Hello and welcome to the Autodidactic podcast, season 2 episode 10. I wasn’t able to publish a podcast last week due to some time constraints. Hopefully this episode will have been worth the wait.
This week I’m going to be talking about a famous mathematician who was vital in the creation of the digital age. I’m going to be talking about George Boole, an English mathematician who helped establish modern symbolic logic and whose algebra of logic, now called Boolean algebra, is basic to the design of digital computer circuits.
George Boole approached logic in a new way reducing it to a simple algebra, incorporating logic into mathematics. He also worked on differential equations, the calculus of finite differences and general methods in probability.
He was born on the 2nd of November 1815 and died the 8th of December 1864.
George Boole’s parents were Mary Ann Joyce and John Boole. John made shoes but he was interested in science and in particular the application of mathematics to scientific instruments. Mary Ann was a lady’s maid and she married John on 14 September 1806. The family were not well off, partly because John’s love of science and mathematics meant that he did not devote the energy to developing his business in the way he might have done. George, their first child, was born after Mary Ann and John had been married for nine years. They had almost given up hope of having children after this time so it was an occasion for great rejoicing. They went on to have three more children, two boys and a girl.
George first attended a school in Lincoln for children of tradesmen run by when he was less than two years old. After a year he went to a commercial school run by a friend of John Boole, where he remained until he was seven. His early instruction in mathematics, however, was from his father.
When he was seven George attended a primary school and his interests turned to languages. His father arranged for him to receive instruction in Latin from a local bookseller. Having learnt Latin from a tutor, George went on to teach himself Greek. By the age of 14 he had become so skilled in Greek that it provoked an accusation of plagiarism after his father had one of his poems published.
At this time George was attending Bainbridge’s Commercial Academy in Lincoln. This school did not provide the type of education he would have wished but it was all his parents could afford. George was able to teach himself French and German studying and studying other academic subjects that a commercial school did not cover.
At 16, George started teaching as an assistant teacher in Doncaster after his father’s business collapsed and he found himself having to support financially his parents, brothers and sister. While he maintained his interest in languages, began to study mathematics seriously at this time. The first advanced mathematics book he read was Lacroix’s Differential and integral calculus. He was later to realise that he had wasted four years in trying to teach himself the subject instead of having a skilled teacher.
In 1834 he opened his own school in Lincoln although he was only 19 years old. Four years later Robert Hall, who had run Hall’s Academy in Waddington, died and Boole was invited to take over the school. His parents, brothers and sister moved to Waddington and together they ran the school which had both boarding and day pupils.
Boole was studying the works of Laplace and Lagrange and working on what would become is first mathmatics paper. He was encouraged by Duncan Gregory who was in Cambridge and was the editor of the Cambridge Mathematical Journal. Boole was unable to take up the offer to study at Cambridge as he needed the income from his school to look after his family. In the summer of 1840 he had opened a boarding school in Lincoln and again the whole family had moved with him. He began publishing regularly in the Cambridge Mathematical Journal.
Again encouraged by Duncan Gregory he began a serious study of Algebra. In 1844 he had a paper published called “On a general method of analysis; applying algebraic methods to the solution of differential equations” in the Transactions of the Royal Society. He received the Society’s Royal Medal in November 1844.
Boole was appointed to the chair of mathematics at Queens College, Cork in 1849. Boole was to become the first Professor of Mathematics at Queen’s College, Cork, and he took up the position in November. He taught there for the rest of his life, gaining a reputation as an outstanding and dedicated teacher.
In May of 1851 Boole was elected as Dean of Science, and he’d met his future wife Mary Everest (a niece of Sir George Everest, after whom the mountain is named) whose uncle was the professor of Greek at Cork and a friend of Boole.
July 1852 when Boole visited the Everest family in Wickwar, Gloucestershire, England. Boole began to give Mary informal mathematics lessons on the differential calculus. At this time he was 37 years old while Mary was only 20. In 1855 Mary’s father died leaving her without means of support and Boole proposed marriage. They married on 11 September 1855 at a small ceremony in Wickwar. It proved a very happy marriage with five daughters
It was in this period that Boole published his most important work. In 1854 he published An investigation into the Laws of Thought, on Which are founded the Mathematical Theories of Logic and Probabilities. Boole approached logic in a new way reducing it to a simple algebra, incorporating logic into mathematics. He pointed out the analogy between algebraic symbols and those that represent logical forms. It began the algebra of logic called Boolean algebra which now finds application in computer construction, switching circuits etc
Boole also worked on differential equations, the influential Treatise on Differential Equations appeared in 1859, the calculus of finite differences, Treatise on the Calculus of Finite Differences (1860), and general methods in probability. He published around 50 papers and was one of the first to investigate the basic properties of numbers, such as the distributive property, that underlie the subject of algebra.
Many honours were given to Boole as the genius in his work was recognised. He received honorary degrees from the universities of Dublin and Oxford and was elected a Fellow of the Royal Society (1857). However his career, which was started rather late, came to a tragic early end when he died at the age of 49.
One day in 1864 he walked from his residence to the College, a distance of two miles, in the drenching rain, and lectured in wet clothes. The result was a feverish cold which soon fell upon his lungs. Boole’s wife believed that a remedy should resemble the cause. She put Boole to bed and threw buckets of water over the bed since his illness had been caused by getting wet.
Boolean algebra has wide applications in telephone switching and the design of modern computers. Boole’s work has to be seen as a fundamental step in today’s computer revolution.
So what can we learn from Boole to use for ourselves as Autodidactics. Boole’s realisation that he had wasted time by not finding a teacher is a critical point.
As an autodidactic you may struggle to understand some concepts which you are learning. You should take some time to evaluate if you should look into getting a tutor to help you. Here are some tips to help you to evaluate.
- Is the work load taking you twice as long as you think it should? In subjects like math and science, concepts build on one another. Missing just one concept can have a snowball effect, and you may need some extra help.
- If you start needing more help than usual—and find your normal go-to people or places can’t help you—you might want to consider enlisting a tutor.
- If you are beginning to dislike the subject it might be a sign of frustration because you aren’t “getting it”.
- You’re putting in the effort, but not seeing the results you expect, then it’s time to pinpoint the problem and get some extra help.
- You are beginning to skip study times, or avoid the work. You’ve probably gotten frustrated to the point of quitting.
If you decide you need external assistance, then review your options. Would some kind of remote classroom or after work classes help? Do you need a lot of help on a particular subject, or is it just some concepts that you need to work on?
Here are some things to think about before going out to find someone.
- How much help do you need? A full course or just some help with a few key concepts?
- What is your budget for tutoring? Keep in mind a difficult subject will take longer to prepare, so expect to pay more for the extra preparation time. Cost varies greatly, depending on subject area, location, and the credentials of the tutor. Neighbors or friends may charge less, but remember, professional tutors charge professional rates.
- What hours do you expect to have available for tutoring?
- What references or qualifications do you want to see? You get references for electricians, doctors and dentists. Doesn’t it truly make sense to get a reference for a tutor?
How do you find a tutor? There are a number of places you can look and a lot depends on your location. Some places to start are:
- Local colleges or universities will often have a bulletin board or lists of tutors per subjects.
- Online websites like: https://www.personal-tutors.co.uk/, https://tutorful.co.uk/ or https://www.tutorhunt.com/
- Ask friends and family. If you’re learning music perhaps your neighbour knows someone?
Depending on what you’re learning the way to find a tutor or mentor will be different. But before paying anyone you should check credentials, and remember to be safe before allowing anyone inside your home.
Well that is all for this week.
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