polymath with a love of poetry and the classics, who learned to speak multiple languages at a young age. The modern innovator can learn some valuable lessons from the way Boole saw the world.
Drawing a comparison between modern thinkers and Boole and his contemporaries, MacHale says that we’re so busy trying to push the boundaries of knowledge that we have, to a degree, lost our powers of analysis.
“Learning from George Boole, I would always think that the thing to look for [when problem solving] is simplicity. When someone comes up with an invention or solution you always think, it’s so simple, now why didn’t I think of that.
For a genius who became the founding father of complex mathematical and computing concepts, Boole’s legacy is not so complicated; it is the gift of thinking logically and with simplicity.
